ECE ILLINOIS

The ECE 313 FAQ

Answers to Frequently Asked Questions

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ECE 313 attempts to teach you the elements of probability theory, a few topics in statistics, and the applications of all these to various problems in electrical and computer engineering. Most of the faculty teaching the course are interested in communication systems and networks, signal processing, and control systems, and hence the problems tend to be drawn from these areas. The choice of topics from statistics included in this course is also biased to some extent because of these interests.

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  • What are the prerequisites for ECE 313?

The official prerequisite for ECE 313 is ECE 210.

Unofficially, you are expected to understand the application of calculus to the solution of physical problems. For example, you should understand that an integral is the limit of a sum and that the integral represents the area under the curve, and you should know the difference between the (related) notions of integral and antiderivative. Some two-dimensional integrals will be used but, on the other hand, vector calculus is not needed. Tricky integrals requiring very clever substitutions for their solution will not be used; in fact, knowing the derivatives and antiderivatives of xn, ex, sin x, and cos x will generally be adequate.

Understanding the interpretation of the mathematics is far more important than facility in the rote mindless manipulation of symbols. If you make an inadvertent sign error and write

you are expected to worry that something is awry because you have just found a negative value for the integral of a positive function. If you find the average of a set of numbers to be smaller than the minimum of the set or larger than the maximum of the set, you are expected to consider the possibility that you made a mistake while entering the numbers into your calculator instead of just accepting the result because that is what the calculator says. In short, you are expected to be able to think rationally about the results of your mathematical calculations.

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  • Is there life after ECE 313?

Yes, indeed, there is life after ECE 313. Many students not only do very well in ECE 313, but they also use what they have learned in ECE 313 in later life: in everyday life, in further studies, and in their careers. In particular, ECE 313 is a prerequisite for the following senior-level electives and graduate courses in the areas of communications, networks, signal processing, control systems, circuits, and computer systems analysis:

  • ECE 361 Digital Communications
  • ECE 417 Multimedia signal processing
  • ECE 418 Image and Video Signal Processing
  • ECE 438 Communication Networks
  • ECE 439 Wireless Networks
  • ECE 459 Communications Systems
  • ECE 463 Digital Communication Laboratory
  • ECE 513 Digital Signal and Spectral Analysis
  • ECE 534 Random Processes
  • ECE 541 Computer Systems Analysis
  • ECE 547 Image Processing
  • ECE 551 Digital Signal Processing
  • ECE 553 Optimum Control Systems
  • ECE 555 Control of Stochastic Systems
  • ECE 559 Topics in Communication Systems
  • ECE 561 Signal Detection and Estimation
  • ECE 563 Information Theory
  • ECE 567 Communication Network Analysis
  • ECE 584 Reliability Engineering for Integrated Circuits

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    • I need to develop (or already have) a strong math background. Shouldn't I be taking a math course such as MATH 463/STAT 400 (or even MATH 461) instead of ECE 313?
    Congratulations on your aspirations and achievements!

    Actually, starting with Spring 2009, you are taking a math course: ECE 313 is cross-listed as MATH 362! In fact, the level of mathematics in ECE 313/MATH 362 is close enough to that of MATH 461 -- in some semesters, the two courses even use the same textbook -- that credit is not allowed for both ECE 313/MATH 362 and MATH 461. Visit the web pages for these courses, look at problem sets, solutions and exams, and decide for yourself. Also, please read the first few paragraphs of the answers to the next two questions.

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    • If ECE 313 is so mathematical, can I count it as a Math course in satisfying the requirements of the Math Minor?

    As of right now, ECE 313/MATH 362 is not on the list of courses that satisfy the requirements of the Math Minor, and cannot be used as a substitute for Math 461 or Math 463 in the Math Major for those pursuing dual degrees in Math and EE/CompE, but this may change in the future. Please contact the Director of Undergraduate Studies in the Mathematics Department about making such substitutions.

    Other courses recommended for the Math Minor are Math 347, 416, 417, 446, and 447.

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    • I have heard that ECE 313 is a very hard course. Do I have to take ECE 313?

    No, you do not have to take ECE 313.

    All BSEE and BSCompE majors must take one of the two courses:

    ECE 313 and STAT 410.

    Note that STAT 410 has STAT 400 as a prerequisite and the latter must be taken as a free elective.

    The following is intended to help you make an informed decision as to which course will best serve your interests.

