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CHAPTER 1 Introduction

We begin by enumerating the problems that we believe must be confronted in any curriculum re-engineering process, and the general solutions we evolved to attack these problems.

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Problems We Addressed

A central tenet of any engineering education is that no elegant solution is likely to be found for a problem that lacks a crisp definition. Unfortunately, curricula are complex, often unwieldy creations subject to conflicting demands from the university, from faculty, from students and their parents, and from the industries that employ graduates. Nevertheless, over the course of its deliberations, our committee kept returning to several specific problems that crystallized as the basic issues to address. We summarize these here.

Student Preparation is Incomplete

American K-12 education can be blamed for the incomplete mathematics and science preparation of many of our students. Nevertheless, allocating blame does nothing to improve the preparation of our students after they arrive. Moreover, entering students are simply different than they were in past decades: less homogeneous, more diverse in their personal goals and career aspirations. Any curriculum redesign must deal with the following facts:

• Students have less facility and depth in the technical areas we expect all students to have seen-for example, algebra and geometry. Some unremarkable mathematical manipulations that appear frequently in introductory science and engineering classes severely tax many students.

• Students-even the best students-have seemingly random gaps in their backgrounds. In the course of our meetings, the Wipe the Slate Clean Committee talked to a superb senior electrical engineering student, a straight-A student who was being aggressively pursued by elite graduate schools. Yet she mentioned to us that she was very uncomfortable in her first circuits class, having never seen a complex variable before.

• Most students have almost no basic laboratory skills when they enter the department, e.g., how to keep a lab notebook; how to observe an experiment; how to deal with significant digits and experimental error; how to use orders of magnitude and quick-and-dirty calculations to estimate whether a measured result is in the right ball park or has gone badly awry; etc.

• A related point: students have virtually no hardware tinkering skills. Previous generations of electrical engineers were notorious tinkerers, with radios and motors and the like. Upon entering college, they knew what a wire was, and a battery. They knew how to solder and read the resistor color code. This is no longer true, and the most elementary of hardware skills-what a wire is, what it does, how it can and cannot connect to a battery-must now be taught explicitly. (This is not exactly surprising, given the inaccessibility of the insides of most electronic products these days.) Our students are now much more likely to have software tinkering experience. However, many students, especially those from less well-off high schools, arrive without any exposure to programming ideas or hardware concepts.

• Student expectations and faculty expectations often differ. Roughly speaking, we tend to assume students have the background, energy and motivation to go acquire whatever mathematics, science, lab skills, etc., that they lack, if we send them off in the right direction. (This has always been true of the best students.) In contrast, many students tend to assume that we will teach them every topic-the big ideas as well as the basic mechanical skills, the central topics as well as the peripheral background material-without independent initiative on their part.

Any solution here must reconsider how and where in the curriculum to teach these fundamentals, and to what level of detail.

Student Perspective on EE, CE and Subdisciplines is Lacking

By the time they are seniors, faculty usually expect students to make intelligent choices when they have the opportunity to choose an engineering elective course. Students are expected to ask their faculty advisers for guidance here, and to listen to whatever advice is offered. Our experience as educators suggests that it is already questionable whether this works for seniors, who have a fairly extensive technical background. However, it is clear that students taking their very first course in a core ECE area like solid state devices or computer architecture are usually not clear about how this area connects to the rest of ECE as a whole.

This was a particular problem in our 1991 curriculum. At this time, ECE offered two parallel curricula: the B.S.E.E. and B.S.C.E. tracks, one of which students had to choose sometime during the sophomore year. The problem was how to educate students to make an informed choice. Certainly, some students arrived absolutely decided on one track or the other. But many relied on our introductory courses to paint a sufficiently broad picture of the discipline for them to make a choice. Unfortunately, these introductory courses concentrated almost entirely on packing in as much engineering material as possible. As faculty, we were often surprised when, after a few weeks in class, in the middle of some intricate technical discussion, a brave sophomore would ask something like this:

Exactly what does a computer engineer do? And how does this material help me to be a computer engineer? Is this different from computer science? Is the difference that we do hardware and they do software? When I graduate will I only be able to design big computers, or do computer engineers do something else as well? And why am I taking all these circuits classes-isn't that for the electrical engineers?

The emphasis on maximizing technical content in those few hours per week left little time to address all these questions satisfactorily. And as the breadth of the discipline continues to expand, we must confront this problem directly if our students are to make informed curriculum choices.

Appreciation of Underlying Ideas is Weak

We are not alone in observing that students often acquire only the mechanical aspects of the topics that we teach, without understanding the underlying ideas. The problem is pervasive in the teaching of technical material. For example, a National Science Foundation article on the teaching of college calculus relates this story [8]:

A mechanical engineering professor mentioned in passing to a class of sophomores that an integral is a sum. He simply assumed that the students had learned this basic idea from first-year calculus. But the students stared uncomprehendingly back at the professor. "Students seem to have a facility for doing things," [the professor] concludes, "but they lack a sense of ideas."

Similar stories were easy to come by in our own department. For example, in [9], one of own faculty observed:

[In several ECE courses] I've worked hard to help students achieve a rich and insightful understanding of fundamental material. Most of them seem to think I do a good job; they say on their FCEs [Faculty Course Evaluations, a survey of each student's evaluation of and reactions to the course, conducted by Carnegie Mellon itself] that I make even difficult and abstract concepts seem clear.

Yet, when I look at the reality of their understanding, as gauged through exams and discussions in and out of class, it's grossly disappointing. The majority simply don't get it. Their survival skills allow many to get through with C's and D's, based mostly upon regurgitation of techniques I've shown them repetitively, as both they and I have forced ourselves through a distasteful process of pounding in material which they find mysterious and useless and which I find beautiful and important.

Students' varying technical preparation, the increasing diversity of their backgrounds, the divergence of student and faculty expectations and the wide-spread practice of packing ever more material into the same number of classes all compound the problem. We argue that curriculum designers must now address this problem directly. The mere mechanical skills that a student acquires in "survival" mode have a disturbingly short half-life in our rapidly moving discipline. The question is how to motivate students to appreciate the connectedness among abstract ideas, concrete applications, their classes and their careers.

Breadth in All Relevant Topical Areas is Impossible

A foundation of many "classical" engineering curricula is the notion that every engineer must know something about every area of the discipline. There was certainly an era in which this was a reasonable assumption for electrical engineers. We argue that this is no longer a viable assumption-especially for an ECE department whose faculty engage in a broad program of research ranging from basic physics to advanced computer science. Distancing a curriculum from this notion is difficult, since it tramples on nearly every faculty member's most cherished subjects. Any attempt to reach consensus on a minimum set of advanced topics to mandate in a curriculum rapidly yields a huge and unwieldy set of essential classes.

One approach that Carnegie Mellon ECE had already tried in 1991 was to partition the undergraduates into separate degree tracks leading to different bachelor of science degrees. As Carnegie Mellon's Electrical Engineering Department evolved into an electrical and computer engineering department, its degree offerings evolved into parallel B.S.E.E. and B.S.C.E. tracks. Computer engineering faculty argued that many required electrical engineering classes were inessential to the education of a computer engineer and should be replaced by more relevant course requirements. Electrical engineering faculty countered that if students did not take the full complement of required electrical engineering classes, they should not be graduated as "electrical engineers." So, a separate computer engineering degree was an agreeable solution.

In hindsight, this debate nicely crystallizes a key problem for curricula as they try to evolve: what is essential to earn a degree with the words "electrical engineer" (or, in our case "computer engineer") in the title? Slicing off portions of the curriculum to award them separate degrees whenever they attain some sort of "critical mass" is not a viable long-term strategy: new technologies and ideas become candidates for core topics in the curriculum faster than old topics expire. Any serious attempt at curriculum redesign must address the necessarily contentious issue of which topics are truly essential.

Interdisciplinary Studies are Difficult

Many engineering curricula are based on a large number of required engineering classes and restricted technical electives. This was certainly true of our early 1991 ECE curriculum. The problem was how to deal with a student who wished to trade some technical depth for breadth. In 1991 one of our B.S.E.E. students could take some computer engineering courses, just as a B.S.C.E. student could take some electrical engineering courses. But we had no mechanism to give a degree to someone who chose to be broad, who chose to take, say, 50 percent of the required electrical engineering core courses and 50 percent of the required computer engineering courses. Some of our best students solved this problem by double majoring in both electrical engineering and computer engineering. But this required completing 100 percent of both curricula, using elective slots in one track to take required core courses from the other track. This challenging but rigid program ended up being a four-year degree with essentially no elective classes.

More generally, we argue that there is a need for mechanisms to allow for students to trade engineering depth for breadth-either breadth within a single department (e.g., electrical engineering and computer engineering), or breadth among other disciplines (e.g., electrical engineering and mechanical engineering).

Demographics Have Changed

In 1991 it was already clear that, on the entering side of the curriculum, our students were less homogeneous than in the past. Today, any department serious about attracting and retaining talented but under-represented minorities to engineering, must expect further diversity in their backgrounds. The problem of students not having the basic skills and motivations we would prefer may yet worsen. Thus, we argue that it is appropriate simply to construct the first few years of courses around this fact.

On the graduating side, there is also increasing diversity. As faculty members, it is common for us to treat our students as though they are replicas of ourselves, i.e., to assume they all wish to become first-class researchers and stay on a technical path for the rest of their lives. But such students are clearly in a minority. Many of our students who graduate to become engineers will not stay in technical positions for their whole lives. Moreover, it has become increasingly apparent in recent years that a few of our best and brightest do not choose an engineering degree with the intent to become practicing engineers, but rather with the intent to enter other post-graduate professional schools, such as law, business and medicine. To encourage a population of more broadly educated engineers, we must refuse any urge to relegate these particular students to second-class status or deride them as defectors from the fold. Indeed, we can see few negatives associated with the idea of a future generation of technically literate legislators, judges, physicians and business leaders.

The central question is how to structure a curriculum to handle the educational needs of all these constituencies: the committed technologist, the mainstream engineer who may be in management in less than a decade and the interdisciplinary student using ECE as a launching point for a career in another professional discipline. In our own curriculum redesign, we concluded that these facts argue for a curriculum in which a strong core of ECE topics can be augmented with advanced ECE classes or preparatory courses for other disciplines.

Rigid Curricula Impede Necessary Changes

As mentioned in Chapter 1, many curricula evolve by accretion, and the resulting web of constraints can render even modest changes difficult. Hence, we suggest that another problem to address directly is planned growth: how to structure the curriculum to add flexibility to its basic organization so that necessary incremental changes are more easily effected.

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Solutions We Developed

Before describing the exact organization of the new ECE curriculum that we created in response to the problems raised in the previous section, we summarize our attempt at general solutions to these problems. The ideas described can be regarded as the "design principles" for our revised curriculum.

Teach Engineering Early, Concurrent with Fundamentals

In 1991 the freshman year was common to all departments in Carnegie Mellon's college of engineering, and emphasized mathematics, science and humanities. A few "freshman elective" slots were available, as well as a few so-called "engineering science" slots (comprising elementary statics, dynamics, thermodynamics, materials science and so forth; see again FIGURE 1), but the choices comprised an ad hoc selection of peripheral engineering courses largely unrelated to the core curriculum of any engineering department. Students were largely disappointed by these courses.

In the new curriculum, every department in Carnegie Mellon's college of engineering offers a freshman engineering course that introduces students to the ideas, problems, modes of thought, tools and techniques of its discipline. All students take at least two such courses in their freshman year, concurrent with their mathematics, science and humanities classes. ECE offers a single course, called Introduction to Electrical and Computer Engineering, that strives specifically to provide an integrated view of connectedness of electrical engineering and computer engineering problems.

The unifying idea here is to expose students to real engineering as early as possible, to motivate their studies in necessary mathematics and science courses while they are taking them, and to teach explicitly some manual skills they mostly lack. The goal is to generate real enthusiasm-the "Aha!" that accompanies insight as students grasp that they can, for example, model interesting physical phenomena with a little mathematics, science and judgment-and let them get their hands dirty on real problems. This experience demonstrates to new students the practical need for more preparation in subsequent mathematics and science classes and also provides students with the elementary hands-on laboratory skills that they often lack. At the college level, it allows undecided students to sample various engineering departments to be sure they are choosing the right one.

Base Curriculum Requirements More on Areas, Less on Specific Courses

The 1991 electrical engineering and computer engineering curricula were each based on a rigid core of required classes. In the new ECE curriculum, we first drastically reduced this required core, from about a dozen courses down to a select few. Next, we replaced the bulk of the remaining specific course requirements with area requirements: ECE was "partitioned" into a spectrum of topical areas, and all upper-level courses assigned to one of these areas. Students are required to demonstrate breadth, depth and coverage across some chosen subset of these areas. However, we no longer require students to take one or two courses in every core electrical or computer engineering area. Instead, we let students demonstrate that they are broad enough to take courses in several-but not all-different areas and that they are deep enough to take more advanced courses in some-but not all-areas. Coverage requirements-to ensure that the student takes enough ECE courses to be called an electrical and computer engineer-and a capstone design requirement complete the basic curriculum.

Increase Flexibility, Elective Courses

The 1991 curriculum featured a hodgepodge of curriculum-specific elective slots (the B.S.E.E. and B.S.C.E. manifested different constraints on allowable electives) restricted in a variety of ad hoc ways. The actual number of completely unconstrained elective slots was amazingly small: one course slot.

The new curriculum substantially increased the number of unconstrained elective slots: we allowed slightly less than one full year of free electives. Aside from the fact that these courses must be ones for which students receive credit and a grade, they were not further constrained. The intent was not to reduce the rigor, complexity or depth of understanding associated with the ECE degree. Rather, the intent was to create new opportunities for more broadly based curricula that integrate ECE courses or courses from other disciplines in innovative ways. We saw no reason to prevent an ECE student with an interest in, for example, integrated silicon sensors, from taking a half dozen courses chosen sensibly from mechanical engineering, physiology, biology, chemistry, mathematics or physics. Nor did we see any compelling reason to prevent an ECE student with an interest in computer speech recognition from taking a year of linguistics, a foreign language, or even music theory and cello mastery. Adhering to some unnecessarily rigid concept of an ECE degree only stifles the creation of innovative programs of study and innovative engineers themselves.

Manage the Workload

In the 1991 curriculum, students typically took five courses per semester. Usually, these comprised four technical classes and one humanities class. Especially in the last two years of their studies, engineering classes tended to inflate in content past their specified units as our faculty members struggled to compress every relevant topic, technique, nuance and anecdote into their classes. During such semesters, the nominal 40 to 50 hours of work per week (computed by tallying the units on each student's classes) was at best an optimistic lower bound on the time students needed to invest to survive. Independent of the merits of demanding course schedules, our students were juggling too many topics, often at unsustainable levels of stress and well beyond an optimal level for real understanding.

In the new curriculum, we first attacked this by reducing the number of courses from five per semester to four. ECE courses remained challenging and work-intensive, but the switch to one fewer class per semester made it possible for ordinary students to concentrate fully on their studies and master their material. We also tightened the requirements for "overloading," i.e., taking a course load beyond a reasonable number of units, in our case roughly 4.5 courses per semester. In the 1991 curriculum, any student with a sufficiently high aggregate grade point average could overload. The problem this occasionally created was students who, having achieved good grade point averages on nonengineering courses in their early years, would later elect an insupportable engineering course load and perform weakly in each course. In the new curriculum, an overload requires a high grade point average for the courses in the preceding semester; now, a student must demonstrate continuously the ability to excel while taking extra courses, or those courses cannot be elected. Again, the strategy here is to encourage mastery, rather than mere survival, in a core set of carefully selected courses.

In addition, we rendered the workload a bit more uniform across all ECE courses by reallocating topics more carefully across course sequences. (In the 1991 curriculum, topics tended to creep downwards through a course sequence, to make room for more topics at the high-end of the sequence.) Finally, we made all ECE courses the same number of units, in some cases adding laboratories to relatively abstract and mathematical courses like electromagnetics and signals and systems to balance out the per-course workload.

Offer One B.S. Degree, Not Two

In 1991 we offered two degrees: the B.S.E.E. and B.S.C.E. In the new curriculum, we offer only one: the Bachelor of Science in Electrical and Computer Engineering, or B.S.E.C.E. There is an appealing symmetry here. We originally offered a single B.S.E.E. degree when we were the Department of Electrical Engineering. As the computer engineering discipline gained stature, we offered a B.S.E.E. "with a computer engineering option," which eventually split off to become the separately accredited B.S.C.E. degree. Now, we have merged all our degrees back into a single integrated B.S.E.C.E. This explicitly recognizes evolutionary trends in the discipline and in industry to emphasize the commonality across electrical and computer engineering, and not the differences.

Structure Curriculum to Accommodate Change

In 1991 the rigid set of interlocking course requirements made even small changes difficult. A key feature of the new curriculum is that it is based less on specific courses and more on requirements to take courses in general topical areas. By organizing the curriculum to be more loosely independent of the content of specific courses we freed it to adapt more easily to change. It is now much easier to see how to add a breadth/depth course, a new topical area or even a core requirement. As the discipline itself evolves, the new curriculum should be able to absorb necessary incremental changes without violating the basic spirit of its design.

