princeton math phd requirements

Graduate Admission

Application deadline:  december 15 (updated 11/1/22), required application materials:.

• Electronic application
• Statement of Academic Purpose
• Three letters of recommendation
• Transcript(s) - One transcript from every college/university from which you have earned, or expect to earn a degree, must be uploaded with your electronic application. The Graduate School does not accept mailed transcripts. The transcript you obtain does NOT have to be official.
• English language proficiency:  TOEFL/IELTS

Note: GREs, both general and subject test scores, will not be accepted for Fall 2023 admissions.

Program Length: Four years; however, a fifth year is usually granted if approved in advance.

If your interest is in applied and computational mathematics, you must apply directly to the Program in Applied and Computational Mathematics (PACM).

Chenyang Xu

Jill leclair, general information.

Graduate School Admissions

• Undergraduate

Requirements

Mathematics majors are expected to have a background knowledge of calculus in one and several variables and of linear algebra and to have had at least some experience with rigorous proofs and formal mathematical arguments before entering the department. The standard calculus sequence 103-104-203-204 covers the basic background material. The 215-217-300 sequence and the 216-218 sequence cover calculus and linear algebra more thoroughly and theoretically and serve as an introduction to some mathematical techniques and results that are a background for further work in analysis. Any of the courses 214-215-216-217-218 will serve as introductions to rigorous proofs and formal mathematical arguments. It is not necessary for students who have had equivalent courses elsewhere to take these specific courses.  For any questions please see the Advisors for Mathematics Majors or the Placement Officer.

Mathematics majors must, of course, meet the general University requirements for graduation. These include a writing seminar, which must be taken during the freshman year, some proficiency in a foreign language, and ten courses in the various distribution areas as described in the undergraduate announcement. It is wise to get these requirements out of the way as early in your undergraduate years as possible, to leave freedom in the junior and senior years for courses in mathematics and other topics in which you are seriously interested. Mathematics majors are required to successfully complete a minimum of 31 courses for graduation, of which a minimum of 19 must be outside the Mathematics Department.  Of these 19 courses, two can be from the list of 200-level prerequisite courses for the department.

Please Note: Students who take more than 12 courses at any level in the Mathematics Department, in addition to two prerequisite courses, must take more than the usual number of courses altogether in order to have at least 19 courses outside the department.

Mathematics majors are required to take at least  eight departmental courses  in mathematics at the 300- and 400-level or higher, including:

• one course in  real analysis  (from the 320s or 420s or 300 or 385 or 520)
• one course in  complex analysis  (from the 330s)
• one course in  algebra  (from the 340s or 440s)
• one course in  geometry  or  topology  (from the 350s or 450s or 360s or 460s, or alternatively,  one course in discrete mathematics from the 370s or 470s)
• an additional four courses at the 300 level or higher.
• Up to three of the eight departmental courses may be cognate courses outside the Mathematics Department, with permission from the Junior or Senior Advisors or Director of Undergraduate Studies. (Courses from other departments that are cross-listed with MAT do not need permission and do not count toward the total of three allowed cognates.)

It is recommended that students complete some of these core requirements by the end of the sophomore year.  Completing these core courses early will give you more options for junior and senior independent work.

The final choice of departmental courses is settled in consultation with the advisors for mathematics majors during the spring term of the senior year.  

The formal independent work requirements in the Mathematics Department consist of:

• a junior seminar and a junior paper, one in each term of the junior year
• or  two junior seminars, one in each term of the junior year
• and  a senior thesis in the final year. 

Students who have particular interests may speak with  faculty members about  reading courses in those areas not covered in the regular curriculum. Reading courses are intended for students who  have taken all the 300/400 level courses in their area of interest and would like to delve deeper into the material.  Normally at most one course each term can be a reading  course. At most two reading courses can count toward the basic "8 mathematics courses" requirement.  Applications for approval of reading courses are available on the Registrar's website, and must be approved by the staff of the Office of  the Dean of the College after departmental approvals are obtained. Permission to take graduate courses in mathematics (other than the bridge courses described below) is granted through a version of the reading course approval process. Because the process has so many stages, reading course applications are due in the department no later than the first Wednesday of the term. If you have questions about this process, please contact the Undergraduate Administrator.

