Applying to Ph.D. Programs in Computer Science, Study notes of Number Theory

Download Applying to Ph.D. Programs in Computer Science and more Study notes Number Theory in PDF only on Docsity! Applying to Ph.D. Programs in Computer Science Mor Harchol-Balter Computer Science Department Carnegie Mellon University Last updated 2014 1 Introduction This document is intended for people applying to Ph.D. programs in computer science or related areas. The document is informal in nature and is meant to express only the opinions of the author. The author is a professor of computer science at CMU, and has been involved in the Ph.D. admissions process at CMU, U.C. Berkeley, and MIT. Please direct any further questions you have after reading this document to our Admissions Coordinator (applyweb@cs.cmu.edu). Do not send email to the author of this document. Contents 1 Introduction 1 2 Do I really want a Ph.D.? What does a Ph.D. entail? 2 2.1 What is a Ph.D.? . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Lack of emphasis on courses . . . . . . . . . . . . . . . . . . . . 2 2.3 The research process and advisor/advisee relationships . . . . . . 3 2.4 Frustrations and joys of research . . . . . . . . . . . . . . . . . . 5 2.5 Funding during the Ph.D. . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Life after the Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.7 Should I get a Ph.D.? . . . . . . . . . . . . . . . . . . . . . . . . 7 1 3 The Application Process 8 3.1 Transcript – grades and classes . . . . . . . . . . . . . . . . . . . 9 3.2 GRE scores and TOEFL . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Personal statement . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Previous Research Experience . . . . . . . . . . . . . . . . . . . 12 3.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5.1 Whom to ask for a letter . . . . . . . . . . . . . . . . . . 15 3.5.2 How to ask for a letter . . . . . . . . . . . . . . . . . . . 16 3.6 Awards and Extracurriculars . . . . . . . . . . . . . . . . . . . . 17 3.7 How many schools should you apply to? . . . . . . . . . . . . . . 17 4 Fellowship Information 18 4.1 Why you need to apply . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 List of fellowships . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Choosing the right Ph.D. program for you 19 6 Current 2014 Rankings of CS Ph.D. programs in the U.S. 21 2 Do I really want a Ph.D.? What does a Ph.D. entail? 2.1 What is a Ph.D.? A Ph.D. is a long, in depth research exploration of one topic. By long we’re typi- cally 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. 2.2 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 2 2.4 Frustrations and joys of research Research can be very rewarding and very frustrating. Most students describe grad- uate school as a roller-coaster with tremendous highs and tremendous lows. Frustrations can come from not being able to solve a problem that you’re work- ing on, or from having someone else beat you to the solution. Frustrations can come from loneliness. However, probably the biggest frustration is the realization that you’re not as great as you thought you were. Here’s a typical story at CMU: Student X comes from famous school Y in country Z, where he was ranked 5th out of over hundreds of thousands of students and #1 in his college graduating class. The student comes to graduate school expecting to be the best and starts working very hard on research. By the end of his first or second year, the student realizes that he has not yet published any papers. His friends and family from home start asking what’s wrong with him. He feels frustrated and ashamed. He blames his advisor, he blames his department, he blames his school. Finally, he grows up and accepts the fact that maybe he’s not the best, but he can still do well if he works hard. He starts listening better, works harder, and ends up quite successful. For all the frustrations, research can be extremely joyous. For some people, the joy of research is the joy of discovering something new that no one knew about. You might be discovering a new algorithm, a new operating system design idea, a new idea for maximizing the performance of disk arrays, etc.. For others, there’s the joy of truly understanding. You’ve probably noticed that in classes a professor or book will stop just when things are getting really interesting and say, “the rest is beyond the scope of this class.” In research, you can take a problem as far as you want and understand everything about it. For many, the joy of research comes from being able to make an impact – to change the way systems are built and design them in a smarter way. There’s also the joy of doing it right. In a company, the aim is to get a working product and ship it out quickly. In research, you can take your time and plan out your project so that you are proud to defend every one of your design decisions. Research is not about simple heuristics or quick hacks. Many people also relish the joy of being the authority on an area and of having their work read and cited by others. My own story: As a student in the early 1990’s, I was interested in CPU load balancing in networks of workstations. The common wisdom at the time was that it never paid to migrate a process that was already active (already running). I dis- agreed with this logic, since I believed that processes that were already running might be exactly those which were likely to run even longer. Unable to get anyone to listen to me, I went off on my own to measure millions of UNIX processes. This took a whole year, during which time I was often terrified that I was wrong 5 and wasting my time. In the end, I discovered that the CPU lifetimes of UNIX processes obeyed a heavy-tailed distribution, which vindicated my original intu- ition that active process migration could make sense. My research won the ACM Sigmetrics best paper award for integrating systems and theory, and I graduated. 