An interesting (and unexpected) example of this was the creation in 1994 of an integrated five-year bachelor's/master's degree built seamlessly on top of our new undergraduate curriculum. We shall return to this five-year program in Chapter 7.

We can now describe more fully the redesigned ECE curriculum. We begin by surveying the basic components of the new curriculum as it was proposed in 1991, their organization and relationships. We then describe some implementation realities that modified this ideal form of the curriculum, as it has evolved into its present form in 1995. We close with a discussion of our progress toward accreditation.

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Proposed New Curriculum: 1991

FIGURE 2 illustrates the basic components of the curriculum by topic; FIGURE 3 adds detail to show how courses are allocated among these areas. The architecture of the curriculum is essentially simple and comprises the following:

• A typical humanities, social sciences and fine arts component. (8 courses)

• A typical mathematics, science and computer programming component. (7 courses)

• Freshman engineering courses-very much atypical-which use these mathematics, science and programming classes as corequisites. (at least 2 courses)

FIGURE 2. New ECE Curriculum: Basic Organization in 1991

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FIGURE 3. New ECE Curriculum: Allocation of Courses to Areas in 1991

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• ECE core requirements, a set of two fundamentals classes (in addition to a required ECE freshman engineering course) required of all ECE students. These courses are the gateway to all elective upper-level ECE courses. (2 courses)

• ECE breadth requirements, selected from across the set of specified topical areas in ECE, to ensure exposure to different styles of thinking, modeling and problem-solving. (3 courses)

• ECE coverage requirements, to ensure enough exposure to ECE courses to earn a degree called the Bachelor of Science in Electrical and Computer Engineering. (at least 3 courses)

• As part of the coverage requirement, an ECE depth requirement to ensure that students can handle advanced as well as introductory material. (1 course of the

  3 coverage courses)

• Also as part of the coverage requirement, a capstone design requirement, to ensure exposure to the unique problems of building concrete engineering artifacts under tight time, resource and cost constraints. (1 course of the

  3 coverage courses)

• Free electives, nearly one year in all, to be chosen by individual students based on their interests and goals. (7 courses)

Our previous curriculum required 388 units in all for a bachelor's degree. The new curriculum reduces this slightly-by roughly 2.5 classes-to 360 units to satisfy our goal of four classes per semester in a typical semester. At Carnegie Mellon, a typical course is 9 to 12 units, where each unit represents one hour of expected work each week. A 12-unit class is nominally intended to require 12 hours of effort per week.

Freshman Engineering Requirements

Two requirements for obtaining a B.S.E.C.E. are:

• At least two CIT departmental introductory engineering courses must be taken during the freshman year.

• The ECE freshman course, Introduction to Electrical and Computer Engineering, must be taken by ECE majors, although it may be taken as late as the fall semester of the sophomore year.

In other words, a typical student will take two of these introductory engineering courses in the freshman year, and one of them will be our ECE course. However, the student unsure of a major may end up taking three of these courses, without penalty, and defer deciding on ECE until the fall of the sophomore year. This places an implicit upper bound on the length of required course sequences: each CIT department must not require a sequence deeper than five courses.[2] This poses no additional constraints on the new ECE curriculum.

For completeness, the list of all current (1995) CIT freshman introductory engineering courses follows. Each course is permitted to have one science and one mathematics corequisite:

• Introduction to Chemical Engineering ( corequisites Modern Chemistry I and Calculus I )

• Innovation and Design in Civil Engineering ( corequisites Physics for Engineering Students I and Calculus I )

• Introduction to Electrical and Computer Engineering ( corequisites Introduction to Computer Programming and Calculus I )

• Introduction to Engineering and Public Policy ( corequisites Physics for Engineering Students I and Calculus I )

• Fundamentals of Mechanical Engineering ( corequisites Physics for Engineering Students I and Calculus I )

• Materials in Engineering ( corequisites Physics for Engineering Students I and Calculus I )

Flexibility = Core + Breadth + Depth + Design + Electives

The key attribute of this curriculum architecture is its flexibility. Requirements to "take one course in every important area" or "attain basic mastery in every area," which in the past led to cumbersome intertwined course sequences, are avoided entirely. Instead, we mandate only select core knowledge, along with breadth, depth, coverage and design. Within this framework, many sensible plans of study can be formulated, some favoring depth, some favoring breadth, others somewhere in between. Another important consequence of this flexibility is that it accommodates new students with different backgrounds and skills:

• The best students can begin engineering classes earlier and pursue several ECE areas in great depth.

• Students inclined to be generalists can, within clear limits, trade depth for breadth, and explore a wider range of ECE topical areas. At the very least, we can now actually accommodate the students who want to take, say, half of their courses in traditional electrical engineering topics, and half in traditional computer engineering topics.

• Those with more potential than actual preparation can use electives to fill any gaps, and defer some engineering until later; these students in particular may benefit by choosing to trade off some depth for breadth.

• Interdisciplinary students now have the time to dive into another discipline, its background topics, its core classes and even a few advanced courses. This is helpful for students pursuing a parallel technical discipline, as well as students using ECE as preparation for graduate studies in another profession such as medicine, law or business.

The large number of free electives deserves special comment. Interestingly, it seems that the presence of any free electives in an engineering curriculum is rare, let alone nearly a full year as the new ECE curriculum allows. The desire to pound increasing amounts of technical, discipline-specific material into our students in the same number of hours per week is at least partially to blame. However, blame has also been attributed to the engineering accreditation process [10]:

For more than a century and a half, engineering schools in the United States have pursued a variety of educational philosophies, offering programs built around their local comparative advantages. The resulting diversity has been an important source of national technological strength. Today, faced with challenges induced by rapid global political, economic and environmental change, we need diversity and innovation in our new engineering graduates more than ever before. ... But, in contrast to the flexibility of undergraduate science education, heterogeneity and innovation in U.S. engineering education are threatened by the creeping demands of our system for accrediting undergraduate engineering curricula. ... When a school's most basic educational objectives and the ABET [Accreditation Board for Engineering and Technology] constraints have both been met, there is often little or no flexibility left. It is not unusual for an engineering undergraduate to have no opportunity to select a completely free elective course.

Whatever the reason, the pressures for limiting electives to a negligible few have been numerous and well intentioned. Nevertheless, if one of our goals is to increase the diversity among the population of electrical and computer engineers that we educate-both the diversity of their background upon entry and their portfolio of skills upon graduation-a substantial number of free elective courses is a sensible solution.

In the following sections, we discuss each of the component areas of this curriculum. We shall return to the topic of accreditation at the end of this chapter.

ECE Core

The new curriculum introduces three critical new courses. By the end of the sophomore year, the average student will complete the small ECE core, comprising these courses:

• Introduction to Electrical and Computer Engineering, which has introductory calculus and computer programming classes as corequisites, introduces basic engineering ideas related to electricity and computers. It is typically taken during the first year.

• Fundamentals of Electrical Engineering, which has a linear algebra class as a corequisite, is a course in linear circuits. It is typically taken in the second year.

• Fundamentals of Computer Engineering, which has a discrete math class as a corequisite, is a course in digital design, microprocessors and elementary computer organization. It is typically taken in the second year.

These courses are a critical part of the proposed curriculum; we shall return to them in greater detail in Chapter 4.

ECE Breadth

Before describing these requirements, it is best to illustrate what "breadth" means in ECE by referring to the illustration in FIGURE 4. Rather than simply partitioning the department into electrical engineering and computer engineering halves, we chose instead to restructure it as a spectrum of five areas. Going to the left in the figure takes us more toward traditional electrical engineering topics; going to the right takes us toward traditional computer engineering topics. Courses from other departments appear at the far left and far right of the diagram, where our department has obvious interdisciplinary links to other departments at Carnegie Mellon, notably Physics and Computer Science. The idea is that these five areas have unique problems, methods, mathematics and modes of thinking. Courses allocated to an area share some of these attributes. By requiring students to take courses in three of these five areas, we enforce a consistent notion of breadth, without having to resort to requiring specific courses.

FIGURE 4. ECE Breadth Areas in New Curriculum

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Specifically, to satisfy the ECE breadth requirement, students must take at least one first-level course in each of three of the five basic areas of ECE:

• Applied Physics includes courses in electromagnetics, solid state devices, magnetics, data storage, optics, etc.[3]

• Signals and Systems includes courses in signals and systems fundamentals, as well as control, communication, signal processing, robotics, etc.

• Circuits includes courses in both analog and digital electronics, as well as IC and VLSI design, etc.

• Computer Hardware includes courses in digital design and verification, computer architecture, processor design, networks, concurrency, CAD, etc.

• Computer Software includes programming, data structures, formal methods, software engineering, compilers, operating systems, etc. (These courses are all offered by the School of Computer Science, with whom we maintain a reciprocal relationship: computer science students take several hardware-oriented ECE classes, and ECE students can elect software-oriented computer science classes.)

Courses in these areas are referred to as breadth courses. Revisiting FIGURE 4, we see this spectrum of five areas, with several representative types of courses listed in each area. Each area offers at least one, and possibly several introductory courses that can be taken starting with the three ECE fundamentals classes as prerequisites, along with perhaps some additional mathematics or science courses. Other courses in each area are more advanced, and require some earlier area-specific ECE breadth courses as prerequisites.

ECE Coverage and Depth

At least three more courses must also be taken from the areas defined in the ECE breadth requirement; we refer to this as a "coverage" requirement. The idea here is to ensure that students see enough engineering courses to be called "engineers" when they graduate. Two additional requirements, the depth and design requirements, can be satisfied by dedicating two coverage courses to depth and design, respectively.

To satisfy the depth requirement, students must take at least one course that has as a prerequisite one of the courses used to meet the breadth requirement. Since most fundamental topics in our curriculum are covered in two-semester sequences, practically speaking, the depth requirement will cause students to complete at least one such sequence.

ECE Design

Carnegie Mellon has a long tradition of offering aggressive and challenging design courses. The design requirement is satisfied when a student completes one course from an approved list of design courses across ECE. These courses tend to be on the high end of our curriculum and are generally quite popular. The intent is for students to take aim at these courses sometime during their junior year, carefully picking up the required mathematics, science and ECE prerequisites.

Workload, Overload Policy, QPA Policy

The curriculum was designed around the assumption that students should take four courses per semester. Typically, but not necessarily, this will involve one H&SS course and three technical or free elective courses per semester for eight semesters. Our assumed model was that the one H&SS class was 9 units, and the remaining three classes each 12 units. Eight semesters at this workload is thus a 360-unit degree. In fact, during some semesters students may not always be able to take three 12-unit courses because, for example, many science and mathematics courses are only 9 units. In these cases the student may still end up taking five classes, for example, three 9-unit classes and two 12-unit classes. (See page 34 for more discussion of this problem.) Our intent in establishing a workload norm and overload policy was to make four courses per semester the norm rather than the exception, especially for students taking several challenging ECE courses in the same semester.

The term "overload" refers to the maximum number of units per semester a typical student is allowed to carry without getting special permission. In the old curriculum, only students with a high quality point average (QPA) were allowed to overload. In the new curriculum, we modified this somewhat. First, an overload was defined as any schedule with more than 54 units in one semester. This amounts to anything more than three 12-unit classes and two 9-unit classes in the same semester. Second, we now only permit students to overload if they have achieved a QPA of 3.5 out of 4.0 in the previous semester. We wanted the privilege of taking an extra class to be regarded as a reward for exemplary performance, specifically, a high QPA in the previous semester. More importantly, we wanted to encourage students to focus more deeply on fewer courses, and so we consciously erected some barriers to prevent ordinary students from getting in over their heads. We had ample experience with very bright students who achieved a high overall QPA early in their studies, then started overloading every semester, only to watch their QPA crash as they refused to acknowledge that they were overwhelmed. The new overload policy was designed to resolve such problems.

In order to graduate, students must maintain a 2.0 QPA in the set of courses used to satisfy the ECE freshman, ECE core, breadth, depth, coverage and design requirements.

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Curriculum Evolution: 1991 to 1995

Several modifications have occurred to the "original" organization, which was illustrated in FIGURE 2 and FIGURE 3. Nevertheless, the overall organization of the curriculum as it is now implemented has remained surprisingly faithful to our original vision. In this section we discuss the critical changes and their motivations.

Allocation of Units

Most of our changes are simply the result of local idiosyncracies. Most notable among these is that not all courses at Carnegie Mellon have an identical number of credit units (notably mathematics, science and humanities). For example, almost all ECE technical courses carry 12 units of credit; many mathematics and science classes carry between 9 and 12 units. Most nontechnical humanities classes carry 9 units. In addition, a few so-called skills classes (e.g., a university-required computing skills class taken by all freshmen) carry only 3 units. Hence, many non-ECE courses do not completely "fill" one of the planned slots in FIGURE 2, making it difficult in a few places to obey the four-courses-per-semester guideline. One result of this was the inclusion of some extra mathematics requirements to partially fill this units gap. In addition, examination of ABET accreditation guidelines also contributed to these minor changes, resulting in a decision to increase somewhat the overall fraction of the program dedicated to technical subjects. As a result, roughly two and one half of the original free electives were transformed into:

• Math/science electives: Two courses must be selected in mathematics or the sciences-biology, chemistry, physics. These two courses occupy slots equivalent to 1.5 ECE engineering courses.

• Probability and statistics: We added this as a required mathematics course.

In addition, we added constraints to another free elective, requiring it to be technical, resulting in:

• Engineering elective: One course must be selected from across all engineering departments. This occupies one ECE slot.

As a practical matter, the resulting impact on flexibility was offset by changes in Carnegie Mellon's humanities requirements (described on page 34). Two of the eight humanities and social sciences courses (equivalent to 1.5 ECE engineering slots) can now be chosen freely from among nontechnical topics across Carnegie Mellon. Hence, constraining a few of our own free electives to be technical is somewhat offset by these nontechnical free electives; this brings the curriculum back fairly close to its original form.

Updating the original form of the curriculum illustrated in FIGURE 2 and FIGURE 3, FIGURE 5 and FIGURE 6 illustrate more accurately the current, 1995 form of the ECE curriculum.

FIGURE 5. New ECE Curriculum: Basic Organization in 1995

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FIGURE 6. New ECE Curriculum: Allocation of Courses to Areas in 1995

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General Education Requirements

In 1991 Carnegie Mellon required all undergraduates to complete a sequence of humanities and social sciences-called H&SS-courses. Those requirements, totaling eight courses, included:

• One course chosen from a list of designated writing and literature courses.

• One course chosen from a list of designated history courses.

• One course chosen from a list of designated social science courses.

• One course chosen from a list of designated psychology and philosophy courses.

• Three more advanced courses, constituting a so-called depth sequence, chosen from among nontechnical courses in humanities, social sciences, foreign language or fine arts.

• One freely chosen nontechnical course from humanities, social sciences, foreign language or fine arts.

In 1994, the H&SS requirements were reorganized university-wide and renamed the General Education requirements. These again mandate eight classes, but now comprise:

• One course chosen from a list of designated writing and expression courses.

• One course chosen from a list of designated humanistic studies courses.

• One course chosen from a list of designated cognition and institutions courses.

• Three more advanced courses, constituting again a depth sequence, chosen from among nontechnical courses in humanities, social sciences, foreign language or fine arts.

• Two freely chosen nontechnical courses from humanities, social sciences, foreign language or fine arts.

We note that there is slightly more elective freedom in the General Education requirements now-two versus one free course-which somewhat offsets our own changes to the free ECE elective restricting them to be technical.

Timing ECE Course Offerings

Constraints on the size of the department mean that we cannot offer every course every semester. Nevertheless, we offer the three fundamentals classes of the new ECE core every semester, to accommodate students who come into ECE via different sequences of courses during their freshman year and the fall semester of their sophomore year.

In addition, some noncore classes have begun to appear every semester, just to satisfy the demand from the students. The introductory breadth course in the signals and systems area is now offered nearly every semester.

We have also changed the way that we time the offerings of the core sequences in each of ECE's breadth areas. In the past, we synchronized each multiple-course sequence so that the starting courses, e.g., Electromagnetics I, Solid State I, were only offered in the fall. This rigidity is now highly undesirable since the new curriculum has almost no requirements for students to take particular course sequences in a particular order or in a particular semester. Indeed, the flexibility in the new curriculum means students can arrive at most ECE course sequences from a variety of paths. Hence, we have staggered the offerings to ensure that every semester offers a good selection of beginning breadth courses for students.

Note also that FIGURE 5 shows the first breadth course in the spring of the sophomore year rather than in the fall of the junior year. Many students find that this timing gives them earlier access to more advanced courses in their areas of interest. The vertical arrows in FIGURE 5 indicate flexibility in when a course may be taken.

Design Across the Curriculum

Carnegie Mellon in general, and ECE in particular, have a long tradition of infusing aggressive design problems into the classroom. Interestingly, the new ECE curriculum provided yet more opportunities to strengthen our commitment to design.