In addition to undergraduate courses, the Mathematics Department  offers some introductory graduate courses that are accessible to  undergraduates with sufficient background. These are called "bridge"  courses. In general, students interested in taking a graduate course  should consult the instructor about the advisability of doing so. Many  graduate courses are quite specialized, and are directed towards  graduate students and visitors who are working in a particular  area. They do not provide a broad enough overview of the field to be  of interest to most undergraduates. It is not  possible for undergraduates to register for graduate courses online. For bridge courses and graduate courses in other departments, please go to  https://registrar.princeton.edu/forms for the  "Undergraduate Permission to Enroll in Graduate Courses Form". The form must be signed by  three people---the instructor of the course, the Mathematics  Director of Undergraduate Studies or Advisor, and your residential college  dean---and then submitted to the Registrar's office , since it is not possible for undergraduates to register for graduate courses on TigerHub. For more advanced Mathematics graduate courses, permission to enroll is accomplished via the "reading course" process -- contact the Undergraduate Administrator for more information.

János Kollár

Jennifer m. johnson, alexandru ionescu, mark mcconnell, ana menezes, michelle matel, brittany m. king.

Graduate Program

Requirements.

The Program in Applied and Computational Mathematics offers a select group of highly qualified students the opportunity to obtain a thorough knowledge of branches of mathematics indispensable to science and engineering applications, including numerical analysis and other computational methods.

Preliminary Exam

In the first year of studies, it will be the student’s responsibility to choose three areas in which to be examined out of a list of six possibilities to be specified below. This choice of topics should be achieved by the end of October. The director of graduate studies, in consultation with the student, will then appoint a set of advisers from among the faculty and associated faculty. The adviser in each topic will meet regularly with the student, monitor progress and assign additional reading material. They can be any member of the University faculty, but normally would be either program faculty or associated faculty. The first-year students should choose three topics from among the following six applied mathematics categories:

• Asymptotics, analysis, numerical analysis and signal processing;
• Discrete mathematics, combinatorics, algorithms, computational geometry and graphics;
• Mechanics and field theories (including computational physics/chemistry/biology);
• Optimization (including linear and nonlinear programming and control theory);
• Partial differential equations and ordinary differential equations (including dynamical systems); and
• Stochastic modeling, probability, statistics and information theory.

Please check  Faculty Research Interest that may help you select the topics and committee members. 

Other topics as special exceptions might be possible, provided they are approved in advance by the director of graduate studies. Typically, students take regular or reading courses with their advisers in each of the three areas, completing the regular exams and course work for these courses.

The preliminary exam must be taken at the end of the first year. It is a joint interview by students and three first-year advisers. Each student should discuss with their first-year advisers which of these courses are relevant for their areas. In order to assess whether they have sufficient preparation, or whether it would be good to take a particular course, it is a good idea to obtain some typical homework or a final exam from a previous year. If the student fails the preliminary examination or a part thereof the first time, they make take it a second time.  

General Examination

Before being admitted to a third year of study, students must pass the general examination. The general examination, or generals, is designed as a sequence of interviews with assigned professors that takes place during the first year and covers three areas of applied mathematics. The generals culminate in a seminar on a research topic, usually delivered toward the end of the fourth term.

A student who completes all departmental requirements (coursework, preliminary exams, with no incompletes) but fails the general examination may take it a second time. If the student fails the general examination a second time, then Ph.D. candidacy is automatically terminated. 

Master of Arts

The Master of Arts degree is normally an incidental degree on the way to full Ph.D. candidacy, but may also be awarded to students who for various reasons leave the Ph.D. program. Students who have satisfactorily passed required coursework including the resolution of any incompletes and have passed the preliminary exam, may be awarded an M.A. degree. Students must complete the required “Advanced Degree Application form” upon learning the Department’s determination of their candidacy in order to receive the M.A.

Doctoral Dissertation

The doctoral dissertation may consist of a mathematical contribution to some field of science or engineering , or the development or analysis of mathematical or computational methods useful for, inspired by, or relevant to science or engineering.

Satisfactory completion of the requirements leads to the degree of Doctor of Philosophy in applied and computational mathematics.

View the Graduate Student Guidebook

Maria Chudnovsky [email protected] Director of Graduate Studies

Katherine Lamos  [email protected] Program Coordinator & Graduate Program Administrator

The application deadline is December 15 . Please apply online.

Helpful links

• Graduate Admission Office Staff
• On-line Application
• Graduate School Catalog

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How to get into a top mathematics PhD program?