2.5 Funding during the Ph.D. Unlike the B.A., where you or your parents pay many tens of thousands of dollars, or the M.S., where you typically work as a teaching assistant and possibly continue to pay many tens of thousands of dollars, the Ph.D. is a time where funding is not a concern to you. At most schools, you will not pay tuition during the time that you are getting a Ph.D.. Typically, you will also receive a living stipend – on the order of $2000 per month, from which you will pay your living expenses. Ideally, your only responsibility will be research. This is called doing an RAship (Research Assistantship). The Ph.D. is a tremendous opportunity. You get to pick an advisor in any re- search area you like and then you get to do research in that area, receive mentoring, think deeply on problems, publish papers, become famous, while paying zero tu- ition for 6 years and receiving a salary. Your advisor is paying for this opportunity by writing grant proposals to companies and to the government to ask for fund- ing. A single graduate student can cost an advisor upwards of 80K per year (given the cost of tuition, the stipend, the overhead tax charged by the school, cost of equipment and physical space, etc.). Important note 1: At most schools, you can only do an RAship if you have an advisor who has funding for you. Since some advisors don’t apply for grants or are in areas which aren’t well-funded, you may have to work as a teaching assistant every semester to get your stipend. This is called a TAship (Teaching Assistantship). When I was a graduate student, I had a few friends who were forced to TA 13 semesters, to fund their way through school! Alternatively, you will have to restrict your choice of advisors to those who have funding. At CMU, every Ph.D. student is guaranteed a stipend plus tuition regardless of which advisor she chooses to work with. Important note 2: There are many companies and government organizations which offer Graduate Fellowships for Ph.D. students. If you are lucky enough to get one of these, they will cover most of your way through graduate school, and you will never have to worry about whether your advisor has funding or not. Details about graduate fellowships will be discussed in Section 4. 6 2.6 Life after the Ph.D. When making a decision about the next 6 years of your life, it’s good to stop and think about what you might do when you finish. Most students upon completing a Ph.D. either go into academia (research university or teaching school) and become a professor, or they go to a research lab. Some people never do research again after completing a Ph.D. For such people, the Ph.D. was largely a waste of time. If you choose to be a professor at a research university, your life will consist of the following tasks: (i) doing research on anything you like, (ii) working with graduate students, (iii) teaching classes, (iv) applying for grants, (v) flying around to work with other researchers and to give talks on your research, (vi) doing service for your department and school (like giving this talk). Note that I say “your life” rather than your job, because for new faculty, your life becomes your job. It’s a fantastic job/life for me because I love these activities, so I’m happy to work hard at all of them, but it’s not right for everyone. If you choose to be a professor at a teaching college, your job will consist of the following: (i) teaching lots of classes, (ii) doing service for your department or school, (iii) occasionally advising undergraduates on undergraduate research, or doing a little of your own research. If you choose to go to a research lab, your job will consist of the following: (i) doing research (half will be on whatever you want, half will be on whatever the company wants you to do), (ii) working with other people in the company, (iii) traveling around a little to give talks and work with others. 2.7 Should I get a Ph.D.? Here are some things to keep in mind when making this decision: 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.). 7 3.2 GRE scores and TOEFL The GRE exam has 2 parts, which you can take on the same day or different days. i. The general GRE exam – This is very much like the SAT test you took to get into undergraduate school, except that it has Quantitative (Math), Verbal (English), and an Analytic Writing portion. ii. The subject exam – As of 2013, this no longer exists for CS, so you can ignore it if you’re applying to a CS Ph.D. program. This still exists for other areas like Math, and I know that Math departments check this score. Each exam is 3 hours long. You can study for these exams. I did. Most bookstores have study guides with old exams. Study guides are also on the Web. The GRE Verbal (English) portion is very similar to the SAT. However, just because you got an 800 on your Verbal SAT does not mean that you will repeat this performance. If you’ve been in a CS program for 4 years, your vocabulary and reading speed are not what they were 4 years ago. Also, you’ll be competing with people who majored in English for 4 years. The Analytic Writing portion is different from the SAT. You will be asked to write two essays. In the first you will be given an argument and asked to analyze it. In the second you will be asked to give your perspective on some topic. There are examples given on the GRE web page. The Quantitative (Math) portion is very similar to the SAT math test. It doesn’t go beyond the 10th grade level. The GRE exam is offered every 2 months. Check out this web site for more information: www.gre.org Once again: Your score on the GRE will be largely ignored by the top schools, particularly if you are coming from a top school. At lesser-ranked schools, how- ever, your GRE score can be the difference between your getting in or not. Note: If you are planning to work for a few years between completing your undergraduate degree and applying to graduate school, I highly recommend taking the GRE exam before leaving your undergraduate school. The material is fresh in your mind while you are an undergraduate, and more importantly, your test-taking skills will diminish while you’re working. The TOEFL is a test which is required for anyone who is not a native speaker of English. Schools take the TOEFL very seriously. Although all parts of the TOEFL are important, the portion of the TOEFL that CMU pays attention to most 10 is the Speaking TOEFL. Generally, a score of less than 22-23 on the Speaking TOEFL tells us that we may have a lot of trouble understanding you. This will definitely hurt your chances of admission. 