For Potential Graduate Students
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
- 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.
After reading the above, some of you still might want to contact me
regarding joining the graduate program here. That is fine, but do not
feel bad if I do not have a chance to respond to you. If you want to
catch my eye, you have two choices. First, look through my online
papers or preprints and see if you can find a bug. If you do, mention
"paper bug" in the subject line and tell me what the error is. The
other choice is to solve one or more of the following challenge
problems and mention "challenge problem solution" in your subject
- 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
- 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.
While working out the above problems, you are allowed to make whatever
assumptions you feel are necessary that preserve the essential
character of the problem.
- 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)