I'm a first year student undergraduate at a top US university, and I'm going to major in math. Of course, I still don't really know what I want to do with my life, but I'm really excited about going on to a PhD in math. What does one have to do to get into a top PhD program in mathematics? When I say top, I mean absolute top - like Princeton or MIT. Please understand that I'm not being presumptuous in asking this: I don't know whether I'll ever be good enough to do a PhD at an institution such as these, but I'm just asking for reference - and out of curiosity.

I've read a lot of threads about similar topics, but answers there are fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime in the future to even dream of being in a program such as the ones I mentioned?

• graduate-admissions
• mathematics
• undergraduate
• research-undergraduate

• 1 Get good grades and apply when you have finished final year... –  Solar Mike Commented Mar 28, 2019 at 6:28
• 6 Let me be blunter than I or most mathematicians would like to be. There is such a thing as mathematical talent, and, starting where you are and given the level you're aiming for, it matters (though many other things also matter!) Let me make an analogy to making the NBA. One could make a list of things that most basketball players have to do to make the NBA, but almost all of the basketball players who try to do most of these things still won't make the NBA. In fact, so few of them will make it that calling such a list a guide to making the NBA would be ridiculous. –  Alexander Woo Commented Mar 28, 2019 at 8:00
• 2 I think a lot of it has to do with opportunities taken at a young age. Enrolling in a program to skip part of high school and start college early is an example. Basically, one initial requirement would probably be access to math beyond what one typically sees. Another example is participating in the Ross program. Or working with highly motivated students on challenging math. If you can forgo everything and focus on math, that would probably help. Go to a top college and take as much math as possible. It helps to have mathematician parents. –  user74089 Commented Mar 28, 2019 at 9:05
• 1 @AlexanderWoo The problem with the NBA analogy is that there are much clearer ways to measure talent and performance in basketball than in mathematics. Even if "mathematical talent" were a one-parameter quantity, it's more than a little dubious that Princeton and MIT are particularly good at identifying it. –  Elizabeth Henning Commented Mar 28, 2019 at 17:11

2 Answers 2

First off, I have a PhD in a top 20 - not top 3. I believe my school was 16 or 17 when I was doing my PhD. So I'm below what you are aiming for. So feel free not to read this post.

First of all, I'm puzzled by your comment:

fairly vague ("good letters of recommendation", "advanced coursework", etc). What exactly do these terms mean, and what should I - as a first year student - already start doing to at least stand a chance sometime

Good letters of recommendation: You will need to get about 3 profs to write good letters of recommendation when you apply to grad school. That means you need them to say you are smart as in PhD-smart.

Advanced coursework: Take ALL the higher level courses if possible. Take some graduate level courses if possible.

Now about grad school: don't think about the top 1 or 2 or even 3 for now. If your goal is math, then your goal is math, not the school. Just focus on math for now.

I do not know you, so whatever I said below might be useless and meaningless.

What can you do as a first year student? Get a good GPA, as close to 4.0 as you can. You want to take as many math courses as you can right? So do some self-study and test out of your gen ed courses. I had a student who tested out about 8 so that he can have time to take ALL the higher level courses.

Are you taking any math courses now? Then focus on them and do well. Doing well does not mean just getting an A. It means being near the top of the class. Your prof knows. Not all profs will take note. But some do.

You have to figure out which profs are interested in growing PhD students. Profs who care will be open to chat with you and guide you. The only way you can catch their attention and learn from them is to be at the top of your class. Ask questions in class (if possible, when appropriate). Do you study ahead? Talk to them during office hours and ask questions so that they know you are interested and are studying your textbook ahead of the class.

When I was an undergraduate I always study ahead. While studying all the courses, I will pick one book and study ahead until I'm done with the book for that course. Then I'll pick another one and study ahead. Etc. Don't just read the book. Do the problems.

It's also a good idea to think about your favorite area in math and study it on your own. Unfortunately if you are not very deep into math, you might not know where to go with this. That's why knowing a prof well will help. He can guide you.

If you have time and if you have not done so, I suggest you look at the textbooks for math olympiads. Study them and do all the problems. Try to finish as much as you can so that you have some time to try some putnam competition books. Math problems in the math olympiad and the putnam are very different from the type of problems you will solve in your regular math classes. In many ways they are closer to research-type math problems. Again, I do not know you. Maybe you have already done lots of math olympiad training.