One less obvious opportunity arose from the need to make all ECE technical courses the same number of units (to occupy one of the so-called "ECE slots" on FIGURE 2 or FIGURE 5). In the prior curriculum, courses with some laboratory or design exposure were typically 12 units, whereas more mathematically oriented classes (e.g., signals, solid state, etc.) were typically 9 units, and lacked a lab. The new curriculum allowed us to rethink these decisions, with the result that most breadth-area classes now include some laboratory experience. Sometimes this is a new hands-on lab component, constructed from scratch, as with our revised solid state courses. Sometimes this is centered around engineering design, simulation or verification software, such as the use of electromagnetic field solvers and visualization software in the revised electromagnetics courses. Sometimes both hardware and software are used to advantage in new lab experiences, as with the use of signal processing software, combined with PC-based signal acquisition and processing hardware, in our revised introductory signals class.

An example helps make this concrete. In our current Engineering Electromagnetics I class, students create their own Matlab^tm code and use existing software (some commercial finite element software and some educational software created by the instructor) to work on assignments that are relatively open-ended, with an orientation toward design as well as analysis. In the fall of 1994 students in this course created their own software to map out the magnetic field structure in one wing of the building in which the Computer Science, Mathematics and Physics departments are housed. This wing of the building is situated directly above the 24kV - 4kV main step-down transformers that supply power to the Carnegie Mellon campus. The magnetic field levels are high enough to cause significant interference with workstation monitors in this area, and some residents have also expressed concern about possible health effects. Starting from basic principles they had learned in the course and using tools they had created in one of the prior projects, students mapped out the field structure and compared their calculated results with measured results. This project worked well: it was interesting, challenging, relevant to a current engineering design problem and reinforced basic ideas from the course. It also demonstrates clearly how even abstract, mathematically oriented engineering topics can benefit from creative laboratory assignments.

Our advanced classes also continue to offer a spectrum of design experiences. In advanced design classes, students are asked to create a device, a component, a process or a system where the goals or performance criteria are specified, and where a multitude of alternative solutions are possible, so trade-offs must be examined and decisions made.

An industrial design project may involve only a single engineer in a single location, or hundreds of people distributed over the globe. Neither the problem nor the test criteria may be well defined in advance. In fact, the typical industrial project involves three simultaneous activities:

• Design the organization to be used in the project (the people, their responsibilities and their resources).

• Design the problem to be solved (specify the goals, define the "designable" parts of the solution, design the tests to be used in distinguishing good solutions from bad ones and select starting points).

• Design a solution to the problem.

In the typical industrial project, both the organization (who is responsible for which parts of the solution) and the problem itself changes over the course of the project. Industrial projects also tend to be open ended-unanticipated behaviors of a product can come back to haunt its designers years after the product has stopped being made. As a result, risk and liability also play an important role. Thus, topics visited in our design-oriented classes can include:

• Problem specification and requirements

• Verification and test

• Alternatives, choices, decisions and trade-offs

• "Language" of design

• Orderly subdivision

• Analysis and synthesis

• Uncertainty and risk

• Use of design tools

Almost every course in the ECE curriculum involves some design. Some courses focus on design problems faced by individual designers, such as building a performance-constrained circuit or software module as part of a larger system. Other courses offer group design projects with more open-ended goals and realistic limits on resources, alternatives and time. Examples here range from design of complete superscalar processors to telecommunication systems to control systems. In ECE these are referred to as "capstone" design classes, since they require a rigorous sequence of prerequisite courses covering the necessary mathematics, theory and engineering practice. It is also worth noting that many ECE faculty are themselves designers-of systems, of circuits, of manufacturing processes, of software, etc.-and so students have access to world-class expertise in many of these courses.

Our analog IC design courses, for example, teach students design by having them perform several design projects throughout the course of the semester. Generally there will be two or three small design projects during the semester, and one larger design project at the end of the semester. Students normally carry out these design projects individually, but on occasion group projects of large scope are undertaken. Both during and after completion of each design project the students meet one on one with the instructor to review their design. The instructor provides feedback on the design process as well as feedback on the design itself. Because of the nature of analog IC design, these projects typically involve circuit design, circuit simulation, IC layout, estimation of layout parasitics and handling of variation in the IC manufacturing process. Further, students are required to take into consideration reliable and economical testing of their circuit during the design process. On several occasions student's designs have been fabricated through the ARPA/NSF supported MOSIS service and the students have tested their designs in a follow-on course on testing of integrated circuits.

Another interesting example of design is the design of CAD tools themselves. For VLSI circuits, CAD tools are large, interlinked suites of communicating software that successively transform a design specification into a final, finished chip and the manufacturing process for that chip. In ECE, students have the opportunity to actually design examples of these software tools. Recent projects have included partitioning of large gate-level designs across multiple physical chips, wire routing for the newest generations of field-programmable gate arrays, wherein not only the function of each logic block but the pattern of interconnections are programmable by the user, and detailed simulation of electronic circuits.

Advising

An interesting new problem we faced is that a highly flexible curriculum is a more difficult curriculum to advise. Especially during the highly regimented sophomore and junior years of our previous ECE curriculum, too many of our students treated their faculty advisers as "that person who signs my registration forms," a situation arising at least in part because few strategic, career-influencing course choices could be made. This situation has changed dramatically with the new curriculum.

We strongly hope the new curriculum will better engage our students, since they will be required to make more strategic choices earlier in their education, which will require more interaction with knowledgable faculty and advising staff. We have reorganized our advising so that all of our undergraduates obtain consistent and up-to-date information about classes and degree requirements from a central faculty adviser. Professional and area-specific information such as job and graduate school opportunities is obtained from individual faculty advisers. We are also implementing or considering several new mechanisms to improve the advising process generally. These include:

• Curriculum documentation: Although a succinct description of the ECE curriculum can be found in the "Carnegie Mellon Undergraduate Catalog," a more extensive description is contained in a new departmental booklet, "The ECE Curriculum Primer." It describes the structure of the curriculum, which courses can count for what, and general academic and departmental policies. It also gives several example curricula that illustrate typical course choices emphasizing several popular areas within the department. The "Primer" is distributed in both booklet and on-line form.

• Curriculum planning software: Once students have begun to understand the basic structure and requirements of the curriculum, they are encouraged to begin to lay out a four-year schedule plan. They may change and update the plan as they learn more and discover the things they enjoy most, but at any given time they are advised to have a workable four-year plan. To assist with this, the department is developing a software application called the CMU Planner. This is a UNIX-based application that is available on workstations in the department's computer lab as well as workstations available to the campus-wide Andrew network. The software allows students to view catalog descriptions, select courses and move them around like tiles on their four-year plan. The program will check to make sure the course prerequisites have been satisfied, and will ultimately check to make sure the degree requirements have been satisfied. The details of this program are described in documents made available to our students in both paper and on-line forms.

• Template catalog: As mentioned above, several common course plans, or templates, are given in the "Primer." In addition, a catalog of templates that students and faculty work out is maintained by the Undergraduate Office. Students may find that one of these templates matches their interests well, or they may want to start with a template and make some changes. Students are encouraged to submit new templates to be added to the catalog.

• Plain language catalog: This proposal under consideration is to compile descriptions for each ECE course that are designed to be intelligible to someone who has not yet taken the course. Whereas the official catalog descriptions are designed to be concise and precise, the Plain Language Catalog descriptions are intended to give a nonexpert the idea and flavor of the course.

• Registration seminars: Another proposal under consideration is to hold a seminar before registration each semester to give students an opportunity to address questions to the faculty about courses that will be offered during the next semester. The seminar would be structured as an informal panel discussion with representative faculty from each area of the department. From the question/answer discussions students should gain a better "feel" for what the courses will be like than they can obtain from simply reading the catalog description. The faculty will describe how the courses lead to other courses in the area and, where possible, how the course sequences relate to actual job functions and opportunities. An informal "peer advising" session would be held immediately following the panel discussion. This session would be sponsored by the Honor Society for Electrical and Computer Engineers, Eta Kappa Nu. Although every effort would be made to schedule the seminar at a convenient time, the seminar would also be videotaped for those who are not able to attend. Copies of the videotape could be checked out from the Undergraduate Office.

Our advising strategy is very much a "work in progress." We continue to believe that advising is critical and that our recent advising changes have been timely and helpful, but also that it remains difficult to do advising well.

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Accreditation

Despite these changes to the curriculum as it evolved from 1991 to today, many elements of current curriculum remain at odds with existing accreditation criteria: required courses remain few (e.g., there is still no chemistry class), relatively free electives remain numerous, the electrical engineering and computer engineering curricula remain integrated into a single B.S.E.C.E. degree.

During the design of the original curriculum, ABET itself was a national focus of heated debate about the role of accreditation in fostering or stifling curriculum innovation. Indeed, the final report of an ABET task force on this issue [13] wrote in 1991 that:

...there has been a growing divergence of opinion between the engineering academic community, as represented by the Engineering Deans Council, and ABET, on matters critical to engineering education. This comes at a time when engineering education is facing significant challenges. In the future, engineering schools will have to attract and retain a more diverse student body with widely varying levels of preparation; engineering graduates will need a greater knowledge of foreign cultures and business practices as we compete in world markets; measures should be taken to alleviate the shortage of new, young American faculty in engineering schools; and engineering schools must take a role in reversing the current decreasing interest of high school students in engineering as a career. In order to deal with these problems, additional flexibility and innovation in engineering education are urgently needed.

During the last years, ABET has sought to improve the quality of engineering education, yet many of the engineering deans have expressed the opinion that ABET stifles innovation. Many in academia criticize the "bean counting" nature of an ABET evaluation and the uniformity of undergraduate engineering curricula, with ABET criteria leaving little room for experimentation or new ideas.

However, the task force also concluded in [13] that "engineering schools should be encouraged and rewarded for experimentation and innovation in their programs, rather than be stifled and penalized for trying new ideas." After much discussion among our faculty, and with ABET itself, ECE at Carnegie Mellon chose to pursue accreditation as an innovative program under existing ABET guidelines for curriculum experiments.

In the fall of 1992 we presented our new curriculum to the IEEE Committee on Engineering Accreditation Activities (CEAA). This generated much discussion over the course of the year. The concept of a combined ECE degree was less an issue than whether certain courses should be required, such as one on probability and statistics. But the general reaction of this professional group was positive. In February of 1993 we presented the curriculum to the Engineering Accreditation Commission (EAC) of ABET. As a result, the EAC assigned Philip Lopresti of the EAC Executive Committee as the EAC liaison and adviser to Carnegie Mellon as we prepared for the accreditation process.

In early 1994 it was decided that, despite the small-scale modifications to the original 1991 curriculum proposal we actually implemented (see again FIGURE 5 and FIGURE 6 for the architecture of the curriculum as it is implemented now, in the 1994-1995 academic year), ECE would actually apply for accreditation of the "original" curriculum (see FIGURE 2 and FIGURE 3) under the ABET "innovative curriculum" clause that permits thoughtful experimental curricula that diverge from existing ABET standards to be considered on their merits. Our reasoning at the time was that, despite some small-scale changes to deal with local idiosyncracies such as the difference in units awarded in ECE classes versus non-ECE classes, the original, "pure" form of the curriculum was ECE's unique statement of how a curriculum ought to be organized. In September of 1994 ECE was visited to start the accreditation process. Initial results of the visit were quite positive; comments from the review team were favorable. The committee was impressed with the enthusiasm of the students. No deficiencies were found, which should clear the way for final accreditation.

A key part of the current curriculum is the so-called "ECE core" of required classes. This core is extremely small-just three mandated classes-and is aimed at our freshmen and sophomores. The design and "tuning" of these classes has been a critical part of the perceived success of the new curriculum. We describe each of these courses, their structure and motivation, and offer some analysis of how well they are working.

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ECE Core: Freshman Introduction to ECE

Although our incoming freshmen are highly motivated, many have no real understanding of what undergraduate studies in engineering are all about, and few have the hands-on laboratory experience that was common a decade ago. In our old curriculum, our freshmen took preparatory courses such as physics and calculus, but waited until the end of the second year to take any real engineering courses. The result was often a significant reduction in motivation as students worked to understand a wealth of relatively abstract fundamental mathematics and science presented without any supporting ECE-specific engineering context.

FIGURE 7. Syllabus: Freshman Intro to Electrical and Computer Engineering

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Functional decomposition of a system

• Block diagrams

Basic circuit concepts

• Ideal voltage and current sources
• Real voltage and current sources
• Behavioral model of R, C elements
• KVL, KCL, Ohm's law
• Behavioral model of active devices: transistor, diode, Zener diode
• Operation of a DC motor
• Transducers: LED, touch switch, speaker, ultrasonic range sensor
• Ideal op amp model
• Inverting amplifier
• Buffer and noninverting amplifier
• RC time constants

Digital logic concepts

• Digital signals
• Binary numbers
• Logic functions
• Karnaugh maps
• Flip flops and shift registers
• Asynchronous logic
• Synchronous logic
• Coding (BCD)

Building complex systems from basic building blocks

• Interconnecting digital elements
• Interconnecting circuit elements

Laboratory project: Building a working robot

• Electrical safety
• Dealing with the power supply and motor
• Dealing with transducers: LEDs, beeper, touch switch, clock, buffers
• Dealing with digital subsystems: gates, flip flops, counters, reset
• Dealing with the system: memory, programmed and hardwired control
• Integrating all the pieces

Our new freshman introductory course rectifies this situation. The course motivates and introduces basic concepts in electrical and computer engineering in an integrated manner, provides hands-on laboratory experience early, and strives to imbue students with some ability to look at the "big picture" and ask questions that will lead to a solution to the problem at hand. The course has calculus and computer programming courses as corequisites. It introduces fundamental theoretical ideas in both electrical engineering and computer engineering. A simple mobile robot system serves as the experimental vehicle to motivate the teaching of basic concepts like Kirchhoff's laws, dc models of circuit elements, logic gates, flip flops, counters and so forth. The subsystems that comprise the robot provide the basis for a sequence of interesting laboratory exercises. The basic syllabus appears in FIGURE 7.

Structure

Since ECE is a blend of physics, mathematics, computer science and engineering practice, the course covers both theory and applications. Lectures emphasize theoretical aspects, laboratories emphasize experimental techniques, and recitations focus on problem-solving skills. The robot is used to illustrate how complex systems can be decomposed into subsystems and to motivate the need for the theory behind each of these subsystems. In the laboratory, students analyze, construct and test these subsystems to make sure they really do work as predicted by theory. The laboratory experience also demonstrates the thought processes behind the development of complex systems with many component parts. The virtues of focusing on a small robot are that it is simple enough for freshmen to understand, complex enough to illustrate the larger view of how electrical engineering and computer engineering ideas mesh, and provocative enough to keep students interested when the going gets tough.

The course focuses on black box models of systems, such as power supplies, sensor circuits and digital controllers, and the behavioral description of primitive elements, such as resistors, capacitors, transistors, gates and flip flops. We begin by considering a black box model of a system and then move to consideration of black box descriptions of each subsystem. This process is repeated until we ultimately consider primitive elements like circuit components.

For example, while considering the power supply, we introduce notions such as voltage regulation and load capability. At this time, concepts such as an ideal source and a real source are introduced, along with a behavioral model of resistive element-which of course turns out to be Ohm's law. We end up decomposing this subsystem into resistors, capacitors, transistors, batteries (or voltage sources) and Zener diodes. We develop simple models of each of these elements and introduce the relevant physical quantities (e.g., charge, current, voltage) and relationships. For example, for a capacitor, we tell students how the current flowing through the device is proportional to the slope of the curve defining the time-varying behavior of the voltage across its terminals; this can be illustrated quite clearly in graphical form.

Similarly, we illustrate the behavior of an ideal diode graphically, using current versus voltage plots. This serves as a foundation for discussion of elementary transistor behavior. An understanding of each of these circuit elements allows students to grasp the overall structure of the power supply itself and provides us with the context for introducing fundamentals like Ohm's law, Kirchhoff's voltage and current laws, and implicit techniques for circuit analysis. Note also that our behavioral models of the transistor and diode are introduced without ever introducing the concept of electrons, holes, doping, etc. These notions are really not required to understand the basic workings of a transistor or diode, and the engineering context for developing these ideas has not yet been established. This approach has been referred to by some as just-in-time learning [14], since we avoid piling up a potentially confusing inventory of unmotivated and mystifying theory and mathematics taught with the promise that "it'll be good for you-we'll tell you why later."

A set of coordinated laboratory exercises track the lectures and give many students their first hands-on laboratory experience. Although the ultimate aim is to assemble a working mobile robot, students attain this goal through a series of smaller projects that allow them to test the ideas being developed in lecture. For example, while a power supply is being dissected in lecture, students are building, testing and debugging a simple power supply (on a proto-board separate from the robot itself) to ensure that they understand what will actually be happening after they wire up their robot's supply. These exercises are also designed to show how systems are built and tested in a methodical manner.

Similarly, we enumerate, decompose and describe the other subsystems of the robot, such as the motor driver, the sensors, and the digital control and programming components. Digital topics are then similarly introduced as black box behavioral models, and students acquire the fundamentals of Boolean algebra, combinational circuits, simple sequential circuits like counters, memories and so forth. One of the important points we stress is the connection between analog and digital ideas. In our current curriculum, entering students often have no clear vision of the relationships between the electrical engineering and computer engineering "ends" of the department. In the old curriculum, students were exposed to analog systems in the guise of circuit analysis in an introductory circuits class, and then exposed to digital systems in another introductory course on combinational and sequential logic. Accordingly, some students developed an "us" versus "them" parochialism as they came to identify themselves as primarily electrical engineers or primarily computer engineers. The new curriculum strives to remedy this by exposing our students immediately to a more unified view of the different disciplines comprising ECE.

