tips for studying for the electrical engineering phd qualifying exams at stanford.
i took this site down a while back because i do not have the qualifications to give advice about this exam. i am not a top-10 finisher, nor a stellar graduate student by any measure of the word ... far from it. however, i do believe that i learned a lot from the quals experience. so i will just leave my two cents here, for better or worse. certainly some of the most poignant memories of my first two years at stanford were the endless discussions about the quals. it was always lingering in the atmosphere ... people studying for quals, preparing for quals, and telling horror stories about smart people failing the quals. at some point i became rather tired of hearing about this test all the time. even my father had something to say, telling me in thickly accented english about his taiwanese relative who had to leave stanford EE. "That when he realize, their maths just too advanced. He cannot catch up with them." [insert thickly accented laughter here]
nevertheless, i think there exist some good strategies for studying for this exam, in spite of all the random factors present. i think this is evidenced by the fact that quals groups tend to earn nearly homogeneous results within the group: usually almost everyone passes, or almost everyone fails. so study techniques seem to be important.
background for those uninformed about stanford EE quals: http://www-ee.stanford.edu/phd/quals/. in short, you visit 10 professors in one day, and spend 10 minutes with each. during those 10 minutes, you are typically given either about a third of a straightforward problem set to blaze through as quickly as you can, or just one or two less straightforward (tricky) problems.

1. yes, we can! the statistics for this exam are perhaps not as bad as they are reputed to be. in 2006, professor gill compiled some illuminating statistics. between 1997 and 2003, there were 659 students who took the quals once and passed, or took the quals a second time. amongst these students, 615 of them passed. 438 passed on their first try, 122 on their second try, and 55 on appeal. thus, the ultimate passing percentage for these students is 93%. i think this shows that people who are determined to earn the PhD are likely to prevail. maybe you will not pass the first time, or even the second time, but eventually you will get through this. but if you give up after only one try (this is the group of students not included in these statistics), then ... i don't know what the data says. anyways, the point is, don't give up.
   
   
2. get plenty of sleep and a healthy breakfast! sleep deprivation and starvation = bad judgement.
   
   
3. develop good oral communication and reading comprehension skills in English. how much partial credit you earn from incorrect answers will be determined by the instructor's perception of how well you understand the material. thus, i think it helps to clearly speak your thoughts while working through the problems. also, sometimes you may have read technical writing fairly fast, as some quals problems have multi-paragraph descriptions.
   
   
4. concentrate most on your first and second areas, from which you will have 7 out of 10 professors. if you ace these areas, you can fail everything else and still pass. you only need to earn about 60% of the total possible points to reach the "pass" threshold. study the biblical texts in your field. for instance, oppenheim and wilsky in signals and systems.
   
   
5. what areas should i pick? it would be good to know two areas fairly well before taking the exam. for choosing the remaining areas, here are some useful facts: people who specialize in circuits and devices tend to score higher, and often dominate the top 10 list ... maybe because the questions are more straightforward. for electromagnetics, the questions are also allegedly more straightforward; i agree with this, as long as you have a solid mastery of electromagnetics up to the level of at least electromagnetic waves, antennas and basic waveguides (ee142; ee141 alone was insufficient in my own experience). signals and systems are probably most difficult since the questions need not be straightforward, and there's so much ground to cover, including continuous and discrete signal processing, communications, probability and random processes, and control theory. software is a mixed bag spanning far too much material; i have seen problems on everything from databasing to graphics to OSes and even automata theory. however, some professors are known to always ask algorithms puzzles, which can be tricky, but are nice in that they theoretically may not require much background knowledge to solve well.
   
   
6. join a quals study group that focuses on your first and second areas. the benefits of group study are obvious: you can conduct realistic simulations, and you'll learn novel new ways of thinking about problems. some people join multiple study groups to study for all four areas. i guess it depends on how much time you have.
   
   
7. start studying with your group early. i guess summer is ideal, although the beginning of the fall might be more realistic. on one hand, if you study too early, you could forget what you learned when the exam comes around. on the other hand, you will be taking a full courseload in the fall ... but you could choose courses that will help prepare you for the exam.
   
   
8. the ideal group size is four.
   