3.3 Personal statement It’s misleading that the personal statement is called a “personal” statement, since what admission committees are really looking for is a research statement. What admission committees want is a statement about what research you have done, what research you hope to do, and why you like research. Here’s a template if you need one: i. First paragraph – Describe the general areas of research that interest you and why. (This is helpful for a committee to determine which professors should read your application.) ii. Second paragraph, Third, and Fourth paragraphs – Describe some research projects that you worked on. What was the problem you were trying to solve? Why was it important? What approaches did you try? What did you learn? It’s fine to say that you were unable to fully solve your problem. iii. Fifth paragraph – Tell us why you feel you need a Ph.D.. Look back to section 2 and explain what in there appealed to you. iv. Sixth paragraph – Tell us why you want to come to CMU. Whom might you like to work with? What papers have you looked at from CMU that you enjoyed reading? Why is CMU the right place for you? It’s important to realize that the research statement is not a commitment to do research in that area. A third of all applicants end up working in an area different from that which they described on their research statement. Here are the common mistakes that many of our applicants make: • The grade regurgitator – “In my high school, I was ranked Number 1. Then I got a perfect score on my college entrance exams. Then I competed in a statewide math competition and I was the best. Then I competed in a national programming competition and I was 5th. In college, my GPA was 3.95 out of 4.0. For these reasons, I believe I will do well in your graduate department.” What’s wrong with this? This portion of the essay is a waste of space. Awards are certainly relevant, however any award you won should be listed on a separate piece of paper which is titled “Awards and Honors” and which 11 you can include with your application. There is no reason to tell us all this in your essay. It will only piss-off the people reviewing your application be- cause they already read all this information earlier in your application and they now want to hear about research. • The boy genius – “When I was born, my mother gave me a glass ball to play with. I would lay and look at the prisms of light shining through my ball. At age 3, my father brought home our first computer and I disassembled it and then put it back together. It was then that I knew I wanted to become a computer scientist. By age 5, I had taken apart every appliance in our house. At age 6, I became a chess whiz ....” What’s wrong with this? We simply don’t care what you did as a child, and we don’t believe you either. You’d be surprised how many applications from Einstein-wanna-be’s we get. If you really think this is relevant, put the im- portant facts on a separate sheet of paper, and include it in your application. It’s best if your essay can stick with stuff you did in college and later. 3.4 Previous Research Experience As I’ve said earlier, to get into a top graduate school you need prior research ex- perience. This is not necessarily true for schools below the top 10, or maybe even the top 5. Note that prior research experience does not mean that you need to have published a paper. It does not even mean that your research needs to have yielded a result – results can sometimes take years. We just need to have confidence that you know what doing research is like. At CMU we receive hundreds of applications each year from 4.0 GPA students who have never done research. These are all put into the high risk pile and are subsequently rejected. So the question is, where can you get this research experience? There are five places where you might get research experience: i. As an undergraduate, you can do research with a professor. I did this. You can even get course credit for this, and sometimes if you’re really lucky you can get paid a little (e.g., during the summer). ii. As an undergraduate, you can apply for a summer internship at a research lab or another school. I did this. Type “summer internships for undergraduates” into a browser, or type “REU” (research experiences for undergraduates), and you’ll be amazed how many opportunities there are. iii. After graduating, you can get a job, where sometimes you can do research on the job. I did this. iv. As an M.S. student, you will work on an M.S. project, which might involve some research. 