Finally, it is worth noting that, properly motivated, it is possible to treat nontrivial subjects in such a course. FIGURE 8 shows an example of a design problem from a recent final examination in this freshman-level course.

Analysis

Perhaps the most common observation we can share is that entering students are enthusiastic about starting real engineering classes in their first semester. They also simply appreciate the attention paid to them by their chosen departments in their first year, as opposed to the older curriculum in which ECE played no role until late in the second year. There is also evidence that students are using the freshman engineering courses offered by each department to help select their major, or at least, to decide which majors they do not wish to pursue. At least a few students have switched majors from their original choice after sampling the introductory freshman course offered by that department. An unexpected positive side effect of teaching engineering early is that some students have actually been able to land engineering jobs during the summer after their freshman year.

However, there were substantial adjustments necessary in faculty "teaching style" to accommodate very young students making the transition from high school courses with day-to-day, step-by-step guidance to college courses with more demands for individual initiative. One current solution is frequent small exams to test acquisition of the critical concepts. Another is extremely careful synchronization among the lecture material, the recitation problem-solving sessions and the weekly laboratory assignments.

FIGURE 8. Example Final Exam Problem from Introduction to ECE

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This circuit consists of a general transistor inverter that is used to interface to TTL logic. Suppose the range of logical 1 is defined to be anything between 2.5V and 5V and logical 0 is defined to be between 0V and 1.2V. Anything in between 1.2V and 2.5V is an incorrect logic value.

• Draw VOUT as a function of VIN. Mark the beginning and end of each piecewise linear region on the VIN axis. In each of these piecewise linear regions, mark the state of D1, D2, D3 and Q1. For example, write D1=off, D2=on, D3=on, Q1=forward active. Hint: It may help you to think of D2 and D3 as a single diode with VON = 1.4V.

• can vary substantially during manufacturing. Determine the minimum value of such that the logic gate still operates correctly. Hint: the limit on will occur when VIN = 2.5V and VOUT = 1.2 V so you should solve for to make this happen.

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ECE Core: Sophomore Fundamentals of EE

This is the first real "circuits" course. It differs from traditional courses primarily in two ways. First, it exploits the fact that students have had some real exposure, both practical and theoretical, to linear circuit ideas and issues in the robot project from the freshman Introduction to ECE course. The freshman course is a prerequisite; a linear algebra course or the new ECE course Mathematical Foundations of Electrical Engineering is a corequisite. Second, the course uses a nontraditional focus (like the robot in the freshman course) to motivate students and provide a vehicle for developing the fundamentals. This focus is transient analysis of linear interconnect circuitry, or, said another way: how fast can a computer be? The course introduces the idea that computer system speed is measured in millions of instructions per second (MIPS)-the more MIPS the better. Students are assumed to have a rudimentary idea of what a computer instruction is from their assembly and test of the stored program control portion (memory plus state machine) of the robot in Introduction to ECE. We explain how, a decade or so ago, this speed was determined more by transistor size, i.e., how small a device could be made, how many could be packed inside one chip. But now and for the foreseeable future, computer system speed is determined more by the interconnect wiring itself, inside the chips, among the chips, and among the increasingly exotic system-level packages that carry the chips. This focus provides a suitably interesting context to introduce the basics of lumped linear circuits: resistance, capacitance and now, inductance.

Structure

As expected, the course focuses on studying in detail many simple RLC circuits. However, we always motivate these studies by asking the question: what will be the effect on switching signal behavior? The goal is to show that simple circuits provide the right insights to understand even the most complex of interconnections, and that complex circuits can be understood by mastering the basic concepts of circuit theory: Kirchhoff's current and voltage laws; superposition and convolution; series, parallel and ladder circuit analysis; Thevenin's and Norton's theorems; natural frequencies and ; circuit partitioning; and nodal analysis. For additional perspective here, see [11].

The class has lectures, a laboratory session and a recitation session. Lectures motivate and develop theoretical material, laboratories provide more hands-on exposure to circuits to test how well the theory really works and recitations provide opportunities for problem solving and review. FIGURE 9 shows a syllabus of topics for this course.

Analysis

Aside from being a linear circuits course, the sophomore Fundamentals of EE course also introduces and reinforces some crucial mathematics in our curriculum. In our prior curriculum we required three related sets of mathematics courses:

• Calculus I, Calculus II to handle functions, basic derivatives, integrals, etc.

• Differential Equations to handle the functional form of the ordinary differential equations arising in circuits, electronics, signals, etc.

• Linear Algebra to familiarize students with matrix methods to handle the formulation of circuit solution techniques, control systems, etc.

In the 1991 version of the new curriculum, we dropped the differential equations class in favor of an attempt to teach this material in place, "just in time" [14] in the Fundamentals of EE class. This was motivated in part by the coverage of topics in the available differential equations class: the Mathematics Department chooses a broad range of functional forms to teach, while we would prefer deeper coverage of a few critical forms, for example, linear, constant coefficient differential equations arising frequently in physical systems. However, we also sincerely believed that circuits formed an excellent problem domain in which we could motivate differential equations to engineers. We kept the linear algebra course (despite similar concerns about coverage) but recast it as a corequisite to the Fundamentals of EE class.

As of early 1995, we appear to be succeeding in conveying basic circuits, but we are less successful with the mathematics. One problem-in hindsight somewhat obvious-is simply the difficulty in covering in a single course a wide range of mathematics in addition to an aggressive set of circuit topics. Even with our careful treatment of the fundamentals in this course, we still see random gaps in crucial mathematical preparation (e.g., complex analysis, linear differential equations and vector calculus) coming back to cause problems as our students elect more advanced classes.

This problem is sufficiently pervasive that we have proposed an entirely new ECE class just to rectify it: Mathematical Foundations of Electrical Engineering. Starting in the 1995-1996 academic year, this new course can be substituted for the linear algebra class as a corequisite for Fundamentals of Electrical Engineering. We will return to this proposed class (see page 58) later in this chapter.

FIGURE 9. Syllabus: Sophomore Fundamentals of Electrical Engineering

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A brief history and forecast of microelectronics

• Sizes, speeds and complexities of ICs from 1970 - present, projected to the year 2000.

Fundamental electrical concepts

• Review of voltage, current, Kirchhoff's laws and element relations for ideal independent voltage sources and resistors and capacitors.

Single time constant RC circuits and constraints on gate delay

• DC steady state and transient solutions of circuits with DC sources, switches and a single capacitance: exponential waveforms, their asymptotes and time constants.
• Gate delay and limitations on CMOS digital circuit switching speed derived in terms of switch, resistor, capacitor models of constituent transistors of CMOS inverters.

RC ladder circuits and on-chip IC interconnect characteristics

• Distributed and lumped models of uniform RC line for IC interconnect.
• Detailed analysis of transient response in terms of one and two lump ladder circuit models of such lines. Solutions of second-order equations in coupled first-order matrix form.

Switching circuit performance limitations caused by capacitance

• Fanout effects on switching speed with and without consideration of interconnect.
• Switching time speed-up strategies.
• Line-to-line capacitance coupling and its effects on switching speed and crosstalk.

Package inductance and RLC circuit analysis

• Inductance and its differential equation.
• Second order equations that arise from RLC circuits, their natural frequencies and the general forms of their solutions. Overdamped, critically damped, underdamped and undamped cases.

Transmission lines

• Telegrapher's equations; wave propagation down distributed LC lines; signal delay.

Basic AC circuit analysis

• Sinusoidal steady state; superposition of independent frequency components; peak, average, RMS value calculations.

Advanced AC circuit analysis

• Complex representation; phasors; complex impedance; the frequency domain.

Nodal analysis

• Matrix formulation of arbitrary circuit topologies; solution strategies; introduction to simulation methods.

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ECE Core: Sophomore Fundamentals of CE

This course builds upon the rudimentary digital design and computer engineering concepts presented in the freshman Introduction to ECE class. (The new course was actually patterned more closely on an existing course than either of the other two fundamentals classes.) The emphasis is a "vertical slice" through the layers of abstraction that comprise computer design, including a gradual, bottom-up evolution from 0s and 1s up to basic processor architecture and an integrated hardware and software laboratory that closely tracks the lectures. In the older curriculum, this course was our students' first exposure to ECE, and their first hands-on hardware laboratory. The new course benefits from the exposure our freshmen have already had to basic digital elements and real design problems. Hence, the new course is a slightly more aggressive version of its predecessor that relies on students' recently acquired background to revisit digital design ideas in more depth and with a greater emphasis on systematic analysis and synthesis.

Structure

Overall, the course is designed to demystify computers for our students. It builds up the concepts that define and inform each layer of the conventional design hierarchy: combinational circuits, sequential circuits, register transfer level, stored program computing, control path / data path partition and implementation, rudimentary instruction set architecture and assembly language programming.

Advances in programmable logic [12] (e.g., PALs, field programmable gate arrays, etc.) and associated design software have made it possible for laboratory assignments to target more interesting problems; recent examples include floating point arithmetic hardware, chess move generation and video game controllers. Use of a software-simulated processor for assembly language programming allows campus-wide electronic access and easy alteration of the instruction set (via simulated microcode) for faculty and students. The course provides a foundation for students who wish to pursue more advanced computer engineering courses, and for those whose interests lie elsewhere in ECE.

This course has a lecture section, weekly recitation sections and a weekly lab session. A syllabus appears in FIGURE 10.

We note that this is a particularly large course for ECE, with typically 100 to 150 students per semester. This is so because the course is a core requirement for both ECE undergraduates, and for computer science undergraduates at Carnegie Mellon. One result of this is that we have had to be somewhat cautious in how hard we try to exploit the design expertise that our own ECE undergraduates gain from their freshman Introduction to ECE course. Our computer science students, who intermix freely with our ECE students each semester, have more software expertise, but no hardware expertise. Accordingly, we spend the first few weeks of lab gently reintroducing the relevant hardware skills to our ECE students, while rapidly drilling our computer science students in these same basic skills.

Analysis

As mentioned above, this course actually more closely resembles its predecessors in the old ECE curriculum than does Fundamentals of EE, the introductory linear circuits course. It maintains the same flow through combinational design, sequential design, and microprocessor organization and programming, but with more aggressive laboratory design assignments. The course is popular, remains highly rated by our students, and prepares our students to succeed in their more advanced computer hardware and software classes.

FIGURE 10. Syllabus: Sophomore Fundamentals of Computer Engineering

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Binary number systems

• Positional number systems; useful radices: unsigned binary, octal and hexadecimal
• Signed numbers: sign magnitude, one's complement and two's complement
• Floating point numbers: sign, mantissa, exponent; basic arithmetic operations

Combinational circuit design

• SSI logic gates
• Boolean algebra and canonical forms
• Minimization via Karnaugh maps; via Boolean n-cubes; via classical Quine-McCluskey procedure; via 2-level and multi-level computer synthesis tools
• MSI building blocks: multiplexers, decoders, ROMs and PLAs
• Arithmetic circuits for fast addition, multiplication

Sequential circuit design

• Introduction to behavior of sequential circuits
• Basic latches and flip flops, latch/FF timing and triggering
• Sequential (state machine) design methods
• Computer synthesis and optimization tools for sequential circuits
• MSI sequential parts: registers, shift registers, counters

Rapid prototyping technology

• Field programmable gate array architectures and applications
• Synthesis and optimization tools for FPGAs

Processor design

• Register-transfer level ideas, abstractions, design style
• Stored program computers, data path and control path partitions
• Example processor design: a simple instruction set
• General data path design techniques, example data path design
• General control path design techniques: hardwired control, microprogrammed control; example microprogrammed control path design

Assembly language programming

• Basics of storing, manipulating, moving data on a simulated processor
• Basics of control flow: straight-line code, conditional branches and loops
• Breaking programs into manageable pieces: subroutines, stack management, links to higher-level languages

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Elective: Sophomore Mathematical Foundations of EE

Mathematical Foundations of Electrical Engineering is, as of this writing, a proposed new course to be offered for the first time in the fall of 1995. It is the result of our ongoing dissatisfaction with the random gaps in crucial mathematical knowledge that even our best students exhibit, despite our best efforts to better integrate mathematics and engineering in the first two years of our new curriculum.

Structure

A syllabus appears in FIGURE 11. It is worth noting an important philosophical point here: we do not regard this solely as a math class. Rather, this is a class whose purpose is to build basic mathematical techniques that appear widely in engineering applications (and that are not well integrated from an engineer's perspective when not taught in an engineering context).

This course covers topics from engineering mathematics that serve as foundations for descriptions of electrical engineering devices and systems. It has four major parts:

• Complex analysis, including complex numbers and complex analytic functions

• Ordinary differential equations of first- and second-order

• Linear algebra, including matrices, vectors and determinants

• Vector calculus, including the vector differential operators gradient, divergence and curl, and vector integral calculus, including multiple integrations and integral theorems.

The proposed text is Advanced Engineering Mathematics, seventh edition, by E. Kreyszig.

In our current curriculum, the course can replace the required linear algebra corequisite for the required core Fundamentals of EE sophomore class (hence the treatment of complex analysis, differential equations and linear algebra). It can also replace the required prerequisite three-dimensional calculus class that serves as a gateway (or, as we now believe, an obstacle) to the first electromagnetic fields class, and to related magnetics and data storage system classes.

Analysis

The earlier mention of a prerequisite "obstacle" merits further discussion. In our old curriculum, all math classes were essentially required, so there was never any choice involved in selecting a math (or science) class so that a later engineering class could be elected. This is no longer true in the new curriculum. The beginning breadth classes in each breadth area (recall, these are: applied physics, signals & systems, circuits, computer hardware, computer software) can individually require extra mathematics or science classes beyond those mandated in the ECE math and science core. A somewhat unexpected result here is that now, some introductory breadth courses are "easy" to take because they require only mathematics, science and ECE courses that all students take anyway. But some of courses are now "difficult" to take because they require extra mathematics preparation. The notable example is the electromagnetics sequence, which required an extra three-dimensional calculus class. As well as filling in some critical gaps in our students mathematical knowledge, the new Mathematical Foundations of EE class is also intended to lower the barrier to these breadth courses that would prefer a more extensive mathematical background, but which have seen declining enrollments (see Chapter 6 for more on this) in part because of these extra obstacles to enrollment.

FIGURE 11. Syllabus: Proposed Elective, Mathematical Foundations of EE

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Complex analysis

• Complex numbers, complex analytic functions

Ordinary differential equations

• First-order differential equations
• Second-order differential equations

Linear algebra

• Matrices, vectors and determinants

Vector calculus

• Vector differential calculus, grad, div, curl
• Vector integral calculus, integral theorems

We now turn to a more student-oriented view of the new curriculum. One obvious question to address is: exactly what must one take to get the B.S.E.C.E. degree at Carnegie Mellon? We revisit the curriculum, this time laying out precisely all the requirements. A second question is: what alternatives are available as students plan to allocate their electives among various technical and nontechnical topics? As a part of the curriculum design process, the Wipe the Slate Clean Committee constructed example curriculum templates, each illustrating-albeit at that time approximately-a different path to a four year bachelor's degree in electrical and computer engineering comprising eight semesters with four courses per semester. We offer a few of these templates here, now revised in light of current requirements, to suggest ways in which the flexibility of the new curriculum can serve the needs of different students with different preparation and aspirations.

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Detailed Curriculum Requirements

To begin, we enumerate the requirements and constraints specified in the new

ECE curriculum.

General Education Requirements

Eight courses in all, comprising:

• One course chosen from a list of designated writing and expression courses.

• One course chosen from a list of designated humanistic studies courses.

• One course chosen from a list of designated cognition and institutions courses.

• Three more advanced courses, constituting again a depth sequence, chosen from among nontechnical courses in humanities, social sciences, foreign language or fine arts.

• Two freely chosen nontechnical courses from humanities, social sciences, foreign language or fine arts.

Mathematics, Science and Computer Programming Requirements

Eleven required courses in all, comprising:

• Computing Skills Workshop (required of all freshmen in the college of engineering)

• Introduction to Programming and Computer Science (corequisite for Introduction to ECE)

• Calculus I (corequisite for Introduction to ECE)

• Calculus II

• Physics I (corequisite to most other CIT engineering department's freshman Introduction to Engineering course)

• Physics II

• Linear Algebra or Mathematical Foundations of Electrical Engineering (corequisite for Fundamentals of Electrical Engineering)

• Introduction to Modern (Discrete) Mathematics (corequisite for Fundamentals of Computer Engineering)

• Probability and Random Processes

Plus two more elective courses, constrained as follows:

• Two math/science electives, satisfied by any course beyond the elementary level in mathematics, physics, biology, chemistry, statistics, except those specifically aimed at a nontechnical audience.

Freshman Engineering Requirements

Two requirements for obtaining a B.S.E.C.E. are:

• The ECE freshman course, Introduction to Electrical and Computer Engineering, must be taken by ECE majors, although it may be taken as late as the fall semester of the sophomore year.

