I get far too many emails from potential graduate students who want to apply to Berkeley. I do not have the time to respond to everyone individually and so will put the responses to the most common queries here:

- You are encouraged to apply to Berkeley's graduate program. For
the most part,
**the admissions and financial aid decisions here are made by the admissions committee, not by individual faculty members.**Things may be different at other schools, but here, we want you to have the freedom to interact with different faculty members once you get here so you can best pick your research advisor. - We are looking for the absolute best students out there. Having letters of recommendation from people we know counts for a lot, as does evidence of research potential and creativity. If you have done research already, be sure to mention it in your statement of purpose and also to get a letter of recommendation from someone who can talk about your research. External evidence of intellectual horsepower (like gold medals from IMO, etc.) is also given some weight.
- Graduate admissions here are incredibly competitive. In COM alone, there are at least 30 applicants for any given slot. We do not have enough slots to even accept all the applicants who were ranked number one in their universities. While we try to identify the best candidates, there is still an element of chance involved. Don't feel bad if you are not selected and you should hedge your bets by also applying to other graduate schools.
- I
**do not currently have**any openings for summer internship students from overseas. Do not bother asking me. I will be taking on 1-2 graduate students next year.

- Abbey and Beth are friends. So are Carl and Dan. They are having a
little dispute about fairness and they ask you to resolve it.
Whenever Carl and Dan go out to eat each Saturday, they take strict turns paying the tab. If Carl payed last time, Dan will pay this time and vice versa. But they don't bother about consciously keeping track of money and will order a big dish randomly from the menu and share it equally. Big dish prices are uniformly distributed on [5,10]

Abbey and Beth take a different approach to fairness. They too go out to eat and take strict turns paying the bill. But they order small dishes separately. Whenever one of them calculates that she is currently more than $10 behind in her fair share of payments, she will order the salad for $1. Otherwise she randomly picks a dish from the small dish menu where the prices are uniformly distributed on [2.5,5].

Carl and Dan believe that Abbey and Beth are being overly cautious and advise them to trust in the power of averaging to make things work out in the end. Abbey and Beth are skeptical and do not want to risk their friendship.

Assume that if at any time the balance of payments becomes skewed by more than M times the maximum price of a dish in one direction, then unconscious feelings of being cheated will manifest and the friendship will grow distant.

- Setup a model for AB behavior and CD behavior.
- What is the probability that one of Carl and Dan will eventually feel cheated as a function of M? Abbey and Beth?
- As M increases, approximately how does the time till friendship strain increase?
- What if there is inflation in the system and the price of dishes goes up by five percent per year?
- What if there was deflation in the system and the price of dishes dropped by five percent per year?

- You are looking to detect a weak x(t) signal in a particular
2 MHz frequency band: [f - 1MHz, f + 1MHz]. You have access to a
Nyquist-sampled version of y(t) = a x(t) + n(t) where n(t) is
white gaussian noise of unit intensity and a is much smaller
than 1. Your challenge is to give an algorithm to decide whether
x(t) is present with a false alarm probability of at most
1/1000 and a probability of missed detection of at most 1/10.
- Assume you know what the value for a is and x(t) = sin(2*Pi*(f+100kHz)*t). How many samples do you need to look at (as a function of a) in order to meet the target reliability? How would you do the computations?
- Now assume that you do not know x(t) exactly. Rather you know that x(t) = sin(w t) where all you know about w is that it is within +/-20kHz of f+100kHz. Approximately bound how many samples you now require as a function of a. How would you do the computations if your goal was to minimize the number of samples required?
- Repeat the previous part, but now your goal is to minimize the number of computations required.
- Suppose that you had access to a processor that could do a fixed number of MFLOPs. As a function of a, how would your strategy vary if your goal was to minimize the amount of real-time required to get the answer? (count both time to sample and time to compute)