Another very important thing to note is that it is your responsibility to keep your level of interest in your area (i.e. math) as high as possible. That means spending some time reading up on the biographies of famous mathematicians. Don't do too much of that since you do have to study math.

Books are the most important resource for you right now. Ask your profs for good recommendations. Do not be surprised that your class textbook might not be the best textbook on that subject. It's just one that's convenient and easy to use. I have no idea where you are in your math education. But if you are in Calculus, then you can for instance study "Calculus" by Michael Spivak. If you are very strong in math and have already studied that, you can go on to other books.

Check your math library and see if you can find magazines you can understand. Try the American Mathematical Monthly and the Mathematical Intelligencer.

See if there's a math club you can join. Make sure it's a math club and not just a social gathering for math majors. Nothing wrong with socializing, but if the club does not have math related activities, then it won't help your goal.

If you work very hard in the first 2 years, you might know what area you want to go into. (But it might change.) And if you take some grad level course(s) in that area in your third year, you might be able to attend the research seminar in that area, which might be a weekly meeting. You might be able to start doing some research during your senior year.

• 4 This is good advice except the part about math competitions. Those questions are nothing like research problems. –  Tobias Kildetoft Commented Mar 29, 2019 at 5:43

Roughly: good grades (3.8+ GPA) in difficult courses, good test scores (80+ percentile on math GRE subject test [not the regular GRE math, which you should get a ~perfect score on without studying]), strong research background and good letters corresponding to it.

That will get you into schools in the top ~30. To get into the very top programs, you will need to meet this standard and also have either (1) a very nice research background / letters, or (2) something "interesting", such as impressive accomplishments outside of math

Disclaimer: not a mathematician

• 1 Can the downvoters explain? Not a mathematician, will delete if I'm off-base, but I got into a top-10 physics program with basically this formula... –  cag51 ♦ Commented Mar 28, 2019 at 5:52
• 1 I understand that. What exactly do you mean by accomplishments "outside of math" though? What kind of accomplishments? –  gtoques Commented Mar 28, 2019 at 6:18
• 4 Voted this up - can't see why it gets downvotes... –  Solar Mike Commented Mar 28, 2019 at 6:50
• 7 This advice is far too generic. Good grades (3.8 GPA)? There is no mention of the caliber of courses. Median Princeton admit probably has a 4.0 GPA with stellar performance in numerous graduate level courses like differential geometry or algebraic topology. 95+ percentile on GRE is probably a given although I doubt top programs put much weight on it at all. Most importantly, it really helps if a respected mathematician gives an absolutely glowing recommendation regarding your research potential. Impressive accomplishments outside math count for very little. –  zoidberg Commented Mar 28, 2019 at 7:06
• 3 @zoidberg surely the advice has to be generic - the OP is nowhere near completion, has no grades to speak of and not applied to any institution yet.... –  Solar Mike Commented Mar 28, 2019 at 7:14

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Valedictorian Aleksa Milojević ’23 Describes His Princeton Experience

‘It really broadens your perspective, especially having the opportunity to meet so many diverse people’

Published May 30, 2023

Princeton University’s valedictorian for the Class of 2023 is Aleksa Milojević, a mathematics major from Belgrade, Serbia, who has focused on combinatorics while at Princeton and has already written three papers. In addition to earning 16 A pluses at Princeton, he has been a recipient of the Freshman First Honor Prize, the Class of 1939 Scholar Prize, and the Shapiro Prize for Academic Excellence — twice. Milojević spoke with PAW about his Princeton experience, about solving math problems no one has solved before, and about the many friendships he’ll bring with him after graduation, with classmates from around the world.

Listen on  Apple Podcasts  •  Google Podcasts  •  Spotify  •  Soundcloud

Julie Bonette:  Hello, I’m Julie Bonette, writer and assistant editor for Princeton Alumni Weekly. Welcome back to the PAWcast. This is the Commencement edition. Today, I’ll be speaking with Aleksa Milojevic, the valedictorian for the Class of 2023. 

Aleksa, a mathematics major from Belgrade, Serbia, has focused on combinatorics while at Princeton and has already written three papers. In addition to earning 16 A pluses at Princeton, he has been a recipient of the Freshman First Honor Prize, the Class of 1939 Scholar Prize, and the Shapiro Prize for Academic Excellence — twice. He directed the Princeton University Mathematics Competition for more than 500 high-school students and was an early inductee of Phi Beta Kappa. After graduation, he plans to pursue a PhD in combinatorics from ETH Zurich, but first he’ll deliver the valedictory address at Princeton Stadium on May 31. 