• One additional "Introduction to Engineering" course offered by another department in the college of engineering.

For completeness, a list of all freshman introductory engineering courses offered in the college of engineering follows. Each course is permitted to have one science and one mathematics corequisite:

• Introduction to Chemical Engineering (corequisites Modern Chemistry I and Calculus I)

• Innovation and Design in Civil Engineering (corequisites Physics for Engineering Students I and Calculus I)

• Introduction to Electrical and Computer Engineering (corequisites Introduction to Computer Programming and Calculus I)

• Introduction to Engineering and Public Policy (corequisites Physics for Engineering Students I and Calculus I)

• Fundamentals of Mechanical Engineering (corequisites Physics for Engineering Students I and Calculus I)

• Materials in Engineering (corequisites Physics for Engineering Students I and Calculus I)

ECE Core Requirements

There are only two required core courses past the required freshman Introduction to ECE class:

• Fundamentals of Electrical Engineering (corequisite Linear Algebra or

  Mathematical Foundations of Electrical Engineering)

• Fundamentals of Computer Engineering (corequisite Introduction to Modern Math)

ECE Breadth Requirements

Students must take at least one first-level course in each of three of the five basic areas of ECE:

• Applied Physics

• Signals and Systems
• Circuits
• Computer Hardware
• Computer Software: These courses are all offered by the Computer Science Department, with whom we maintain a reciprocal relationship: computer science students take several hardware-oriented ECE classes, and ECE students may elect to take software-oriented computer science classes.)

Engineering Coverage, Depth and Design Requirements

At least three more courses must be taken from the areas defined in the ECE breadth requirement. These courses must be chosen so that two additional requirements, the depth and design requirements, are satisfied.

To satisfy the depth requirement, students must take at least one course that has, as a prerequisite, one of the courses used to meet the breadth requirement.

To satisfy the design requirement, students must complete one course from a list of designated capstone design courses. In some cases, a single course can satisfy both the depth and design requirements.

Engineering Elective

Students must complete one additional technical course beyond the elementary level chosen from among any courses in the College of Engineering or School of Computer Science.

Free Electives

Students may choose up to 4.5 classes (at Carnegie Mellon, this is 54 units) arbitrarily from among any graded courses offered by any degree-granting department.

Overload Policy, QPA Policy

The term "overload" refers to the maximum number of units per semester a typical student is allowed to carry without getting special permission. An overload is defined as any schedule with more than 54 units (three 12-unit classes and two 9-unit classes) in one semester. Only students who have achieved a QPA of 3.5 out of 4.0 in the previous semester may overload.

To graduate, students must maintain a 2.0 QPA in the set of courses used to satisfy the ECE freshman, ECE core, breadth, depth, coverage and design requirements.

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Curriculum Templates: Example Paths through ECE

We now turn to the larger picture: what options do students have to tailor their course elections to their aspirations and goals within our new curriculum? We offer a broad set of different scenarios in the following sections.

First, however, a bit of notation should be explained. ECE courses, and courses in other departments such as Computer Science that are considered to be in core ECE areas, appear in bold print with the appropriate title in the following curriculum templates. All other courses appear as regular print. The number in parentheses in each box represents the units of each course.

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A Traditional Electrical Engineering Curriculum

Perhaps the first observation to make is that a flexible curriculum in no way prevents a student from choosing a "traditional" sequence of courses. Hence, the course template in FIGURE 12 shows how a conventional electrical engineering program-conventional except, of course, for the existence of real engineering classes in the freshman year-can be constructed within the constraints of the proposed ECE curriculum. This template shows the student pursuing the usual component of mathematics, physics, computer programming and ECE fundamentals classes, as well as substantial breadth and depth in electromagnetics, circuits, signals and systems, and solid state. By the standards of any traditional electrical engineering curriculum, this is an exceptionally broad, solid plan of study. This program, or something similar, would be the "default" program suggested by an adviser to a student who is interested in traditional electrical engineering without more specific interest areas. It should be emphasized that this is only one of many possible course selections that could be used to construct a curriculum with traditional electrical engineering emphasis.

FIGURE 12. A Traditional Electrical Engineer

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A Traditional Computer Engineering Curriculum

A "traditional" computer engineering plan of study can also be formulated within the framework of the proposed ECE curriculum. Following the usual mathematics, physics, introductory programming and ECE fundamentals classes, the computer engineering student pursues a variety of computer hardware and computer software topics. Note that the ECE breadth requirement (which mandates that students elect one course in three of the five different ECE breadth areas) will not permit a course of study so narrow that only hardware-related topics, or only software-related topics are selected to the exclusion of other areas. Here, the breadth requirement means that even after taking courses in the computer hardware and computer software areas, a third area must be selected for study. In the template shown in FIGURE 13, the student attains this breadth in the circuits area, after having acquired the necessary preparation in the Fundamentals of EE class required of all ECE students. The senior year culminates in a capstone design project in digital systems design, along with yet more depth and breadth in signals and systems, software and hardware. Again, by the standards of any traditional computer engineering program, this is a solid and well-balanced course of study. It should again be emphasized that this is only one of many possible course selections that could be used to construct a curriculum with traditional computer engineering emphasis.

FIGURE 13. A Traditional Computer Engineer

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A Novel Preparatory Curriculum: The ECE Generalist

We have seen that the flexibility inherent in the proposed ECE curriculum does not preclude traditional avenues of study. Now let us consider instead new avenues of study that it creates. One possibility is illustrated by the course template shown in FIGURE 14 that we call a "preparatory curriculum." Such a curriculum has exactly the same connotation that a traditional liberal arts curriculum usually carries: a broad, solid course of study emphasizing a variety of different areas that is worthy of a degree in itself, but undertaken specifically as preparation for a subsequent professional degree. It has become increasingly obvious in recent years that not all students who pursue a bachelor's degree in ECE actually remain electrical or computer engineers for the rest of their lives. Moreover, we are seeing significantly more students who consciously choose an engineering degree as preparation for post-graduate study in other professional disciplines such as law, business or medicine. In the past, such preparatory curricula were, it seems, exclusively undertaken under the rather broad umbrella of liberal arts. We are specifically interested now in supporting an ECE degree as a general preprofessional degree-but without compromising the integrity of the ECE bachelor's degree itself.

The plan of study shown here is one middle-ground approach. Observe that this student still takes the usual mathematics, physics, computer programming and ECE fundamentals classes. In addition, the breadth, depth, ECE content and capstone design requirements are met, in this case with a combination of courses in signals and systems, circuits, computer hardware and computer software. Note that the emphasis in such a curriculum is breadth of experience, and exposure to many different technical topics. Nevertheless, the result is not a weak or simplified program, but rather, a program for what might be called the "ECE Core Generalist." Significant here is that the curriculum still leaves room for six free elective courses, in addition to Carnegie Mellon's already stronger-than-average requirement of eight general education (humanities, social sciences, fine arts) classes. With appropriate choices among these nontechnical classes, a very strong preparatory program can be created. In the example shown, we have populated the elective courses with economics, biology and a foreign language. Of course, some of these elective choices could also be accomplished within the eight general education courses themselves; the point worth noting is that taken together, the general education and elective slots provide considerable flexibility. With appropriate course choices, this course of study will produce students with a solid background in ECE core material, along with good preparation for further study in, for example, business or law.

FIGURE 14. An ECE Core Generalist

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Alternatively, the new curriculum permits a much broader curriculum within ECE than was previously possible. The breadth, depth, design, coverage and free electives taken together give more than 13 courses that may be chosen to span the entire range of areas within the department. Such a program might be called the "ECE Technical Generalist." An example of such a curriculum is shown in FIGURE 15. A student following this curriculum would be well prepared for interdisciplinary engineering projects, as well as further study in engineering management, business or law

FIGURE 15. An ECE Technical Generalist

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A Focused Preparatory Curriculum: The Premedical Student

This template shown in FIGURE 16 is a more specific example of the Core- Generalist template presented in FIGURE 14 in the previous section. The student in this program is specifically tailoring an ECE program toward a career in medicine. Notice, for example, the choice of the Introduction to Chemical Engineering class as a freshman engineering elective (in addition to the Introduction to ECE freshman course). This requires a chemistry class as a corequisite, which displaces a General Education class to the spring of the sophomore year. In addition to the usual mathematics, physics, programming and ECE fundamentals classes, this student pursues breadth in signals and systems, circuits and computer software. Depth in signals and systems ultimately leads to a capstone design course in controls and instrumentation. Observe that it is possible to pursue a fairly traditional ECE core that also meshes nicely with the overall interest in medicine. In particular, using the elective slots, this student manages to take three biology classes and five chemistry or chemical engineering classes, to strengthen preparation for medical school. (Note: this curriculum is for illustration only; no assurance is given that the requirements of any given medical school are satisfied.)

FIGURE 16. An ECE Premedical Student

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A Curriculum with One Year of Study Abroad

Carnegie Mellon has recently strengthened its commitment to the concept of spending one year abroad during undergraduate studies. Foreign study can be extremely rewarding, but structural impediments in an overly rigid curriculum can render such plans unattractive to even the most committed student. The template shown in FIGURE 17 is merely one example of how this might be accommodated in the new ECE curriculum. Using the flexibility in the proposed curriculum, we have "stacked" the junior and senior years as shown here. During the junior year spent abroad, this student emphasizes humanities and foreign language studies. Upon returning, the student plunges back into a technical program, in this example, a plan of study emphasizing computer hardware, with breadth in computer software, circuits, and signals and systems. Of course, other strategies are possible, but the point to note is that the proposed curriculum can adapt itself to those students intent on pursuing foreign studies.

FIGURE 17. An ECE Student Who Studies Abroad for One Year

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A Curriculum with Specific Technical Focus: The CAD / VLSI Designer

The flexibility in the new ECE curriculum allows an ECE bachelor's program to be used as preparation for other post-graduate professional studies. However, the skeptical reader should not jump to the conclusion that the new ECE curriculum is thus specifically tailored to those students who will not pursue engineering as their livelihood, to the detriment of those who will actually become practicing electrical and computer engineers. The critical attribute of a flexible curriculum is that it can adapt to a variety of students. Accordingly, we now consider yet another kind of curriculum: the "focused" program of study that emphasizes particular technical strengths at Carnegie Mellon.

The template shown in FIGURE 18 focuses on Computer-Aided Design (CAD) for Very Large Scale Integrated Circuits (VLSI). Carnegie Mellon's ECE Department houses the Center for Electronic Design Automation, an internationally recognized leader in this area, and a number of our faculty devote their research to its problems. The plan of study illustrated here has substantial breadth and depth in the areas of circuits, computer software and computer hardware. The senior year culminates in a capstone design course in VLSI design that integrates all these skills. In addition, the senior year is also used to attain CAD-specific depth, as well as general breadth in signals and systems and computer architecture. Note that this highly focused plan of study sacrifices none of the general breadth or exposure one would expect of a strong undergraduate ECE degree.

FIGURE 18. A CAD/VLSI Designer

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Another Curriculum with Technical Focus: The Data Storage Systems Designer

FIGURE 19 shows a template for a plan of study that focuses on data storage systems, with particular emphasis on magnetic recording media and the computer applications that use these media. This program is another example of a focused technical curriculum that exploits particular strengths at Carnegie Mellon. The ECE Department houses a National Science Foundation-supported engineering research center called the Data Storage Systems Center. This center is the focus of interdisciplinary work on a variety of topics in data storage, from the material properties of magnetic media to the architecture of distributed file systems for computer networks. The template shown here is an example of how the new ECE curriculum can support interdisciplinary studies, surmounting some of the barriers between disciplines. The interesting feature of this course of study is its two seemingly disparate areas of concentration: magnetic media and computer systems. Normally, one just does not expect a student to take courses in, say, device physics and computer operating systems. And yet, engineers with precisely such an interdisciplinary background would be ideally positioned to understand and attack the interesting problems in data storage system design. This student achieves breadth in applied physics, circuits, signals and systems and computer software, as well as depth in relevant physics- and computer-related topics. The senior year culminates in a capstone design project in data storage systems.

FIGURE 19. A Data Storage Systems Designer

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A Program for the Late Starter

All CIT incoming freshmen must take two introductory engineering courses during their freshman year. It is possible that a student may not take the introductory ECE course during the freshman year but still decide to purse an ECE degree. The template shown in FIGURE 20 shows a program that accommodates such a student.

FIGURE 20. A Late Starting ECE Student

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Implementation of the new ECE curriculum began in the fall semester of 1991. The first class of graduates will finish in the spring of 1995. Hence, some obvious questions, e.g., employer response to our new graduates, cannot yet be answered as of this writing. However, over the last year we have begun to gather data-both anecdotal and quantitative-about the impact of the new curriculum and how our students are navigating its manifold elective choices. We offer some preliminary data and analysis in this chapter.

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First Impressions

To date, four cohorts of students have entered the new ECE curriculum, entering in the fall of 1991, 1992, 1993 and 1994 respectively. Each cohort had roughly 150 students. The most advanced typical student is now finishing the senior year of his or her curriculum. Although a few students have finished ahead of schedule, we still have insufficient data about graduates from the curriculum. However, we have a wealth of anecdotal impressions about the first three of these cohorts.

On the qualitative side, perhaps the most common observation is that the entering students are enthusiastic about starting real engineering classes in their first semester. They also simply appreciate the attention being paid to them by their actual chosen departments in their first year, as opposed to the older curriculum in which ECE played no role until late in the second year. There is also evidence that students are using the freshman engineering courses offered by each department to help select their major, or at least, to decide which majors they do not wish to pursue. At least a few students have switched majors from their original choice after sampling the introductory freshman course offered by that department. An unexpected positive side effect of teaching engineering early is that some students have actually been able to land engineering jobs during the summer after their freshman year.

The second year's Fundamentals of EE and Fundamentals of CE classes also appear to be succeeding-although mathematics coverage remains an issue we are working to address (see Chapter 4). The extra facility in the laboratory gained during the freshman year helps considerably, allowing more interesting labs earlier in the curriculum. There is also evidence of students making active choices to select one or another of these courses early in the second year, to attain the prerequisites necessary to elect an ECE breadth course in the second half of the year. One common example is the election of Fundamentals of EE in the first half of the year, followed by Signals and Systems in the second half. Again, students especially like the idea of being able to elect real engineering classes early in the curriculum, and often use this flexibility to get an early start on their breadth electives, rather than taking a free elective in their sophomore year. We had originally envisioned this unconstrained slot in the sophomore year as a free elective, as illustrated in FIGURE 2 on page 22. Instead, students often prefer getting into an ECE breadth class as early as possible.

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Impact on Course Choices

To answer questions about what students are actually doing with their newfound flexibility in this curriculum, we performed an experiment illustrated in FIGURE 21. Two populations of students were identified for comparison:

• Students in the graduating class of 1992 who were juniors during the 1990-1991 academic year and whose previous three years of courses were taken in the old (pre-1991 version) ECE curriculum.

• Students in the graduating class of 1995 who were juniors during the 1993-1994 academic year and whose previous three years of courses were taken in the new ECE curriculum.

FIGURE 21. Experiment to Compare Course Elections Between Old and New ECE Curricula

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We looked at all the courses elected over the preceding three years in each population of students, and counted where (department and college at Carnegie Mellon) each course was taken, and for how many units of credit. At Carnegie Mellon, typical courses range from 9 to 12 units, the number representing the estimated hourly workload of the class. In the old curriculum, the typical workload was between 44 and 54 units per semester; in the new curriculum the target is for this to be 45 units per semester. The old curriculum required 388 units to complete the bachelor's degree; the new curriculum requires 360, a reduction of essentially 2.5 classes. The data provide an interesting picture of how students are reacting to the new curriculum.

FIGURE 22 tallies the number of units elected within ECE, and across the various colleges of Carnegie Mellon. One obvious fact is that, despite the flexibility to avoid some ECE courses, students are still spending most of their units inside ECE; there is no mass flight to easier courses. Election of courses in engineering outside ECE is down, primarily due to the elimination of old requirements to elect a few ad hoc courses in other engineering departments, e.g., thermodynamics, statics and so forth. The new curriculum requires all students to take two introductory courses in the freshman year, one of which is usually in the student's major area-Introduction to ECE for our students. Election of computer science courses is up. There was always an unmet demand in the old curriculum by non-CE students to take more computer-related courses, but it was extremely difficult to fit them in. This appears to have been resolved in the new curriculum. Election of math/science classes is slightly down due to some changes in the required courses, e.g., three 9-unit physics courses were replaced by two 12-unit courses, and the chemistry requirement was eliminated altogether.

There are also some interesting lower-level changes not apparent in this chart. For example, FIGURE 23 shows the number of unique, i.e., different courses elected by the two populations. Students in the new curriculum are taking a wider variety of courses.

FIGURE 24 refines the data related to ECE-specific courses in the top two bars of the chart of FIGURE 22. Here, each course elected in ECE has been tallied based on the relevant ECE breadth area, as defined by the new curriculum. Courses in the old curriculum were matched to their best fit in the new curriculum. In addition, the freshman Introduction to Electrical and Computer Engineering was arbitrarily counted as being half in the computer hardware area and half in the circuits area. FIGURE 24 shows where the 1994 juniors chose to exercise their flexibility within the new curriculum, versus the mix of required and elective courses for 1991 juniors in the old curriculum.