12 3.5.1 Whom to ask for a letter Ideally you would like to make all your letters of recommendation count. Consider the following two letters: i. Letter 1: “I highly recommend student X for your graduate program. Student X received an A+ in my undergraduate algorithms class. He was ranked Number 2 out of 100 students. He got the highest score on the final. He worked very hard all semester, never missed a class, and was always able to answer the questions that I asked in class. This conscientious attitude makes him an excellent candidate for any graduate program. ” ii. Letter 2: “I highly recommend student Y for your graduate program. Stu- dent Y received a B in my undergraduate algorithms class. He was ranked Number 29 out of 100 students. Halfway through the semester we started working on network flows. Student Y seemed extremely excited by this topic. He disappeared for 4 weeks and even missed an exam. However when he came back, he showed me some work he had been doing on a new net- work flow algorithm for high-degree graphs. He had done some simulations and had some proofs. I’ve been working with student Y for the past couple months since then and he is full of ideas for new algorithms. I think student Y’s initiative makes him an excellent candidate for any graduate program.” Which letter do you think is stronger? It turns out that Letter 2 is very strong. Letter 1 actually counts as 0. At CMU we mark all letters like letter 1 with the acronym D.W.I.C.. This stands for “Did Well In Class” which counts for 0, since we already know from the student’s transcript that he did well in class. By contrast, student Y’s letter gives us a lot of information. It explains that the reason student Y didn’t do better in class was that he was busy doing research. It also tells us that student Y started doing research on his own initiative, and that he is quite good at doing research. The professor was impressed enough with student Y’s ideas that he took him on as a student researcher despite student Y not having high grades. You want your letters to all be of type 2 (this doesn’t mean that you should skip class!). Remember that letters of type 1 will not count. You want words like self-motivated, strong research potential, own initiative, independent, and driven to appear in your letters. These are the words that we circle when reading recom- mendation letters. You therefore want to ask letters from people who have seen you do research. These may be professors or employers. One caveat: It makes a difference whom you ask for a letter. A letter counts a lot more if the admissions committee knows the recommender. It also helps if the recommender can compare you with current PhD students and other applicants to graduate school. As a general rule of thumb, letters from professors count the most. Next highest are letters from research scientists. After that come letters 15 from lecturers, systems scientists, employers, or postdocs. Please do not get a letter from a graduate student. If you found yourself doing research where you were supervised by a graduate student or postdoc, you should ask the professor for whom they work if she can co-write the letter. The reason is simple: professors are the ones reading the letter, and they are most likely to know other professors. There is an issue for students who have been working for a while. You will certainly want a letter from your employer, but you will also want two letters from professors. This was an issue for me when I applied to graduate school. What I did was to keep touch with a few professors during my time at work. When I was ready to apply to graduate school, I contacted the professors who knew me well and scheduled a meeting with them to discuss the research that I had done while I worked. I gave them each an oral presentation. I also gave them each writeups of each of my projects. 3.5.2 How to ask for a letter Asking for a letter of recommendation won’t be a problem if you have been do- ing research with this person, but that won’t be possible in every case. Here’s a guideline which will maximize the contents of your letter. This works on the the- ory that professors have very little time and little memory (both of which are good assumptions): i. Prepare a packet for each recommender. This packet should contain all the relevant information about you that could help the recommender. Be careful not to make the packet too large. Here’s what should be in it: (a) Your statement of purpose. (b) A summary of every research project you worked on and with whom, regardless of whether this was at a school or research lab. If you have published a paper, or have a technical report, please include that too. (c) A sheet of paper listing all math/cs/engineering/science classes you have taken with the names of professors and grades. (d) A list of extracurricular activities and awards/competitions. At the top of the packet should be: (a) A recent photo of you – professors receive many such packets and don’t remember you the second after you leave the office. (b) Directions. E.g., please send to this address by Jan. 5. Put an earlier date than the real deadline – professors are notoriously late. (c) Confirmation information: Please send me email at blank address after you send this off. If I don’t hear from you by Jan. 5th, I will send you 16 an email reminder. (You need this confirmation information because otherwise you’ll never know if the recommendation was sent and you’ll be sitting around biting your nails wondering.) ii. Go to your potential recommender with your packet and ask her the follow- ing question: “Do you feel comfortable writing a strong letter of recommen- dation for me to graduate school?” You need to phrase the question this way so that the potential recommender has a way out. Do not be upset if the po- tential recommender says no. It is good that she let you know. This is much better than getting a weak letter. iii. Check with the school to confirm that they have received a letter from each of your recommenders. iv. Remember to send your recommender a thank you card (or chocolate!). It’s a lot of work to write a decent recommendation letter, and you may need more letters in the future :-) 3.6 Awards and Extracurriculars Often applications do not have sufficient space for listing awards you may have