Welcome, Aleksa, and thanks for joining me today.

Aleksa Milojević:  Thanks for inviting me.

JB:  Absolutely. So, I know your grandfather was a math teacher and your parents were engineers. Do you think you were destined for this line of study?

AM:  I’m honestly not sure. I mean, especially being here at Princeton with so many different, you know, fields that I had the opportunity to explore during my undergrad, I think it was very easy for me to end up in any other field. But I guess at level of high school it started becoming obvious because I went to a specialized math high school and then I did a lot of math competitions and somehow at that point I started directing myself. But I definitely had many other passions during elementary school.

JB:  If you weren’t studying math, what do you think you would be focusing on?

AM:  In elementary school I had this love for history and somehow during my time here I think it combined slightly with literature. So during my time at Princeton I really enjoyed 19th-century Russian literature. And then I think I would be either like a historian of literature, I don’t know if there is such a thing, but definitely either history major or a literature major, focusing on some earlier part of the tradition, either one of these two.

JB:  Hmm. What do you like most about math?

AM:  About math as a science, I think it’s very precise? So you are told the rules and then you know, the rules doesn’t, don’t change through the game. There’s no, nothing’s unexpected. I think at least in terms of the proofs, you are, we always know what the proofs needs to satisfy before we can call it approved. And I think that sense of definiteness and just being clear what’s enough and what’s not enough to prove your is something very, very valuable. You’re never lost — is this enough, is this not enough? You know, we always know exactly what’s enough. 

JB:  And now that you’re coming to the close of your Princeton experience, when you reflect back, what stands out?

AM:  So definitely many math classes, but I think I’ve heard this many times and I think it’s definitely come true that the classes that you remember the most are not the classes in your major but rather the one-off classes that you take in other departments. So I’ve taken three classes now in Russian literature, which I enjoyed very much and that’s definitely something that I’ll remember throughout.

JB:  Wonderful. Tell me about some of your challenges on your Princeton journey.

AM:  So definitely one of the big challenges that came early on was COVID because it hit somewhere halfway through my freshman year. And then there was some adapting obviously as everyone else did, just some time difference, being away from everyone. So that was the first challenge and then readapting back. I think given that we were here only for a couple of months, we didn’t really get a feel for campus as much as some older students did. And then it was like rediscovering it all over again during COVID and during the first semesters when we were timidly coming back to campus. And then this year when actually everything started going normally. So definitely there’s been  a trajectory there.

JB:  Yeah, definitely. Have you found some favorite spots here on campus?

AM:  So given that I’m a math major, I really enjoyed spending time in Fine Hall. I think there is a really nice common room and a community build around it. There’s the daily math and cookies at 3:30, so I tend to go to that every day and that’s been one of the highlights, I think, for me this year.

JB:  Any professors stand out?

AM:  Definitely a couple of them. I think my junior paper advisor, Professor Noga Alon was very influential to my home Princeton experience because he first taught two of the classes that I took in my freshman-sophomore years. Then I did a junior paper with him my junior year and now my senior year I’ve been something like an undergraduate course assistant for two of his classes. So I think we’ve had a very, very deep relationship at least while I was here. 

And then obviously my senior thesis mentor Peter Sarna, who’s also an amazing professor and an amazing inspiration, at least for me, this year to learn the topic surrounding my senior thesis and so on.

JB:  I know you’ve studied a couple of different branches of math while you’ve been here. Can you tell me about that and which one’s your favorite?

AM:  I think early on I started doing combinatorics perhaps because combinatorics doesn’t require you to have as much background before coming into the research. So you could essentially do research maybe after a couple of months of studying the problem as opposed to, for example, number theory, which I did later on. And even now I don’t think I’m at the level of doing research there, but I definitely think that both combinatorics and number theory are immensely interesting. 

And then I think it’s good to know as many areas as you can because you never know when ideas from one field of math can be used in another. And the biggest breakthroughs I think over the decades in math have been exactly coming from that interplay between different fields and just using ideas from one field into the other and vice versa. 

JB:  And I understand for your thesis you kind of switched tracks a little bit. Can you tell me about that?