FIGURE 22. Comparative Course Elections: Across Carnegie Mellon Colleges

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FIGURE 23. Comparative Course Elections: Unique (Different) Courses

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FIGURE 24. Comparative Course Elections: Across ECE Breadth Areas

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Again, there are several interesting observations. Election of applied physics courses is down substantially. In part this reflects the elimination of a required solid state devices class for all students (electrical engineering and computer engineering) in the 1991 curriculum, and of required electromagnetics courses for electrical engineers. More interesting though is the choice of courses in the new curriculum. The elective solid state breadth course in this area has seen its enrollment increase nearly 50 percent in comparison with the old introductory solid state course. More students are now electing to sample the applied physics area via the solid state course, instead of via the electromagnetics course. Conversely, enrollment in electromagnetics courses has fallen by about 50 percent, though there is some evidence that the prerequisite of an extra calculus class (3-D methods) is making electromagnetics less attractive. (See again our discussion of the motivations for the proposed Mathematical Foundations of EE class, Chapter 4, page 58.) It has also been suggested that the lack of recently offered advanced design-oriented capstone classes in this area that pull students toward electromagnetics is also a contributing factor; new capstone design classes planned for this area (e.g., microwave design) might change this.

Election of signals and systems courses is up, primarily due to the popularity of the introduction breadth course in this area as a first ECE course beyond the Fundamentals of Electrical Engineering requirement. Circuits units are also up, due in some part to counting freshman Fundamentals of ECE partly in this area, as well as Fundamentals of Electrical Engineering, both of which are required. Computer hardware units are up, again for a similar reason due to Fundamentals of ECE and Fundamentals of Computer Engineering. Computer software elections are also up strongly, reflecting continued interest in programming classes that now more easily fit into the schedules of ECE students who are not specifically trying to become computer engineers.

Overall, there is still substantial breadth of course elections among the ECE topical areas, and among Carnegie Mellon colleges, albeit with some shifts in emphasis. None of the worst-case scenarios we might have imagined-mass flight from difficult courses, for example-have come to pass. Most students continue to elect challenging courses, now somewhat more widely distributed across ECE's breadth.

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One entirely unexpected recent spin-off of our curriculum design efforts is the recent creation of an integrated master's degree in ECE. We briefly discuss the motivation and current structure of this program in this chapter.

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Motivation

There has been widespread discussion about how the best among our undergraduate students typically elect graduate school, but the solid middle-of-the-curve student typically enters industry immediately-despite the fact that another year of course and project work would be immensely helpful to that student's career. Similar to the model now in place within Electrical Engineering and Computer Science at MIT, our program offers automatic admission to students who achieve a specified minimum grade point average over certain courses and ECE breadth areas.

The primary purpose of the new Integrated M.S./B.S. Degrees program is to provide students with superior breadth and depth of technical material, which will better prepare them for careers in industry. The program normally requires an additional year of coursework beyond the bachelor's degree requirements. However, students who pursue the Integrated M.S./B.S. Degrees substantially enhance their readiness to contribute in an industrial position. The advanced education attainable via the program is likely to be better integrated and more sophisticated than the further education pursued at "local" colleges or universities as a part-time or evening student.

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Requirements

This program is available to all undergraduates who maintain a cumulative QPA of 3.0 out of 4.0. No course with a grade lower than C is counted toward the master's degree requirements for the integrated degree.

The following are the additional requirements for the Integrated M.S./B.S. Degrees over and above the requirements for the bachelor's degree. Note, no course can be counted as satisfying more than one of the requirements listed below and no course used to satisfy the basic bachelor's degree requirements can be used to satisfy one of the requirements listed below. The requirements total 96 units (nominally eight 12-unit courses).

1. Breadth Requirement (12 units): To increase the breadth in ECE, students must take 12 units of course work in a "new" area-an area in which they have not already taken an introductory course (this makes four breadth areas rather than the three required for the bachelor's degree).

2. Additional Design Capstone Requirement (12 units): To further prepare students for engineering design work, they must take an additional course from the list of acceptable engineering design capstone courses (this makes two design capstone courses rather than the one required for the bachelor's degree). Both design capstones can be in the same area or in different areas.

3. ECE Graduate Course Work (12 units): Any mezzanine-level senior- graduate or higher course(s) can be used to satisfy this requirement. (Within ECE these are numbered as 18-5xx courses.)

4. Advanced ECE Course Work (36 units): Any graduate-level or higher courses can be used to satisfy this requirement. (Within ECE these are numbered as 18-7xx courses.)

5. Advanced Engineering Course Work (24 units): Any graduate-level (18-7xx) advanced courses in ECE or any courses drawn from a list of designated non-ECE advanced engineering courses can be used to satisfy this requirement.

Up to 15 units of graduate project can be used in place of any of the course work from areas 3, 4 or 5 listed above. The graduate project must contain substantial design and/or research experience. Graduate projects must be proposed (one page abstract describing project), supported by a faculty adviser and approved by the ECE Graduate Education Committee.

A final, salient point here was the unexpected ease of extending our undergraduate B.S.E.C.E. program to become an integrated master's program. FIGURE 25 again shows the overall structure of the ECE undergraduate degree, now with the requirements of the Integrated M.S./B.S. added.

FIGURE 25. Integrating Master's Requirements into ECE Bachelor's Degree

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Curriculum Evolution: 1991 to 1995

In the fall of 1991, after approximately two years of work, a novel electrical and computer engineering curriculum was implemented at Carnegie Mellon. The curriculum features a small core of required classes, engineering courses beginning in the freshman year, area requirements in place of specific course requirements, mandates on breadth, depth, coverage and design, and a unified electrical and computer engineering bachelor's degree.

Four cohorts of students are in the pipeline of the new curriculum to date; the first class will graduate in 1995. Measurements suggest that even with large amounts of flexibility, students continue to elect difficult, broad courses of study. We believe that flexibility in the election of courses, avoidance of rigid requirements and notions of exposure to all "critical" topics, and tolerance of students with widely varying preparation and aspirations are the essential features of the curriculum. In 1994 the curriculum was extended to incorporate the Integrated M.S./B.S. ECE Degrees. Four years into the new curriculum, we still have high rankings in the national media, e.g., [15].

Rather than being a divisive exercise, we believe that our overall curriculum design process, including an analysis of the problems to address and the generation of some basic guiding principles to solve these problems, was a useful exercise in involving all of our faculty in the evolution of the curriculum. Somewhat to our surprise, the curriculum and its design philosophy continue to be widely discussed outside of Carnegie Mellon, e.g., [2] [3] [4] [5]. Several hundred copies of the original curriculum design document [1] were requested from colleagues around the world. In this document, we have revisited some of this same material, but tried to offer some additional insights (and hindsights) on that design process, some analysis of its impact on our students and some guidance to others undertaking this important task.

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Acknowledgments

The new ECE curriculum was originally designed by the Wipe the Slate Clean Committee, whose membership included ECE faculty L. Richard Carley, Stephen W. Director, James F. Hoburg, Pradeep K. Khosla, B. V. K. Vijaya Kumar, Ronald A. Rohrer, Rob A. Rutenbar (Chair), T. Ehud Schlesinger, Daniel D. Stancil, Jay K. Strosnider and Donald E. Thomas. Professor Ronald P. Bianchini is the principal architect of the course planning software mentioned in Chapter 3. Much of the early implementation of the curriculum was overseen by Professors James F. Hoburg and Daniel D. Stancil. The current evolution of the curriculum is being overseen by Professor B. V. K. Vijaya Kumar. Professor Charles P. Neuman is coordinating the department's revised advising strategy. Contributors to this document were ECE Professors L. Richard Carley, Stephen W. Director, James F. Hoburg, Pradeep K. Khosla, B. V. K. Vijaya Kumar, Charles P. Neuman, Ronald A. Rohrer, Rob A. Rutenbar, Daniel D. Stancil, Sarosh Talukdar and Robert M. White. Professors

B. V. K. Vijaya Kumar, Rob A. Rutenbar and Daniel D. Stancil edited this revision. Sandra Salmonsen assisted with the production of this document.

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References

[1] Rob A. Rutenbar, L. Richard Carley, Stephen W. Director, James F. Hoburg, Pradeep K. Khosla, B.V. K. Vijaya Kumar, Ronald A. Rohrer, T. Ehud Schlesinger, Daniel D. Stancil, Jay K. Strosnider, Donald E. Thomas, "A New ECE Curriculum for Carnegie Mellon," Technical Report, Dept. of Electrical and Computer Engineering, Carnegie Mellon University, 1991.

[2] Donald Christiansen, "New Curricula," IEEE Spectrum, vol. 25, no. 9, July 1992.

[3] George F. Watson, "Refreshing Curricula," IEEE Spectrum, vol. 29, no. 3, pp. 33-35, March 1992.

[4] "Coming Off the Drawing Board: Better Engineers?" Business Week, McGraw-Hill, August 2, 1993.

[5] R. M. White, D. E. Thomas, T. E. Schlesinger, J. K. Strosnider, L. R. Carley, R. P. Bianchini, R. A. Rohrer, D. Stancil, "CMU's New Electrical and Computer Engineering Curriculum," National Technical University (NTU) Broadcast, April 19, 1994; more than 2,600 attendees.

[6] Jack Gourman, "Leading Institutions - Rating of Undergraduate Programs," The Gourman Report, National Educational Standards, p.35, 1987.

[7] Massachusetts Institute of Technology, EECS Committee on the First Professional Degree, "Revised Proposals for New Degree Structures for EECS Students," memorandum, MIT, March 4, 1991.

[8] Billy Goodman, "Toward a pump, not a filter," Mosaic, National Science Foundation, vol. 22, no. 2, summer 1991.

[9] Jim Hoburg, "Some thoughts on engineering education by a converted `radical,'" FOCUS Carnegie Mellon University, vol. 20, no. 1, September, 1990.

[10] M. Granger Morgan, "Accreditation and diversity in engineering education," Science, vol. 249, no. 4972, August 31, 1990.

[11] Ronald A. Rohrer, "Taking circuits seriously," IEEE Circuits and Devices, vol. 6, no. 4, pp. 27-31, July 1990.

[12] Randy H. Katz, Contemporary Logic Design, Benjamin/Cummins Publishing Company, Redwood City, California, 1994.

[13] John W. Prados, Winifred M. Phillips, George D. Peterson, James E. A. John, Mac Van Valkenberg and William J. Wilhelm, "Final Report of the ABET/EDC Task Force," March 11, 1991; presented at the Annual Meeting of the Engineering Deans Council, Alabama, March 27, 1991, and at the ABET Board Meeting, Chicago, Illinois, April 13, 1991.

[14] Van Valkenburg, M., "Changing Curricular Structure," Engineering Education, vol. 79, no. 4, May/June 1989.

[15] "Engineering Specialties: Programs ranked best by engineering-school deans in the U.S. News reputational survey," U.S. News & World Report, p. 103, vol. 118, no. 11, March 20, 1995.

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Jump to: [ Courses listed by Area | Courses listed by Number | Available Graduate Courses ]

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We provide here complete new lists of the courses that satisfy the various requirements of the ECE curriculum with the exception of courses in the humanities and arts used to satisfy the general education requirements. However, it is important to emphasize that the curriculum is still evolving, especially for the upper-division classes.

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ECE Course Lists, by Area

In the following lists, courses satisfy one or more of the ECE requirements as indicated by the symbols: B = Breadth, Ds = Design, Co = Coverage, Dp = Depth.

Courses within ECE are numbered 18-xxx. Courses from other departments start with numbers other than 18. Some relevant other departments are:

• Computer Science, 15-xxx

• Mathematics, 21-xxx

• Physics, 33-xxx

• Statistics, 36-xxx

• College of Engineering, interdisciplinary, 39-xxx

Mathematics, Science and Computer Programming Requirements			 
									Units
99-101	Computing Skills Workshop					3
15-127	Introduction to Programming and Computer Science 
		(corequisite to Intro. to ECE)				10
21-121	Calculus I							10
21-122	Calculus II							10
21-241	Linear Algebra (possible corequisite to Fund. of EE)		9
21-127	Introduction to Modern Mathematics 
		(corequisite to Fund. of CE)				9
33-106	Physics for Engineering Students I				12
33-107	Physics for Engineering Students II				12
xx-xxx	Math/Science Elective (see below)				9

The math/science elective may be satisfied by any course in biology, chemistry
or physics, or any 200 level course or higher in mathematics or statistics
except for certain courses intended exclusively for nontechnical majors. Some
suggested math courses of interest to electrical and computer engineers are:

21-259	Calculus in Three Dimensions					9
21-260	Differential Equations						9
36-217	Probability Theory and Random Processes				9
36-220	Engineering Statistics and Quality Control			9
36-225	Introduction to Probability and Statistics I			9
36-226	Introduction to Probability and Statistics II

Any of the last four courses listed above (36-xxx) can be used to
satisfy the probability/statistics requirement.	
 

Freshman Engineering and ECE Core 
18-100	Introduction to Electrical and Computer Engineering		12
18-220	Fundamentals of Electrical Engineering				12
18-240	Fundamentals of Computer Engineering				12
 

Applied Physics 
18-303	Engineering Electromagnetics I (B, Co)				12
18-304	Engineering Electromagnetics II (Dp, Co)			12
18-311	Semiconductor Devices I (B, Co)					12
18-312	Semiconductor Devices II (Dp, Co)				12
18-316	Introduction to Data Storage Systems 
		Technology (B, Co)					12
18-400	High Frequency System Design (Ds, Co)				12
18-405	Computer-Aided Design of Electromagnetic Systems
		 (Ds, Co)						12
18-501	Electromechanics (Dp, Co)					12
18-517	Data Storage Systems Measurement Design
		Laboratory (Ds, Co)					12
18-701	Electromagnetic Field Theory (Co)				12
18-702	Finite Element Methods in Electrical Engineering (Co)		12
18-708	High Frequency Engineering (Co)					12
18-711	Solid State Electronics (Co)					12
18-712	Microwave and Optical Magnetics (Co)				12
18-713	Fundamentals of Carrier Transport (Co)				12
18-714	Introduction to Superconducting Devices (Co)			12
18-715	Physics of Applied Magnetism (Dp, Co)				12
18-716	Advanced Applied Magnetism (Co)					12
 

Signals and Systems 
18-370	Fundamentals of Control (Dp, Co)				12
18-373	Computer-Controlled Testing and Measurement 
		System Design (Ds, Co)					12
18/15-384	Artificial Intelligence: Robotic Manipulation (Co)	9
18-396	Signals and Systems (B, Co)					12
18-474	Computer Control Systems Design Laboratory (Ds, Co)		12
18-550	Fundamentals of Communications Systems (Dp, Co)			12
18-551	Digital Communications and Signal Processing 
		System Design (Dp, Ds, Co)				12
18-575	Control Systems Design (Ds, Co)					12
18-751	Applied Stochastic Processes (Co)				12
18-752	Estimation, Detection and Identification (Co)			12
18-754	Error Control Coding: Theory and Applications (Co)		12
18-756	Circuit Switching & Packet Switching (Co)			12
18-757	Principles of Broadband Communication (Co)			12
18-771	Linear Systems (Co)						12
18-772	Multivariable Control (Co)					12
18-773	System Identification and Adaptive Control (Co)			12
18-774	Digital Control (Co)						12
18-775	Optimal Control (Co)						12
18-776	Nonlinear Control Systems (Co)					12
18-777	Model Predictive Control (Co)					12
18-778	Discrete Event Systems (Co)					12
18-791	Digital Signal Processing I (Dp, Co)				12
18-792	Digital Signal Processing II (Dp, Co)				12
18-793	Optical Image and Radar Processing (Co)				12
18-794	Pattern Recognition Theory (Co)					12
18-796	Numerical Optimization Methods (Co)				12

 

Circuits 
18-321	Analysis and Design of Analog Circuits (B, Co)			12
18-322	Analysis and Design of Digital Circuits (B, Co)			12
18-523	Analog Integrated Circuit Design (Dp, Ds, Co)			12
18-525	Integrated Circuit Design Project (Dp, Ds, Co)			12
18-723	Advanced Analog Integrated Circuit Design (Co)			12
18-725	Digital Integrated Circuit Design (Ds, Co)			12
18-728	Applications of Analog Integrated Circuits (Ds, Co)		12
18-762	Circuit Simulation: Theory and Practice (Co)			12
 

Computer Hardware 
18-345	Introduction to Telecommunications Networking (B, Co)
12
18-347	Introduction to Computer Architecture (B, Co)			12
18-349	Concurrency and Real-Time Systems (B, Co)			12
18-360	Introduction to Computer-Aided Digital Design (B, Co)		12
18-545	Advanced Digital Design Project (Dp, Ds, Co)			12
18-547	Superscalar Processor Design (Dp, Co)				12
18-549	Time Critical Computing Systems (Dp, Co)			12
18-742	Advanced Computer Architecture (Co)				12
18-746	Parallel Processing (Dp, Co)					12
18-748	Dependable System Design (Dp, Co)				12
18-760	VLSI CAD: Logic to Layout (Dp, Co)				12
18-761	VLSI CAD: Layout to Manufacturing (Co)				12
18-763	Physical CAD for VLSI (Co)					12
 

