My advice is based on my experience with the Digital Signal Processing (DSP) prelim, but may also be useful for people taking other prelims. The DSP prelim, when I took it, was one hour long, with three 20 minute segments. Each segment corresponded to one of the three subject areas from the syllabus. I did the DSP prelim twice, in Aug 2001 and Jan 2002.
From a student's point of view, the oral format makes the prelim useful as preparation for teaching and for answering questions after conference presentations or job talks. The similarities to teaching mean that being a discussion section GSI (graduate student instructor) for a related course can be useful preparation for the prelim.
Sometimes committee members say that they want to feel that the exam-taker is capable of teaching the corresponding classes. This suggests a thought experiment that some people might find useful in judging their own preparedness: if the professor for one of the corresponding classes went out of town next week, would you be able to prepare lectures to give in his or her place, without relying heavily on a textbook? (If you wouldn't need to use a textbook at all, that's even better!)
In my experience, being prepared for the prelim requires a significantly higher level of knowledge, understanding, and skill regarding the material than is needed to be prepared for final exams in undergraduate courses. I was struck in particular by the amount of material I was expected to have memorized and by the speed at which I was expected to solve problems. (You can get a feel for the pace of the exam by looking at question sets from past prelims.)
Maybe it is worth asking the professors on your committee what they are looking for. I don't know anyone who's tried this, but it might be useful.
However, I think the best presentation style probably depends on the individual taking the exam. For one thing, the presentation style has to work well with the individual's problem-solving style (e.g., perhaps some people would be able to focus better on the problem if they stopped talking for a while). Mock prelims with study partners can help you figure out what works well for you.
(The EE graduate assistant, who is Ruth Gjerde as I write this, can supply you with a set of questions from old prelims. There is a list of other resources later in this article.)
Study partners were very important for me, and I think most people find them useful. One way to find potential study partners is to ask the grad office which other students have signed up to take the exam. Meeting rooms with whiteboards in Doe Library can be reserved by talking to the library staff.
When preparing to take the prelim for the second time, I met with a single study partner weekly (usually) all through the fall semester. Each time we met, he gave me a full-length mock prelim with strict time limits (he played the role of the committee), and I gave him the same. I felt this was very effective because: (1) I was able to practice solving problems at the whiteboard and explaining myself, (2) I developed a better feel for the time constraints of the exam, (3) the questions that he asked me sometimes revealed holes in my preparation, and (4) the meetings provided me with motivation to study. (We held our mock prelims in the same room in Cory Hall that we expected the actual prelim would be held in, which we hoped would help us to feel comfortable during the actual exam.)
I also had one-on-one meetings with other people besides my main study partner. I think that was good, because it exposed me to more perspectives. I did very well on the prelim the second time, because I was lucky enough to be asked three questions that were the same or similar to questions I had studied. One of those questions was from a mock prelim from another student (not my main partner) and one of them was from a practice question that someone in my research group gave me. The third was something I had thought about when trying to understand a concept better.
When preparing to take the prelim for the first time, I had group meetings with about four other people. I think this larger group was fine for discussing concepts, but for problem-solving practice it was much less efficient than practicing with a single partner. Because there were about five people, each person did not get much time up at the board. Also, we did not keep time limits for practice problems, and as soon as the person at the board had trouble solving a problem, other people would try to help, so the level of pressure was unrealistically low. Overall, these group meetings were less useful for me than what I did the second time.
The graduate reading room in Doe Library was a good place to study. It is full of grad students working hard, so there is a nice peer pressure effect.
At first I had trouble balancing prelim preparation with my research, and my research was taking too much of my time. I addressed this by keeping a time log of how many hours I spent on studying each of the three prelim areas each week. I required myself to reach a weekly minimum in each area, and a weekly minimum total studying time. This was helpful.
When I took EE 226A in fall 2001, I tried doing homework questions at the whiteboard in my office, with a time limit, as if they were prelim questions. I maintained a monologue in my head of what I would say to the committee.