   
9. study with people that are both smarter than you and very dedicated. i think i was the dumbest person in my group. my teammates all came from India and the Middle East. somehow when they were growing up, they learned some speedy mathematical techniques, like how to do mental logarithms of any real number in a couple seconds with an accuracy of +/- 0.1. things like that didn't seem that useful to me at first, but later i realized they were perfect for timed exams like quals. too bad i never learned anything cool like that while studying for the SAT! anyhow, we spent about 9 hours a week together during the fall quarter, not including preparation time before meetings, and we met almost every other day during winter break. (note: recently i learned that many asian immigrants spend over 50 hours a week studying for quals in the fall ... i had thought we studied really hard, but apparently we didn't?! whatever.) choose your members carefully, and avoid the default ee201a random group formation if possible. you don't want anyone who will bail out midway.
   
   
10. set a schedule and plan ahead. first decide when are the best times for group meetings throughout the week, what the format of meetings will be, and who will be responsible for which years of quals problems. by what date do you plan to finish reviewing the theory? when will which concepts be covered, and in what order should we tackle the concepts? when will simulations begin? set ambitious time constraints. even if you plan to finish reviewing all the theory by mid-november, it's more likely you won't even ever finish it, because your plans will be contorted by many meeting cancellations due to absent members or examination periods.
    
    
11. don't immediately dive into quals simulations. use many -- if not most -- of the group meetings to review and discuss concepts. assign members to present different topics, and include good example problems in the presentations. even the most rudimentary concepts often have subtleties that make them well worth reviewing. simulations should come gradually, testing those concepts that have already been reviewed.
    
    
12. conduct realistic simulations. be strict about the ten minute time limit. speak your mind so the examiner can hear your thoughts. demand that examinees explain themselves properly. alternate between the whiteboard and sheets of paper. the person playing the role of professor can vary his or her personality from time to time, ranging from a bad poker player to a good one. use hints sparingly.
    
    
13. after conducting a simulation, verbally review the answers with your group. have the examiner present the solution at the whiteboard. are there multiple ways to solve it? what was the quickest way? what was the easiest? how did the fastest person think about it?
    
    
14. memorize useful facts. don't waste precious minutes re-deriving things you've seen before a million times! just memorize it. a few examples are trigonometric identities, the electric field generated by a finite length linear charge density, the resonant frequency of an RLC circuit, the equation for doppler frequency shift, the variance of a uniformly distributed random variable, the closed-form expression for a finite geometric sum, or common FT/FS/Laplace/Z/DTFT/DFT pairings and duality properties. it also helps to memorize common approximations (first-order taylor series expansions), such as 1/(1+x) ~= 1-x for small x.
    
    
15. memorize the fundamental formulas. if you forget any facts, you can fall back on the fundamental formulas to rederive what you need, if you have to. some examples are maxwell's equations, the fourier transform, and the means, variances, and pdfs of canonical probability distributions. also, sometimes having a deep understanding about fundamentals can result in time-saving leaps of intuition.
    
    
16. brush up your mental math. during the exam, you may have to do some quick proofs and computations -- sometimes lengthy -- and you will not have a calculator or symbolic math engine. practice to get faster. get familiar with certain patterns of algebraic manipulation that repeatedly show up, so that you can skip a bunch of tedious steps as soon as you've recognized that a certain pattern is supposed to be applied. for example, in signals and systems, some techniques you should be able to recognize and quickly apply include: 1) how to swap the order of summations/integrals, 2) change variables (perhaps to prove some fourier identities), 3) break complex expressions into real and imaginary parts, 4) find eigenvalues of simple matrices, 5) use parseval's/rayleigh's theorem, 6) recognize how dirichlet kernel summations reduce to delta functions, and 7) how uncorrelated zero-mean random variables distill a double summation product into a single summation of squares.
    
    
17. do as many of the past quals problems as you can. then you will have a much better idea of what to expect from particular professors. having only one year of information can be misleading. even if professor X asked something easy last year, he may be more likely to ask something very difficult this year if he has asked mostly very difficult things over the past ten years. by studying more of the past problems, you can get better acquainted with the styles of professors: who is unpredictable, who is predictable, who asks hard questions, who asks easy questions. none of these qualities are necessarily good or bad -- they all have tradeoffs. furthermore, by studying past problems, you will discover what knowledge certain professors expect from you. often their expectations exceed the content in the "official list" of courses that questions are allegedly restricted to. an example is wireless communications (ee359) -- it wasn't in the list when i took the quals, but i saw questions pertaining to wireless communications in the quals sets past years, as well as during the exam.
    