Computer Software 
15-211	Fundamental Structures of Computer Science I (B, Co)		12
15-212	Fundamental Structures of Computer Science II (Dp, Co)		12
15-312	Programming Languages Design and Processing (Co)		9
15-381	Artificial Intelligence: Representation and Problem 
		Solving (Co)						9
15-385	Artificial Intelligence: Computer Vision (Co)			9
15-411	Compiler Design (Co)						12
15-412	Operating Systems (Co)						12
15-413	Software Engineering (Ds, Co)					12
15-414	Structured Programming and Problem Solving (Co)			9
15-451	Algorithms (Co)							9
15-453	Formal Languages and Automata (Co)				9
15-462	Computer Graphics (Co)						9
15-612	Distributed Systems (Co) 					12
 

Professional, Policy and Interdisciplinary Topics 
18-480	Senior Seminar							0
18-482	Telecommunications: Technology, Policy and 
		Management (Co)						12
18-483	Civilian and Military Applications of Space (Co)		12
18-489	Basic Trends in the Evolution of Modern 
		Microelectronics (Co)					12
39-405	Engineering Design: The Creation of Products 
		and Process (Ds, Co)					12
 

Undergraduate Projects 
18-231	Sophomore Project-Fall (Co)					variable	
18-232	Sophomore Project-Spring (Co)					variable
18-331	Junior Project-Fall (Co)					variable
18-332	Junior Project-Spring (Co)					variable
18-431	Senior Project-Fall (Co)					variable
18-432	Senior Project-Spring (Co)					variable
18-439	Special Topics in ECE (Co)					variable
39-500	CIT Honors Research Project (Ds, Co)				variable

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ECE Course Descriptions, by Course Number

18-100
Introduction to Electrical
and Computer Engineering
Fall and Spring: 12 units

The goals of the introductory course are: to introduce basic concepts in electrical and computer engineering in an integrated manner; to motivate basic concepts in the context of real applications; to illustrate a logical way of thinking about problems and their solutions; and to convey the excitement of the field. These goals are attained through analysis, construction and testing of an electromechanical system (e.g. a robot) that incorporates concepts from a broad range of areas within Electrical and Computer Engineering. Some of the specific topics that will be covered include system decomposition, real and ideal sources, Kirchh
Off's and Ohm's Laws, Linear and Nonlinear circuit elements, Ideal Op-Amp characteristics, combinational logic circuits, Karnaugh Maps and Flip-Flops. The course will culminate in a final project that will provide an opportunity for creative design. 3 hr. lec., 1 hr. rec., 3 hr. lab. Corequisites: 15-127 and 21-121.

18-113
Basic Electrical Engineering
Spring: 9 units

The objective of this course is to provide solid understanding of the basic sciences underlying electrical circuits; dielectric and magnetic devices, rotating machinery, and the development of capacity to apply this science with creative skill in a variety of applications selected from the fields of electrical engineering. 2 hrs. lec., 3 hrs. lab. Prerequisites: junior standing in Mechanical Engineering, 33-107, 24-245.

18-200
Mathematical Foundations of Electrical Engineering
Fall: 12 units

This course covers topics from engineering mathematics that serve as foundations for descriptions of electrical engineering devices and systems. It has four major parts: (1) Complex analysis, including complex numbers and complex analytic functions; (2) Ordinary differential equations of first- and second-order; (3) Linear algebra, including matrices, vectors and determinants; (4) Vector calculus, including the vector differential operators gradient, divergence and curl, and vector integral calculus, including multiple integrations and integral theorems. 3 hrs., 1.5 hrs. rec. Prerequisite: 21-122.

18-220
Fundamentals of Electrical Engineering:
Introductory Circuit Analysis
Fall and Spring: 12 units

The course thoroughly covers the fundamentals of linear circuit analysis necessary to perform design of digital and analog electronic circuits: Kirchh
Off's Voltage and Current Laws; Superposition and Convolution; Series, Parallel and Ladder Circuit Analysis; Thevenin's and Norton's Theorems; Natural Frequencies; Circuit Partitioning; Nodal Analysis; Fourier series representation of periodic signals and frequency domain analysis. This course will cover these principles thoroughly in the context of the transient and sinusoidal steady state analysis of RLC circuits. Theoretical investigations presented in the class will be reinforced with laboratory experiments. A recurring motivational theme throughout the course is the study of high performance digital system switching speed limitations imposed by electronic circuit interconnects. 3 hrs. lec., 1 hr. rec., 3 hrs. lab. (every other week). Prerequisite: 18-100. Corequisite: 21-241, or 18-200.

18-231
Fall: Variable units

18-232
Spring: Variable units
Sophomore Projects

Experience in independent planning and conduct of engineering research, development or design projects, usually in concert with the research interests and programs of individual faculty members. Prerequisite: sophomore standing in Electrical and Computer Engineering.

18-240
Fundamentals of
Computer Engineering
Fall and Spring: 12 units

This course introduces basic issues in design and verification of modern digital systems. Topics include: Boolean algebra, digital number systems and computer arithmetic, combinational logic design and simplification, sequential logic design and optimization, register-transfer abstractions of digital systems, basic machine organization and instruction set issues, assembly language programming and debugging, and microprogramming. Emphasis is on the fundamentals, the levels of abstraction that allow designers to cope with hugely complex systems and connections to practical hardware implementation problems. Students will use computer-aided digital design software and actual hardware implementation laboratories to learn about real digital systems. 3 hrs. lec., 1 hr. rec., 3 hrs. lab. Prerequisite: 18-100, Corequisite: 21-127.

18-303
Engineering Electromagnetics I
Spring: 12 units

The objective of this and the subsequent course is to develop an understanding of fundamental electromagnetic principles and of electromagnetic field analysis methods. Maxwell's Equations in integral and differential forms, boundary conditions; Electroquasistatics, potential and voltage, Poisson's equation; Method of images; Capacitance; Laplace's equation, solutions in Cartesian, polar and spherical coordinates, numerical methods; Conduction; Polarization; Magnetoquasistatics, vector potential, Biot-Savart Law; Induced voltages as described by Faraday's Law, inductance; Magnetization, magnetic circuits; Numerical simulation laboratory and projects. 3 hrs. lec., 2 hr. rec., lab additional. Prerequisites: 18-220 and 21-259 or 18-200.

18-304
Engineering Electromagnetics II
Fall: 12 units

Maxwell's equations, differential and integral forms; Energy conservation, Poynting Theorem; Plane waves; TEM waves on 2-conductor transmission lines, sinusoidal steady state, Smith Chart, reflection and transmission of transients at discontinuities; Modal description of waveguides and cavities; Radiation, antennas; Numerical simulation laboratory and projects. 3 hrs. lec., 2 hr. rec., lab additional. Prerequisite: 18-303.

18-311
Semiconductor Devices I
Spring: 12 units

In this course students will build a fiber optic communication system, capable of transmitting and receiving amplitude-modulated audio information over a glass optical link. The fundamental concepts central to understanding, applying and modeling electronic devices are introduced and studied in the laboratory using this system. The goal is to develop an understanding of the operation of semiconductor devices, both electronic and optical, in terms of relevant physical concepts and to apply these devices in practical circuits.

Devices studied in this course include bipolar junction transistors, PN diodes, Zener diodes, photodetectors, light emitting diodes, glass optical fibers and Schottky diodes. The fundamental physical principles governing their operation, how to use them in circuits by applying the appropriate DC and AC voltages, and how to predict the performance of the circuit using simple models and approximations, will be covered.

The description of the fundamental principles will make use of energy band theory, and will include the following topics: electron and hole generation in solids; carrier transport (drift and diffusion); carrier mobility; doping and conductivity; band diagrams; Fermi level and energy distribution functions; carrier recombination; generation, transmission and absorption of light in solids as a function of wavelength; minority carrier diffusion equation; PN junction electrostatics and carrier transport. 3 hrs. lect., l hr. rec., 3 hrs. lab. Prerequisite: 18-220.

18-312
Semiconductor Devices II
Fall: 12 units

This course, a continuation of Semiconductor Devices I, will focus on the physics and operation of field effect devices, including MOS capacitors, MOSFET's, JFET's and MESFET's, as well as more advanced devices, such as charge coupled devices (CCD's), metal-semiconductor junctions and heterostructure transistors. The course will begin with a thorough description of the MOS capacitor: electron affinity and metal work functions; accumulation, depletion, weak and strong inversion regimes; flatband and threshold voltage; ionic, fixed, oxide trapped, and interface trapped charges and their effects; high and low frequency capacitance-voltage measurements. We will then develop and solve the charge transport equations for the MOSFET to obtain terminal I-V curves. Nonidealities encountered in modern field effect devices, such as the narrow width effect, drain induced barrier lowering, hot carrier generation, etc., will be investigated in detail. The course will conclude with similar treatments of other technologically important semiconductor electronic devices. 3 hrs. lect., 1 hr. rec., Prerequisite: 18-311.

18-316
Introduction to Data Storage
Systems Technology
Spring: 12 units

This course teaches the fundamentals of magnetic and optical recording technology as used in data storage systems, audio and video recording. It begins with a description of the fundamental properties of magnetic materials. The origins of magnetism, demagnetizing fields, anisotropy, magnetostriction, domains and coercivity are explained. With this as a basis, the operation of magnetic and magneto-optical recording devices such as rigid and floppy disk drives, tape recorders, compact disk players and optical disk drives is explained. 4 hrs. rec. Prerequisites: 33-107 and 18-200 or 21-259.

18-321
Analysis and Design of Analog Circuits
Spring: 12 units

The purpose of this course is to introduce the student to the fundamentals of the analysis and design of basic analog circuits. Topics to be covered include: DC bias calculations and circuits, MOSFET and BJT large- and small-signal device models, small-signal gain and frequency response characteristics of single-stage amplifiers, operational amplifier design, basic theory of feedback amplifiers, frequency stability and compensation techniques, large-signal characteristics and nonidealities. In the hardware laboratory, the student will gain experience designing and implementing analog circuits, and comparing actual to simulated performance using the SPICE circuit simulation program. The analysis and design of analog circuits incorporating both Bipolar and CMOS technologies will be considered. 3 hrs. lec., 1 hr. rec., 3 hrs. lab. Prerequisite: 18-220.

18-322
Analysis and Design of Digital Circuits
Fall: 12 units

The purpose of this course is to introduce the student to the fundamentals of the analysis and design of basic digital circuits. Topics to be covered include: MOSFET and BJT large-signal device models, propagation delay calculations, MOS and BJT combinational and sequential gates, physical layout techniques, semiconductor memories, programmable logic arrays, pulse-generation techniques, and TTL and ECL technologies. The necessity of circuit simulation (SPICE), timing simulation (COSMOS) and physical layout (MAGIC) computer tools is stressed. The lab includes the design, analysis, layout and verification of a digital system such as a simple microprocessor. 3 hrs. lec., 1 hr. rec., 3 hrs. lab. Prerequisites: 18-220 and 18-240.

18-323
Analog Filter Design
Offered intermittently: 12 units

Analog filtering is an indispensable aspect of signal processing. Passive filters for high frequency applications and active filters employing inexpensive operational amplifiers are emphasized in both the theory and laboratory/project portions of the course. Specific topics to be covered are the following: Overview of Analog Filter Design; Review of Resistor Operational Amplifier Circuits; Butterworth and Chebyshev Low Pass Filter Approximations; Frequency Scaling; Active Circuit Realizations of Low Pass Filters; High Pass Filter Specification; Low Pass to High Pass Transformation; Active Circuit Realizations of High Pass Filters; Inverse Chebyshev Approximation; Cauer Filters; Low Pass to Band Pass and Band Stop Transformations; Active Circuit Realization of Band Pass and Band Stop Filters; Passive Filter Design; Sensitivity; Active Circuit Equivalents for Passive Filter Elements; State Variable Forms of Filter Design; Delay Filters; Switched Capacitor Filters. This course will be conducted as a series of design exercises, each starting with a solution in theory and ending with a practical realization in the laboratory. 3 hrs. rec., 3 hrs. lab. Prerequisites: 18-220, 18-396, 18-321.

18-331
Fall: Variable units

18-332
Spring: Variable units
Junior Projects

Experience in independent planning and conduct of engineering research, development or design projects, usually in concert with the research interests and programs of individual faculty members. Prerequisite: junior standing in Electrical and Computer Engineering.

18-342
C/Unix Survival Skills
Spring: 3 units

This course provides a practical introduction to C programming in the Unix workstation environment for students who will not be exposed to it in advanced computer science courses. Lectures will focus on C itself, Unix and Unix Utilities (csh, make, awk, grep, etc.). Example applications will be drawn from the breadth areas of the ECE curriculum. A secondary focus of the course will be software engineering (portability, reuse, etc.) for engineering/scientific programs. Particular attention will be paid to software engineering issues and how they complement/conflict with rapid software prototyping. Weekly programming labs will form the keystone of the work. Most labs will be short (1-2 hours) and will introduce a broad spectrum of tools. A few larger programs will be built over multiple weeks. Upon completion of the course students should be familiar with techniques and tools for engineering practical programs in C under Unix. Prerequisite: 15-127.

18-345
Introduction to Telecommunication Networks
Fall or Spring:12 units

This course introduces the fundamental concepts of telecommunication networks. Underlying engineering principles of telephone networks, computer networks and integrated digital networks are discussed. Topics in the course include: telephone and data networks overview; OSI layers; data link protocol; flow control, congestion control, routing; local area networks (Ethernet, Token Ring, FDDI); transport layer; introduction to high-speed networks; performance evaluation techniques. 4 hrs. lec. Prerequisite: 36-217.

18-347/15-347
Introduction to Computer Architecture
Fall: 12 units

The goal of this course is to develop an understanding of the structure and operation of contemporary computer systems from the instruction set architecture level through the register transfer implementation level. We explore: theory of computation, levels of abstraction, instruction set design, assembly language programming, processor data paths, data path control, pipeline design, design of memory hierarchies, memory management, input/output. Several of the principles presented in lecture are reinforced through laboratory projects including assembly language programming, evaluation of instruction set architectures by benchmarks, behavioral simulation of an instruction set architecture, and design/simulation of a register transfer implementation of an instruction set architecture. A contemporary behavioral/functional/logical simulator will be used for the laboratory projects. 3 hrs. lec., 3 hrs. lab. Prerequisite: 18-240. Corequisite: 15-211.

18-349
Concurrency and Real-Time Systems
Spring: 12 units

This course teaches the fundamentals of concurrency and time constrained computing both at the hardware and software levels. These notions are developed through the study and implementation of real-time systems. The fundamental problems and issues of timing correctness, synchronization, deadlock and contention are described. Solutions to these problems, which have evolved in the software realm, are presented along with the hardware required to implement these solutions. Topics include real-time interrupt driven systems; concurrency in digital systems; synchronous, asynchronous and self-timed systems; and hardware and software synchronization mechanisms. 3 hrs. rec., 3 hrs. lab. Prerequisites: 18-240 and 15-211.

18-360
Introduction to Computer-Aided Digital Design
Spring: 12 units

The design of digital integrated circuits (ICs) has grown in complexity to where typical designs have several hundred thousand transistors and leading-edge ICs have several million. Computer-aided design tools are required for designers to produce such complex systems in an economically productive manner. This course introduces the techniques of modeling digital systems at various levels of abstraction and computer-aided design algorithms that are applied to these models to support design and analysis tasks. The course covers modeling through the use of a modern hardware description language. The language is used to model an IC in the early stages of design using behavioral modeling techniques and in later stages using structural modeling techniques. The course will cover: synthesis algorithms, which produce structural designs from the behavioral; physical design, which is used to map the synthesized logic design onto physical IC area; simulation, which is used at several levels of abstraction to analyze a design; and testing, which is used to determine if a manufactured design is correct. Prerequisites: 18-240 and 15-211.

18-370
Fundamentals of Control
Fall: 12 units

An introduction to the fundamental principles and methodologies of classical feedback control and its application. Emphasis is on problem formulation and the analysis and synthesis of servomechanisms using frequency and time domain techniques. Topics include analytical, graphical and computer-aided (MATLAB) techniques for analyzing and designing automatic control systems; analysis of performance, stability criteria, realizability and speed of response; compensation methods in the frequency domain, root-locus and frequency response design and pole-zero synthesis techniques; robust controller design; systems with delay and computer control systems; transfer function and state space modeling of linear dynamic systems; nonlinearities in control systems; and control engineering software (MATLAB). 3 hrs. lec., 1.5 hrs. rec., 3 hrs. MATLAB lab. Prerequisite: 18-396.

18-371
Design Optimization Techniques
Offered intermittently: 12 units

This course introduces the student to the concepts and techniques of design optimization by computers using various proven methods, both algorithmic and heuristic. The need to acquire each optimization tool is demonstrated through a design exercise of an actual device or system. The tools covered include modeling of engineering problems, matrix solution of linear equations, unconstrained quadratic optimization with and without constraints, nonlinear problems, mathematical programming techniques, Newton-Raphson methods, and nonlinear and geometric programming algorithms. Design exercises will include iron-core inductors, transformers, thermal power plants, servo systems and economic dispatch of power plants. 4.5 hrs. rec. Prerequisite: 21-341.

