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PhD, Graduate Studies

Mor Harchol-Balter article, CMU

A Ph.D. is a long, in depth research exploration of one topic. By long we’re typically talking about 6 years. By in depth we mean that at the end of the Ph.D. you will be the world expert or close to it in your particular area. You will know more than your advisor about your particular research area. You will know about your research than anyone at your school. By one we mean that by the last couple years of your Ph.D., you will typically be working on only one narrow problem. The Ph.D. is not about breadth, it is about depth.

Lack of emphasis on courses

The M.S. and B.A. degrees are about breadth not depth. The main requirement in the M.S. and B.A. degrees is often a large numbers of courses. A B.A. or M.S. in CS often entails taking 3 or 4 classes each semester. In contrast, a Ph.D. program typically requires typically less than 10 courses during the entire 6 years (at CMU there are 5 required “core” courses, and 3 required “electives”). The emphasis in the Ph.D. is not on classes, but rather on research. A Ph.D. student will typically take classes only when she feels that they will be useful in her research. The classes she takes may not even be in CS at all. They may be in Statistics, Operations Research, Math, Psychology, Linguistics, or anything else useful for her particular research topic.

The research process and advisor/advisee relationships: As stated earlier, the main focus of a Ph.D. is research. You typically begin your research at the time when you select an advisor. At most schools you pick an advisor sometime after your first year. At CMU, we like you to start research right away, so you pick an advisor within a month or two of starting the program.

Research is very different from taking classes. Many students never make the transition between taking classes and doing research – in fact, at most schools only 1/2 of the students who enter the Ph.D. program leave with a Ph.D. (at CMU, about 3/4 end up with a Ph.D.). Keep in mind that we’re typically talking about students who came in with 4.0 GPA’s from a top undergraduate program

Some key differences between classes and research:

In classes, the homework problems all have known answers and the techniques needed for solving the problems have (usually) been introduced in class. In research, you may be working on a problem for years without a clue of whether it is solvable. You will be the one inventing or finding the techniques for solving the problem.

• In classes, you are assigned certain problems to work on. In research, you get to pick the problems. In fact it is your job to find good problems. By “good” we mean problems which are “fundamental.” For example, finding a system hack which makes a particular product like Cisco’s Local Director run better is something that Cisco would love, but would not count as fundamental research. However discovering better algorithms for the problem of task assignment of jobs to hosts in a server farm is considered fundamental research. You are also responsible for making sure that no one else has already solved this problem. This typically involves reading hundreds of papers on earlier research in this area.

• In classes, if you can’t solve your homework problem, you can always ask other classmates. Even if none of your classmates know, you can ask the professor, who certainly knows the answer. In research, you are often working alone, or at best with you advisor and maybe one other student. You are free to ask anyone in the world for help, but they will typically not be able to help you, since they don’t know the answer either – if they did, it wouldn’t be research. Many students have a hard time with working independently

• In classes, you are constantly being given grades and you are constantly being told what to do next. In research, there are no grades. There is some instruction (from your advisor), but mostly it’s up to you to be self-motivated and pro-active. In the classroom, there is a distance between you and your professor. In research, you and your advisor will work side-by-side. Your advisor will still tell you what to do – give you ideas for problems to work on, assign papers for you to read, give you programming assignments, and often give you a time-line and schedule. However, when you and your advisor are working on a problem together, you will work as equals. You will both learn from each other. You will make discoveries together. Many students are surprised to find that their advisor is very different in research than in the classroom. A professor who is very dry in the classroom and often looks bored and uncomfortable will often become extremely enthusiastic and excited when working on research problems. In the classroom, you hear your professor discuss results which he/she has already worked out. All problems are always solved by the end of lecture. In research, you will watch your advisor think out loud and see how he/she thinks and reasons. Students often find this very exciting. You may find that you think more quickly than your advisor, but your advisor has more ideas than you. Or you may find that you are better at computations or coding, but your advisor is better at proofs or writing or speaking. This surprises many students, who expect their advisor to be better than they are at everything. Don’t pout, this is an unrealistic expectation. As in all of life, you will be most successful if you simply figure out what skills your advisor has that you don’t and work hard at picking up all of those skills without complaining.

When taking classes, you will almost never see your professor alone. When doing research with an advisor, you will typically have 1 hour per week when you meet with your advisor alone. If your advisor is especially busy (remember, professors have to do research, teach, apply for grants, serve on committees, fly around giving talks, etc.) you may only get 1/2 hour a week. If your advisor is a newer faculty, you may get as much as 2 hours per week. It’s your job to plan ahead so as to maximize the utility of your time together.