    ECE 313 is primarily a course in probability theory together with a few statistical methods most relevant to communications, control, signal processing, and computer engineering applications. Some students find the course to be very challenging, but most also discover that their efforts are well rewarded, and that what they have learned in ECE 313 stands them in good stead in later courses as well as in later life. We chauvinistically assert that if you are an average or better-than-average student or if you are considering graduate studies, then you should favor ECE 313 over the Statistics courses, and that ECE 313 is very definitely the course that should be taken by superior students. Even if you do not consider yourself to be in these categories, you can still get a lot out of ECE 313, but you may need to put in considerable effort in order to complete the course successfully.

    In contrast to ECE 313, which is mostly about probability theory together with some topics in statistics, STAT 400 (4 hours) and STAT 410 (3 hours) are standard courses in statistical methods.

    Taking ECE 313 or the STAT 400 + STAT 410 combination satisfies the requirements of the EE and CompE curricula. However, the courses are not equivalent in terms of course syllabi, and which one you should take depends on what courses you plan on taking in the future. The undergraduate and graduate ECE courses listed above all require good understanding of probability theory, not statistics, and they all require ECE 313 as a prerequisite; not STAT 400 + STAT 410 which mostly teach you a lot about statistics, and relatively little about probability as it is needed for advanced ECE courses. Taking the Statistics courses and then attempting a course that lists ECE 313 as a prerequisite might be hazardous to your grade.

    On the other hand, STAT 400 + STAT 410 might be the best choice for you

    • if you would like to have a thorough introduction to statistical methods instead of the idiosyncratic coverage in ECE 313

    • if you would like to gain an appreciation of the use of statistics in various fields of scientific inquiry

    • You have no intention of taking any of the advanced courses listed above

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    • OK, I have decided to drop ECE 313 and take STAT 400 + STAT 410 instead.

    We wish you all the best in your future career.

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    • I have decided to stick it out in ECE 313. How can I make my life any easier?

    Probability and statistics can be difficult subjects because you have to learn a wholly different way of thinking about systems. You will find it difficult to absorb these new ideas rapidly, e.g. by pulling an all-nighter just before the exam. Systematic study is really the only way that you will learn the material. For each hour of lecture, you should spend at least ninety minutes in reading the text and class notes that very same day. The lecture material is presented at a rapid pace, so that it is very helpful to have spent some time before the class in looking over the material to be discussed. You may not understand everything that you will read on this first pass, but a general familiarity with the material will help you in various ways. For example, prior study will suggest questions that you might want to ask during the lecture. Prior study will point out areas where you need to make careful notes of what is said in class. Following the lecture, you should re-read the material covered on the lecture that very same day. The repetition will be of great help in fixing the relevant ideas in your mind. In addition to the reading, trying the examples on your own, answering the questions raised in your mind, and working out the suggested noncredit exercises from the weekly problem sets will help in improving your understanding of the material.

    Discussions with students over many years suggest that most students spend about three hours of non-classroom time per week on this course, mostly in trying to learn just enough to get through the problems assigned on the current homework, with much frantic page-turning in search of that one magical formula that will solve the problem immediately at hand. Unfortunately, this is exactly the wrong approach to this course. What is learned in this manner is very specific for the assigned problems on the current homework and is of no help in the future (e.g. on exams.) Furthermore, being done with a problem because you got the same answer as your friend is not enough, especially if all you have done is blindly apply a formula. You are only done when you understand why the methods you used had to have worked. The problems and the solution method should make sense to you, and if they do, they will make sense a few weeks later on the exam too!

    No one expects to develop muscular strength or build athletic skills by exercising or practicing just once a week or all night before a contest. Similarly, cramming and all-nighters are no way to get your brain into top shape for exams. Yet this is just how many students prepare for exams. If you work at a regular pace throughout the semester, you will find that you will not need as much last-minute study for an exam. Steady systematic work is the way to train muscles and brains. With diligent practice, you can prepare yourself to the point where, on exams, instinct and learned behavior patterns take over and the problems seem straightforward and obvious because you have seen so many similar ones before.

    If you spend ninety minutes per lecture just reading, trying examples, exercises, completion of derivations and proofs, etc. as suggested above, you will find that homework is a lot easier, and takes a lot less time to complete than you might have expected. Overall, you might well end up spending no more than six or seven hours per week on the course instead of the nine hours mentioned above. The more your (mental) muscles are used to exercise, the easier it is.

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    Revised 1/17/09