AM:  For my thesis I did something closer to number theory and even a little bit of algebra geometry, which was completely different from what I’ve been doing for my junior paper. And I think that’s been a part of this somewhat intentional push to try to broaden out and to learn some more different areas. Because I think when one does a Ph.D. in math, people tend to specialize into one area exactly. And undergrad is pretty much the last time we had the opportunity to explore very broadly different areas without any pressure to produce papers or anything. So I think I’ve been just trying to use my undergrad for that.

JB:  Nice. How valuable do you think a math major is?

AM:  From Princeton? I think if one wants to do academia or wants, wants to go into academia, I think it’s very valuable precisely because of the close interactions that you can get with professors and if you step out and if you try to reach out to them, I think they’re very open to both collaborations and just mentorship. So I think that’s amazing. And then also the community here, both undergrad and grad students at the math department I think are amazing. So I think for me at least, it’s been very valuable.

JB:  I’ve noticed that there’s been a little bit of a decline in math learning during the pandemic. Do you have any thoughts on how we can maybe address this gap and what is the future of the field of mathematics?

AM:  I definitely agree that math is very useful. Whether one ends up doing math or doing something else, I think just the way of thinking that math develop in, in a student is very important. And I think that’s why being an educator is very important. 

Now I’m not sure that they have a very valuable thoughts for how to improve math education because, in starters I don’t even know exactly how it works in the U.S. because I come from a different system and it works completely differently there. And then the other thing, I think I’m not, I don’t even have enough knowledge to say anything about how to teach kids, but I think it’s definitely very important to try to get across that way of thinking that, you know, logic and trying to argue things step by step and not just, you know, guess the answer. So I think that’s perhaps the most valuable thing even though maybe the students want to remember the exact way to solve a quadratic equation or whatever. I think at the end of the day that way of thinking is the most important one.

JB:  I know you’ve started to give back with your time with young people, especially the Princeton University mathematics competition and tutoring. Tell me why that’s important to you.

AM:  I think one of the big things that got me into math science in general were the competitions that I went to in high school. So I always felt indebted to these people who organized these competitions who wrote problems for them, who graded, who made all these things possible for me, who prepared me for these, who showed me actually all the problems and math behind these problems. So I really felt the need when I, once I graduated from high school, to somehow get involved on the other side because I really felt I had some debt to repay. And I feel my engagement with the PUMaC, the Princeton University Math Competition, has been at least one way to do that. The other way has been of course tutoring. I’ve been doing some tutoring both here at Princeton and back home in Serbia online during COVID and so on for people going to math competitions for high schoolers. So I think both of these have been very meaningful to me. 

JB:  You have lived in different parts of the world. How do you feel like that adds to your overall perspective?

AM:  I think the perspective, at least for me, these four years of living in the U.S. have been amazing. I think it really broadens your perspective, especially having the opportunity to meet so many diverse people, so much diversity in the student body here at Princeton. It’s — I think it’s a unique experience. Honestly, I don’t think I would’ve experienced something like that had I stayed in Serbia and that’s why I think it’s very valuable to switch countries as often as you can, essentially. I mean I’m going for my Ph.D. to Switzerland, to Zurich, so I think that’s going to be yet another side and yet another story. So I’m really looking forward to that as well.

JB:  Yeah, congratulations. That’ll be exciting. 

AM:  Thank you.

JB:  Looking past that, what do you hope your job is in a couple of decades?

AM:  Well, it’ll be very nice if I had a position in academia and if I somehow could work as a professor somewhere. But that’s definitely not the only option. I’m also open to going into industry or, I don’t really have any particular job that I am set on doing. I think I’ll just try to enjoy my work, whatever it is. And then as soon as I don’t enjoy it I’ll probably switch it up.

JB:  But before then, you have a couple more days left as a Princeton student.

AM:  That’s right. 

JB:  Tell me a little bit about what clubs or groups you’ve been involved with here, besides the ones that we’ve already mentioned.

AM:  I think my freshman year I’ve been involved with the Princeton Triangle Club, the theater group here on campus. Over the years, unfortunately due to Covid, partially, I started getting less involved in that. But I think that’s been a very fun experience to, again, that’s one of the things why Princeton is so unique to me. I think because as a math major who doesn’t have any background in theater, I still had the opportunity to be a part of a theater group and help them build their set or whatever and just see how things work behind the stage. I think that was, that was a really big experience for me.

JB:  Very cool. Any others that you want to mention?