18-373
Computer-Controlled Testing and
Measurement System Design
Offered intermittently: 12 units

The aim of this course is to familiarize the student with the fundamentals of measurements, data acquisition, control and the role of a microcomputer in carrying out these activities. This course will consist of lectures and extensive laboratory experiments and a final project. Of special interest will be the following areas: sensors, measurement techniques, signal transmission methods, noise sources and noise suppression, signal conditioning techniques, fundamentals of computer control, A/D and D/A conversion techniques, sampling and data compression, and error analysis in experiments. In general, the course will concentrate on the use of a microcomputer in obtaining measurement data for the purposes of testing and control. The course has a practical slant and is intended to give the student a cohesive understanding of the relationships amongst different areas of electrical and computer engineering and their application in practice. 3 hrs. rec., 3 hrs. lab. Prerequisite: 18-220 or 18-113 or permission of instructor.

18-384/15-384
Artificial Intelligence: Robotic Manipulation
Fall: 9 units

Foundations and principles of robotic manipulation. Topics include computational models of objects and motion, the mechanics of robotic manipulators, the structure of manipulator control systems, planning and programming of robot actions. Prerequisites: 21-122 or permission of the instructor.

18-396
Signals and Systems
Fall and Spring: 12 units

This course is a breadth course that is also a prerequisite for most courses in communications, signal processing and control systems. The objective of this course is to provide students with an integrated understanding of the relationships between mathematical tools and properties of real signals and systems. This is accomplished by motivating lectures and recitation problems using demonstrations and laboratory assignments that cover such topics as radio transmission and reception, audio synthesizers, CDs, image processing and prosthetic devices. In the course of the semester, students are introduced to industry-standard computing and simulation tools that will be used in subsequent courses. Continuous and discrete-time signals and systems are treated in a unified manner through the concept of sampling. The course covers the basic concepts and tools needed to perform time and transform domain analyses of signals and linear time-invariant systems, including: unit impulse response and convolution; Fourier transforms and filtering; Laplace transforms, feedback and stability; and a brief introduction to z-transforms in the context of digital filtering. Prerequisite: 18-220.

18-400
High Frequency System Design
Offered intermittently: 12 units

This course is intended to familiarize students with the characteristics of various radio frequency / microwave components and the design of representative systems. Waveguide components are available at X-band (8.20-12.40 GHz) and K-band (18.0-26.5 GHz). These include oscillators, attenuators, phase shifters, wavemeters, directional couplers, circulators, isolators, horns, detectors, etc. For example, an intruder alarm system (Doppler radar) can be designed, constructed and tested at both X- and K-bands. Various coaxial components enable operation down to several 100 MHz at least. An RF / microwave sweeper ranging up to 12 GHz is available. Planar transmission line circuitry (microstrip) can be fabricated. CAD programs are available for laying out and analyzing microstrip circuitry. At frequencies of 4 GHz or so, various resonators, filters and directional couplers can be designed, constructed and tested. Microwave amplifiers can be designed and constructed at frequencies up to 4 GHz using drop-in components on wafers and PC boards. 2 hrs. rec., 3 hrs. lab. Prerequisite: 18-304 or equivalent or permission of the instructor.

18-405
Computer-Aided Design of
Electromagnetic Systems
Offered intermittently: 12 units

This course employs field theory based CAD tools to simulate the behavior of electromagnetic systems. Students learn to use finite element computer programs to determine the electric and magnetic fields in printed circuit boards and in other high-speed digital and microwave devices. Course topics include: Electromagnetics CAD; finite element methods; finite element mesh generation; electrostatics and magnetostatics of PCB and IC interconnects; capacitance and inductance matrices; cross-talk, insertion loss and return loss; dispersion; eddy currents and skin effect; use of CAD packages for computing signal characteristics; microwave CAD; S matrices; use of the Hewlett-Packard High-Frequency Structure Simulator; hybrid and MMIC microwave design; propagation of optical signals; modal characteristics of optical ICs. 2 hrs. rec., 3 hrs. lab. Prerequisite: 18-304.

18-431
Fall: Variable units

18-432
Spring: Variable units
Senior Projects

Experience in independent planning and conduct of engineering research, development, or design projects, usually in concert with the research interests and programs of individual faculty members. Prerequisite: senior standing in Electrical and Computer Engineering.

18-439
Special Topics in Electrical
and Computer Engineering
Fall or Spring: Variable units

Offered from time to time on topics of current interest. Specific details will be announced prior to registration.

18-474
Computer Control Systems
Design Laboratory
Spring: 12 units

A senior design elective in Electrical and Computer Engineering focusing on issues in the design of feedback control systems using digital computers. Lectures and laboratory experiments cover basic switching control methods, collection and analysis of data for modeling system dynamics, PID control, design methodologies for setpoint control and disturbance rejection, state variable feedback, dynamic state observers and methods for adaptive control. Major emphasis is placed on a project involving the analysis, design and implementation of a computer control system developed by each lab group. 2 hrs. rec., 3 hrs. lab. Prerequisite: senior standing in Electrical and Computer Engineering.

18-480
Senior Seminar
Fall: 0 units

The senior seminar provides students with information that should be of use in making the transition from undergraduate studies to graduate life. The seminar features discussions led by faculty members and invited guests, with student participation in the discussions. 1 hr. lec./rec. Prerequisite: senior standing in Electrical and Computer Engineering.

18-481
Analysis, Synthesis and Evaluation
Offered intermittently: 12 units

Analysis, synthesis and evaluation in the context of realistic engineering situations. The student learns through practice to formulate and solve problems that require the application of skills, which include modeling, analyses that range from mathematical to heuristic, experimental methods, inventing, making judgments of value and need, making decisions and recommendations, and producing an engineering report containing an analysis of the problem and an evaluation of the solution. 3 hrs. lec., 3 hrs. lab. Prerequisite: senior standing in Electrical and Computer Engineering.

18-482/19-402
Telecommunications: Technology,
Policy and Management
Fall: 12 units

This course provides a comprehensive introduction to basic principles of telecommunications technology and the telephone network, and the legal, economic and regulatory environment of the telecommunications industry. Role of new technologies such as fiber, integrated digital networks, computer communications and information services. Common carrier law and the economics of natural monopoly as the basis for regulation of the telecommunications industry. Issues of competition, monopoly and technical standards. Spectrum allocation and management. International communications and transborder data flow. Special emphasis on how the new technologies have altered and are altered by regulation. Prerequisites: 73-100, junior or senior standing.

18-483/19-430
Civilian and Military Applications of Space
Spring: 12 units

Space is an arena of growing activity and importance. The use in space puts specific requirements on the technology of remote sensing and communication. Furthermore, the access to space requires rocket engines. Operation in space supposes the ability of controlling automatically the attitude of spacecraft. Navigation and guidance requires a very large and powerful infrastructure. Most space endeavors are very ambitious and long-term projects. The cost of space projects are often easier to estimate than the benefit. The goal of this course is to penetrate somewhat in the world of space policy dilemmas by studying the interface between the technology and what space programs could or try to accomplish. 3 hrs. lec. Prerequisites: junior standing in engineering or science.

18-489
Basic Trends in the Evolution
of Modern Microelectronics
Offered intermittently: 12 units

Recent rapid changes and future trends in the evolution of the microelectronics are determined by three factors: market needs, manufacturing capabilities and efficiency of design. Each of them has its own dynamics and limitations. Understanding all of them is necessary to explain the current structure of the microelectronics industry and to predict future developments in the areas of IC technology, design and CAD tools. The goal of this lecture is to introduce technical aspects related to the above mentioned three areas. Prerequisite: 18-322.

18-501
Electromechanics
Offered intermittently: 12 units

This course provides a broadly based introduction to interactions between mechanical media and electromagnetic fields. Attention is focused on the electromechanical dynamics of lumped-parameter systems, wherein electrical and mechanical subsystems may be modeled in terms of discrete elements. Interactions of quasistatic electric and magnetic fields with moving media are described and exemplified. Unifying examples are drawn from a wide range of technological applications, including energy conversion in synchronous, induction and commutator rotating machines, electromechanical relays, a capacitor microphone and speaker, and a feedback-controlled magnetic levitation system. 4.5 hrs. rec. Prerequisite: 18-303.

18-517
Data Storage Systems
Measurement and Design Laboratory
Fall: 12 units

This course is designed to provide students with an opportunity to gain hands-on experience in designing and carrying out a small research project on storage devices such as a disk drive, or an optical recording device. The students will be taught the principles of operation of a variety of magnetic measurement devices including magnetometers, hysteresis loop tracers and magnetic and magneto-optic recording device testers. Having learned the use of these instruments, students will select, design and carry out a research project related to storage technology in the research labs of the Data Storage Systems Center. 1.5 hr. rec., 10.5 hrs. lab scheduled at student's convenience. Prerequisites: 33-107 and 18-200 or 21-259.

18-523
Analog Integrated Circuit Design
Offered intermittently: 12 units

Advanced techniques for the design of analog integrated circuits. Emphasis will be placed on the design process. Design issues associated with both MOS and BJTs devices will be explored. Students will be expected to design and simulate several projects. Topics will be selected from the following: modeling of basic IC components (in MOS & BJT processes), wideband amplifier design, operational amplifier design, the design of switched-capacitor circuits, the design and analysis of phase locked loops, analog-to-digital conversion techniques (including the design of sample-and-hold amplifiers), and digital-to-analog conversion techniques. 4 hrs. lec., 3 hrs. lab. Prerequisites: 18-321 and 18-322 or equivalent with permission of instructor.

18-525
Integrated Circuit Design Project
Spring: 12 units

The purpose of this course is to study the design process of VLSI circuits. The first part of the course will be devoted to the standard cell design methodologies. Major emphasis will be put on layout design, circuit and parasitic element extraction and verification of circuit performance via simulation tools. In the second part of the course, students will design functional blocks of digital ICs and verify their performance using such simulators as COSMOS and SPICE. The collection of these functional blocks will constitute a multiproject chip, which will be submitted for fabrication to MOSIS. 4 hrs. rec., 3 hrs. lab. Prerequisite: 18-322.

18-545
Advanced Digital Design Project
Fall: 12 units

This is a project oriented course on advanced digital design. It provides the background needed for developing design skills of large digital systems at a professional level. The course covers fundamental design principles and extensive pragmatic implementation considerations. A substantial project will be designed and built by each project group of three students. A typical project is a single-board microprocessor that is implemented for a specified general purpose instruction set or special purpose embedded application, such as a network controller. Contemporary building blocks and design tools will be used, including programmable logic devices (PLDs), advanced field programmable gate arrays (FPGAs), schematic capture, Verilog simulation and PLD design tools. Industry standard practices of interim design reviews and final project presentations are followed. 3 hrs. lec., 3 hrs. lab. Prerequisites: 18-347 or 18-349, 15-212.

18-547
Superscalar Processor Design
Fall: 12 units

This course presents the fundamental principles, critical issues and latest techniques involved in the design of advanced modern processors. The course emphasizes the design of processors capable of extracting and exploiting instruction level parallelism (ILP). The topics covered include: arithmetic (floating-point) unit design; design space exploration via profiling and trace-driven simulation; microcoded CISC and pipelined RISC processors; instruction level parallel processing (ILPP) principles; superpipelined, superscalar, and VLIW (very long instruction word) processors; dynamic (run-time hardware) and static (compile-time software) techniques for achieving ILPP; aggressive instruction scheduling and machine-dependent code optimization. This course also incorporates case studies of a number of ILP processors e.g. IBM RS/6000, Motorola PowerPC and DEC Alpha, and the use of software tools in experimenting with performance evaluation, machine simulation and code transformation. 3 hrs. lec. Prerequisites: 18-347 and 15-212.

18-549
Time Critical Computing Systems
Spring: 12 units

The analysis and design of time critical computing systems is emphasized in this course. Engineering skills necessary to build embedded/multimedia systems are presented. This course includes a significant project where students will build/analyze a system. Typical systems include control systems, signal processing systems, and multimedia systems. A real-time scheduling theoretic approach will be used to quantitatively explore the design space. Performance models will be developed to explore the hardware/software boundary issues for the following subsystems: CPU's, buses, disks arrays, LANs, switching networks, and video/rendering subsystems. 4 hrs. rec. Prerequisites: 18-240, 15-212 and (18-349 or 15-412).

18-550
Fundamentals of Communication Systems
Fall or Spring: 12 units

A general introduction to analog and digital communications. Review of relevant aspects of linear systems and probability theories. Fourier analysis. Analog modulation systems: amplitude modulation (AM), frequency and phase modulation (FM and PM) and pulse amplitude modulation (PAM). Digital modulation systems: pulse code modulation (PCM), delta and differential PCM. For each modulation system, the course covers the basic structure of the transmitter and receiver, the trade-
Offs between bandwidth/data rates requirements and signal to noise ratio for desired levels of performance and waveform design. Applications are drawn from broadcasting (radio and TV), telephone networks (multiplexing), satellite communications, radar, digital communications (matched filter and optimal detection). Time permitting, the course will cover error detection and correction and elements of information theory. 3 hrs. lec., 1.5 hrs. rec. Prerequisites: 18-396, 36-217.

18-551
Digital Communications and
Signal Processing Systems Design
Spring: 12 units

This course provides students with a rich, integrated design experience in the area of digital communications and signal processing systems. Lectures will highlight component blocks needed to produce a viable systems technology. Labs early in the semester will be used to explore the use of standard instrumentation and simulation tools in the context of the development and performance of these component blocks. Homework will be used to develop the students' skills at using "back-of-the-envelope" calculations to ascertain the validity of their simulation and/or experimental results. Recitations will be used to help students in proposing, planning and designing their final project. Topics include: multimedia signals including speech and music, digital communication systems, FFT and practical digital Fourier analysis, voiceband modems, linear prediction, adaptive FIR filters, wireless HDTV, MPEG, Data Storage, CD, etc. 3 hrs. lec. Prerequisite: 18-396.

18-575
Control System Design
Spring: 12 units

A senior design elective in Electrical and Computer Engineering integrating the computer-aided analysis and design of feedback control systems from both the classical (transfer function) and modern (state-space) points of view. The perspective spans the dynamic modeling of physical systems and the analysis and computer-aided design (utilizing MATLAB) of linear and nonlinear, continuous-time and discrete-time, robust multivariable feedback systems. In illustrating the centrality of numerical linear algebra in control engineering, case studies are selected from pole placement, linear-quadratic design and Kalman filtering. A significant emphasis is placed upon student selected design projects. 4 hrs. lec., 3 hrs. MATLAB lab. Prerequisite: 18-370 or equivalent.

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Graduate Courses, by Number and Name

The following graduate courses are available to undergraduate students who have appropriate prerequisites. Descriptions of these graduate courses may be found in the graduate catalog of the Department of Electrical and Computer Engineering.

• 18-701Electromagnetic Field Theory
• 18-702Numerical Methods in Electromagnetics
• 18-708High Frequency Engineering
• 18-711Solid State Electronics
• 18-712Microwave and Optical Magnetics
• 18-713 Fundamentals of Carrier Transport
• 18-714Introduction to Superconducting Devices
• 18-715Physics of Applied Magnetism
• 18-716Advanced Applied Magnetism
• 18-723Advanced Analog Integrated Circuit Design
• 18-725Digital Integrated Circuit Design
• 18-728Applications of Analog Integrated Circuits
• 18-742Advanced Computer Architecture
• 18-746Parallel Processing
• 18-748Dependable System Design
• 18-751Applied Stochastic Processes
• 18-752Estimation, Detection and Identification
• 18-754Error Control Coding: Theory and Applications
• 18-756Packet Switching and Computer Networks
• 18-757Principles of Broadband Networks
• 18-760VLSI CAD: Logic to Layout
• 18-761VLSI CAD: Layout to Manufacturing
• 18-762Circuit Simulation: Theory and Practice
• 18-763Physical CAD for VLSI
• 18-771Linear Systems
• 18-772Multivariable Control Systems
• 18-773Adaptive Control
• 18-774 Digital Control
• 18-775Optimal and Stochastic Control
• 18-776 Nonlinear Control Systems
• 18-777 Model Predictive Control
• 18-778 Discrete Event Systems
• 18-791Digital Signal Processing I
• 18-792Digital Signal Processing II
• 18-793Optical Image and Radar Processing
• 18-794Pattern Recognition Theory
• 18-795Sensory Processes: Perception & Psychophysics
• 18-796Numerical Optimization Methods
• 18-809Special Topics in Electromagnetics
• 18-813Optical Electronics
• 18-815Integrated Circuit Fabrication Processes
• 18-816Magnetic and Optical Data Storage
• 18-819Special Topics in Solid State Devices
• 18-828Design and Testing of Analog Integrated Circuits
• 18-829Special Topics in Circuits
• 18-846Theory of Distributed Systems
• 18-845Computer Engineering Applied Graph Theory
• 18-849Special Topics in Computer Engineering
• 18-859Special Topics in Communications
• 18-869Special Topics in Computer-Aided Design
• 18-879Special Topics in Systems and Control
• 18-899Special Topics in Signal Processing

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