Here is another grad student's advice to me. I didn't follow it but it is interesting. "I would strongly try to study from a problem solving perspective... What design problems do you know how to solve? Design an signal compression scheme from scratch... what are the important things that you need to know about? The statistics of the signal, what kind of channel you have... OK.. the channel is a digital channel, so you have to take sampling and quantization into account, or the channel is a bandwidth limited analog channel, so you have to take that into account. Is the signal stationary? Is it locally stationary? How can you figure these things out? How do you take that information and make use of it? What if I say that you have to use linear prediction? or what if I say that the transmitter is not ideal and has filtering built into it?... etc.etc.etc. .... all of these problems have good solutions that are already known... how would you find those solutions in the literature? what are the key concepts? orthogonality, aliasing, correlation, prediction, whitening, adaptive filters.... All of these can be used as a framework for solving the problems above."
I found it was important not to naively follow examples or advice without understanding the differences between me and the people they came from.
Someone who had already taken the exam told me that I was going to do fine because I had started studying earlier than he did, and he passed. However, he had taken EE 123 in the fall before the prelim, as a refresher. I had not. This meant that I had more studying to do that he did.
Similarly, someone told me that she felt three weeks of full-time study was enough. Based on that, I set a target of around 150 hours for my summer of studying. But I had not taken 226A the previous semester like most people taking the DSP prelim had, so in hindsight I see that I should have set a higher target. (As for whether the 150 hour target is appropriate for the average student taking the DSP prelim, I don't really know. I think it really does depend on the individual.)
The prelim syllabus gives a course number and a reference book for each of the three sections of the exam. It also gives a paragraph for each section, listing covered topics. I thought that if a topic was listed in the topics paragraph but was not in the section's associated course or the reference book, the committe was unlikely to ask about it. I was wrong. The Leon-Garcia book does not cover hypothesis testing, and neither did EECS 126 in spring 2001. But in August 2001, both DSP prelim groups (two different committees) were asked questions on hypothesis testing. So, it appears that some committee members will look at the topics paragraphs and not the readings when they are preparing questions. Some other committee members will ask about material which is not mentioned in the topics paragraphs but is in the readings (I was asked about overlap-add convolution).
I know of at least one question that was in neither the topics paragraph nor the readings: "Can a signal be limited in both time and frequency?" (Or something like that.) This shows that it is good to spend time thinking about the concepts, and not just studying from books. (It also suggests that you may benefit from looking at other books. I saw a theorem about the minimum time-bandwidth product in a DSP book in a library once.)
The exam's first section, according to the syllabus, has EE 123 as the course and the reference book is Oppenheim and Shafer. However, as the topics paragraph suggests, questions may be asked about analog-to-digital sampling, and the relationship between discrete-time and continuous-time Fourier analysis. Also, knowledge of analog filters is relevant to digital filter design. Therefore, some EE 120 material is testable. As I recall, the Oppenheim and Shafer book does not discuss continuous-time topics much. The Signals and Systems book by Oppenheim, Wilsky, and Nawab book helped me with those. (As an undergrad, I also found a book by Lathi on continuous-time signal processing useful. I mention it here because his discussion of the relationship between the Fourier series/transform and the cosine series/transform helped my understanding of the meaning of phase spectra and negative frequency values.)
The second section is titled "Random Processes (EECS 126)". However, I think most people taking the DSP prelim have taken 226A, and if you do not take 226A you may be at a disadvantage.
The syllabus lists Haykin as the only 225A reference book. I think Statistical Digital Signal Processing & Modeling by Hayes is also worth checking out. I used both. Here is a recommendation written by an anonymous student studying for the prelim.
The class web sites at inst.eecs.berkeley.edu are a great source of lecture notes, homework assignments (sometimes available with answer keys), and old exams. Some webcast lectures are available too.
The EE undergrad student society (HKN) have many old undergrad exams online at hkn.eecs.berkeley.edu, under "Online Exams" (which is under "Student Services"). They also have a cabinet full of old undergrad final exams, which can be borrowed and photocopied.
The engineering video library (in 205 McLaughlin, last I used it) keeps a set of videotapes of Prof. Edward Lee's lectures for 225A. I think they are excellent lectures and they spend a lot of time on material that is important for the prelim. If you can find homeworks, exams, or notes from Lee's class, that may be useful too.
If you feel weak on the linear algebra content of 225A, the Gilbert Strang book Linear Algebra and its Applications book may be useful. It is well written, has a nice treatment of the SVD and has a lot of the theorems that were invoked or assumed when I took 225A. The David Lay book Linear Algebra is more basic and very easy to read; it might be helpful too.
There is a undergrad probability book with many solved problems at http://www.mit.edu:8001/people/dimitrib/Probability.html. Prof. David Tse recommended it to me for prelim review.