received, or extracurricular activities which you participate in. Think about any- thing relevant and include it on a separate sheet of paper, which you attach to your application. A particularly relevant extracurricular activity which many people do, but don’t think to note is tutoring or previous TA experience. A long history of tutoring suggests that you are a good teacher, which is highly correlated with being a good researcher as well. 3.7 How many schools should you apply to? There is no rule about how many applications you should send out. People gen- erally apply to 3 schools at their level, 2 schools above their level (you may get lucky), and 1 or 2 schools below their level (you need a safety school). If you are unsure about what your level is, find a student with a similar application to yours and consider where he was accepted/rejected. You can also ask your rec- ommenders to evaluate your application and tell you your approximate level. In choosing a school, you may also want to consider schools which are very strong in your particular area of interest, but possibly not as strong overall. Read Section 5 on how to choose a school. 17 looking at the seating arrangements: Are areas separated by floor, or mixed up? Are the students within an office all working in the same area, or are stu- dents mixed up? Are the faculty offices separated in floors from the student offices, or are faculty offices side-by-side with student offices. iv. How are graduate students treated within your area? Perhaps the most im- portant question here is: How frequently do the grad students in your area meet with their advisors? Talk with students of professors with whom you are considering working with. What do they work on? Are they excited by their research? Is their advisor helpful? Do they like the other students? Graduate students will reveal all! v. How are graduate students treated by the department overall? What is the equipment and office space given to students? Does the department have a method for reviewing grad students and sending them progress reports every semester (this is very important to get you through your Ph.D.). What is the fraction of students who come in wanting a Ph.D. and actually leave with a Ph.D., (not an M.S.)? vi. How does funding work within the department? Are you restricted to choos- ing an advisor who has funding? What happens if that advisor loses her funding? Will you have to then become a teaching assistant? vii. What are the hurdles associated with completing the Ph.D. degree? What are the course requirements? What exams will you have to pass? What are the teaching requirements? viii. Pay some attention to what is outside the department. For example the De- partment of Computer Science at CMU (which consists of about 66 faculty) is contained within the School of Computer Science (which consists of over 200 faculty). The School of Computer Science comprises 7 individual de- partments including the Computer Science department, the Robotics Insti- tute, the Machine Learning department, the Human Computer Interaction Institute, etc. ix. Consider the overall ranking of department. This is important only because it determines the average quality of your peers (the other graduate students). Your peers are the people who will teach you the most in graduate school. x. Lastly, keep in mind the cost of living. At almost every graduate school, you can expect a stipend of around $2000 per month. In some cities, you will live like a king off of this. In others you will be live like a church mouse. This may not bother you at first, but it can grow old after 6 years. 20 6 Current 2014 Rankings of CS Ph.D. programs in the U.S. I’m including the 2014 Rankings from the U.S. News & World Report for the top 40 CS PhD programs: (Ranking score is out of 5) Note that the top 4 schools in this list have been fixed since the time I applied for graduate school, over 20 years ago. 1. Carnegie Mellon University (PA) 5.0 Massachusetts Institute of Technology 5.0 Stanford University (CA) 5.0 University of California -- Berkeley 5.0 5. University of Illinois -- Urbana-Champaign 4.6 6. Cornell University (NY) 4.6 University of Washington 4.5 8. Princeton University (NJ) 4.4 9. Georgia Institute of Technology 4.3 University of Texas -- Austin 4.3 11. California Institute of Technology 4.2 University of Wisconsin -- Madison 4.2 13. University of California -- Los Angeles 4.1 University of Michigan -- Ann Arbor 4.1 15. Columbia University -- 4.0 University of California -- San Diego 4.0 University of Maryland -- College Park 4.0 18. Harvard University (MA) 3.9 19. University of Pennsylvania 3.8 20. Brown University (RI) 3.7 Purdue University -- West Lafayette (IN) 3.7 Rice University (TX) 3.7 University of Southern California 3.7 Yale University (CT) 3.7 25. Duke University (NC) 3.6 University of Massachusetts -- Amherst 3.6 University of North Carolina -- Chapel Hill 3.6 28. Johns Hopkins University (MD) 3.5 29. New York University 3.4 Penn State University -- University Park 3.4 University of California -- Irvine 3.4 University of Minnesota -- Twin Cities 3.4 University of Virginia 3.4 34. Northwestern University 3.3 21 Ohio State University 3.3 Rutgers State University -- New Brunswick (NJ) 3.3 University of California -- Davis 3.3 University of California -- Santa Barbara 3.3 University of Chicago 3.3 40. Dartmouth College 3.1 Stony Brook University -- SUNY 3.1 Texas A&M University -- College Station 3.1 University of Arizona 3.1 University of Colorado -- Boulder 3.1 University of Utah 3.1 Virginia Tech 3.1 Washington University in St. Louis 3.1 Take this ranking with a grain of salt. Ranking is based on people’s opinions. Even very low ranked schools have some truly great professors and some very famous professors. Also remember that a famous professor does not imply a great advisor. 22