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Should I get a Ph.D.?

i. A Ph.D. is not for everyone!

ii. A Ph.D requires 6 years on average. The opportunity cost is high.

iii. Do not even think of applying for a Ph.D. if you have not tried research and/or teaching and found that you like at least one of those. (Note: the Ph.D. program will require mostly research, not teaching, but a love of teaching may help motivate you to get through, so that you can go on to be a teacher. I have seen many examples of this.)

iv. A Ph.D. requires a particular type of personality. You need to be someone who is obsessed with figuring out a problem. You need to have tremendous perseverance and be capable of hard work. You need to be willing to do whatever it takes to solve your problem (e.g., take 5 math classes, learn a whole new area like databases, rewrite the whole kernel, etc.).

v. You need to know why you want a Ph.D. You need to have vision and ideas and you need to be able to express yourself.

vi. Obviously, many people are still unsure straight after a B.A. I was one of them, so I understand. For such people working in a research lab or in an industrial lab which involves doing research for a few years will help them decide. If you are unsure, I highly recommend working for a few years before starting a Ph.D. Do not apply to graduate school until you are sure you know what you want.

My own story: After I finished my B.A. in CS and Math, I went to work at the Advanced Machine Intelligence Lab at GTE in Massachusetts. At first I was very excited by my paycheck and the great feeling of being independent. I also really enjoyed my area of research at the time: pattern recognition and classification. I was working with frame-of-reference transformations involving eigenvectors of autocorrelation matrices. It was exciting! However I quickly realized that I wanted to know more. I wanted to know why some algorithms produced good results and others didn’t. I wanted to come up with my own algorithms. I worried that I didn’t have enough of a mathematics background to answer my own questions. In summary, I wanted to delve deeper. Everyone around me thought I was very odd for wanting these things. I left after 2 years and went to graduate school. That first month of graduate school I looked around and realized that everyone there was just as weird and obsessed as I was, and I knew I had made the right decision.

Manuel Blum

THE PhD: GETTING STARTED

I remember a great summer job I once had at IVIC. A top neurophysiologist, name of Svaetichin, gave me a splendid problem... one that I unfortunately could not solve. The problem was to find a way to focus light on a single cell of a goldfish retina so that the light would not spill over onto any of the adjacent cells. Svaetichin had tried making a pinhole in a sheet of black tin, and shining his light thru the hole. This worked for moderate size holes, but failed for really small holes, which caused the light to diverge, to form diffraction patterns.

Since Svaetichin couldn't solve the problem, I decided I couldn't. Or perhaps it's that I thought his problem physically unsolvable. In retrospect, I should have taken out books on physics, especially optics, read as much as I could, talked to others and kept on talking to him. Svaetichin would have helped me if I had shown him I was reading thinking working.

Don't expect your thesis advisor to give you a problem that he or she can answer. Of course, she might.

Your thesis advisor may encourage you to work in an area that she feels completely comfortable in... in which case you can rely on her for sage advice and sound guidance. Or she may encourage you to work on something she knows little or nothing about, in which case it will be up to you to inform and teach her. In the latter case, you will have to learn all you can for yourself...You will have to learn from other faculty, from courses, from books, from journals. from peers. Both kinds of advisors can work out for you. I don't know that one is necessarily better than the other. But you should know which you got.

Whatever you do, you got to like doing it.... You got to like it so much that you're willing to think about it, work on it, long after everyone else has moved on.

THE PhD: DEEP IN THE MIDDLE OF IT.

There's a wonderful quote from ANATOLE FRANCE: "A University Student" -- and this is especially true for a PhD Student -- "should know something about everything and everything about something."

You know the jokes about PhD's... A PhD knows more and more about less and less until he knows everything about nothing.

When working on a PhD, you must focus on a topic so narrow that you can understand it completely. It will seem at first that you're working on the proverbial needle, a tiny fragment of the world, a minute crystal, beautiful but in the scheme of things, microscopic.Work with it. And the more you work with it, the more you penetrate it, the more you will come to see that your work, your subject, encompasses the world. In time, you will come to see the world in your grain of sand.

To see a world in a grain of sand

Or a heaven in a wild flower,

Hold infinity in the palm of your hand

And eternity in an hour.

WILLIAM BLAKE (1757-1827)

This gorgeous quartet is followed by a large number of sometimes deep sometimes questionable aphorisms, which I see much like the occasionally grinding work of a PhD thesis.

There's all kinds of research you can do.

There's research to prove what you know to be true.

There's research -- maybe better called SEARCH -- to figure out what is true.

Some of the best such search succeeds in DISPROVING

what you initially believed to most certainly be true.

For a relatively minor but personal example: When I was working on the MEDIAN problem, my goal was to prove that any deterministic algorithm to find the MEDIAN of n integers must necessarily make roughly as many comparisons as it takes to sort n integers, i.e. n log n comparisons. I was shocked to discover that the median of n integers can be found with just O(n) comparisons.

When working on proving some statement S true, you should spend at least some time trying to prove it false. Even if it's true, trying to prove it false can give insight.And in any case, too often, our intuition is dead wrong.

There is yet another sense in which, when working on a hard problem, you may find that the answer is NOT what you expected. You may be looking for a YES or a NO; it may be something else.