    
18. try to study everything, not just the past quals questions of particular professors. the year i took the exam, several curve balls were thrown, in the sense that quite a few professors deviated from questioning patterns they had previously always followed. from past questions, you can have a fair idea of what to expect, but you can also expect the unexpected. thus, it's always better to know all you can. survey the material covered in the courses listed for your respective quals areas. if there are gaps in your knowledge, you may want to take some of those courses, even if they are undergraduate level. good problems can come from all places, so don't limit yourself to simulating problems from past quals packets. you can even make up your own problems. in fact, if you study enough problems, there is a decent chance you will see some of them again on the actual day. yes! it can happen. sometimes they're taken straight out of the classic texts.
    
    
19. when choosing professors, keep their point variances in mind. be aware that all scores are curved, even for each professor. some professors are "easy", or at least predictable, in that they ask the same kinds of things over and over each year. because the questions are so predictable and thus relatively easy, the mean is very high and the variance is very low. thus, if you don't get almost everything right, you will be severely penalized after normalization! in some sense, this can be risky. thus, if you can train yourself to handle a difficult professor, you could possibly incur many more with less risk. finally, some professors are not easy and yet still have low variances. this is rather undesirable from the perspective of testees like us. you could solve most of the problem and end up with merely tenths of a point ... and just one more point could have jumped you a couple ranks. ask friends from previous years for advice.
    
    
20. when choosing professors, keep their personalities in mind. some will smile and help you along the way, while others are expressionless and barely talk. some are very strict about time-limits, while others are more lax. if you have trouble dealing with certain examination styles, select accordingly. again, ask friends from previous years about this.
    
    
21. when choosing professors, keep their specializations in mind. what do they research and teach? in many cases, professors give problems directly based on their courses.
    
    
22. the group II professor elimination technique. in december you will fill out a quals preference form, arranging twenty professors of your choice into groups of five. you will be told the following:
    
    
    1. you will be granted 4 from the first group, 3 from the second, 2 from the third and 1 from the last.
    2. you will not get more than 4 professors from the same area.
    3. the maximum number of professors from the same area you can put down is 6.

    exploiting these rules, one trick is to put five professors from the same area in your first group. thus you will get four of these five. then place a sixth professor from the same area in your second group. since you cannot get more than four professors from the same area, that sixth redundant professor is automatically thrown out. thus from your second group you will be assigned three out of four professors, instead of three out of five.

    however, if the professors you are most comfortable with don't happen to reside in the same area, please don't feel obligated to use this trick -- it doesn't do you any good in that case.

    
    
23. don't make up excuses for not studying. get your group to stay at stanford over winter break if you need the peer pressure.
    
    
24. should i take the quals in my first year? a hard question. on one hand, we are running out of time. at other schools with less taxing qualifying exams, students start research upon arrival, whereas at stanford, many EE students are still hunting for work long after passing the quals. so, by delaying the quals, we may potentially delay our research more. furthermore, statistically speaking, most first time-takers fail the exam. so if we fail during the 2nd year, then we'll have to take it during the third year, which could be a bad scenario because we might spend three years to conclude that the PHD is not a possibility, while at most other schools, students get masters degrees in roughly one year. consequently, almost everyone who is allowed to take quals during their first year does seize the opportunity. however, on the other hand, there's no point in wasting a shot at the exam if we're simply not prepared. we may need time to acquire more knowledge. most quals problems derive from certain core courses taught at stanford, and often those taught by the examiner. in short, if you had a solid foundation at your alma mater, and studied your depth areas to a sufficiently advanced level, then i think it's fine to take it during your first year, since these core courses probably won't teach you much new material. otherwise, you may want to wait till your second year, by which time you will have learned more.

finally, a few useful links:

the end. if you're a prospective quals examinee, i wish you all the best, and i hope this document was useful.

- w.wu, 1/23/2005 (original write date)

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