AM:  I don’t think I have any others which are particularly standing out, but—

JB:  Sure, sure. You’re going to be delivering your address in a couple of days here. Do you have a theme for your classmates or a message that you want to send?

AM:  I didn’t actually think about it cause my speech is not due for maybe a week or so, so these days it’s been a little rough for me. But apart from that, yeah, I, I think, I mean generally the message that they try to give anyone to anyone who asks for advice here at Princeton is just to make sure that they’re enjoying what they’re doing. Because I think here at Princeton it’s sometimes easy to get caught up in all the requirements that we need to do and, you know, I need to do this for that and it’ll be good for my CV if I had this requirement and that certificate, and so on. And I think if you don’t enjoy your time here at Princeton, then I don’t think it’s worth it.

JB:  Hmm. But now you’re almost done.

AM:  That’s right.

JB:  What was your reaction to being named valedictorian?

AM:  I was honestly a little surprised. I definitely didn’t expect that. I didn’t know how to react when I was told that, but definitely very happy. I think, I mean, it’s the biggest academic honor that one can get here at Princeton, so I feel incredibly lucky to have it. I think having gone through the process and everything, I realized that luck also plays a factor in me getting it, and I consider myself incredibly honored and lucky to have it.

JB:  What did your family think?

AM:  Oh, they were surprised and I guess very happy as well. I mean they were very proud of me, I guess.

JB:  Are they going to be able to come to the ceremony?

AM:  My mother and sister will come, looking forward to that.

JB:  Definitely. Awesome. That’s so cool. Is there anything you do differently if you could start Princeton over again?

AM:  Probably worry a little bit less about my assignments. I don’t know. Other than that, I mean, of course I’d spend more time with friends, but I think I tried that during Princeton as well. I’m not sure if I have anything else.

JB:  Fair enough. I also noticed in the University article that announced you were a valedictorian, that it mentioned that you actually kind of solved problems that some of the Princeton faculty have posed here. Can you talk a little bit about that? What’s it like to kind of go toe to toe with the faculty while you’re still a student?

AM:  Oh yeah, that’s been very interesting. I, I consider myself very lucky to have had the opportunity to work on that problem and to solve it in the end. So actually the way that came about is that I was a part of the undergraduate research experience in the University of Duluth, Minnesota. And my mentors were actually graduate students from Princeton who were working together with their adviser at the time. And they wrote this paper but they couldn’t complete all the questions that they had and they’ve let out some questions unanswered. And then of course with the help of some other people who gave me some inspiration, I tried looking at these questions and modifying their arguments slightly. I managed to solve it, but I think at least my argument is very much builds on their arguments and on their ideas from their paper. So I don’t think it’s any kind of like competitiveness or anything. I think it’s just collaboration to just try to answer some interesting questions in math. 

JB:  How has that been for you? Has it been a joy to kind of rise to that level?

AM:  Oh yeah. I think doing research in math is incredible fun. I think just that feeling of not being able to solve the problem at first and you know, it’s not like a problem on the test that, you know, the teacher knows the solution, but you just have to figure it out on the test. Generally, like, no one knows the solution to this problem. No one even knows if it’s like solvable or true or anything. So just trying to find your way around it and trying to convince yourself in the first place that it is true and then later on trying to actually provide like a formal proof, I think that’s been a very rewarding process. Very, very much different from just taking a math test.

JB:  What’s been your favorite memory over the course of your Princeton career?

AM:  I think I mentioned some of them in the interview that I did for the valedictorian story. I think a very warm memory that I have is the first semester after we were allowed to come back on campus, the restrictions were still there and COVID was still very much a thing. But that idea that we could come together and I think that’s perhaps the semester where we did it with the most joy and with the most, I think, intention, just trying to hang out together. I mentioned the story when my friends bought me a cake for my birthday and that’s been an amazing memory for me. But also all the other times that we just came out to hang out or just take a walk because usually we couldn’t hang out in the rooms because we had restrictions on that. We were just trying to get together and finding ways to do that. I think that’s, that’s been something that definitely stuck with me during Princeton. 

JB:  What do you think you’ll bring with you after you leave Princeton? What lessons or memories or takeaways?

AM:  I think I’ll definitely bring many more perspectives than I came in with. I think just the friends that I met. I actually met mostly international friends, so it’s, I think I know people from like 20-plus countries which are like close friends of mine. And then just being able to look at different issues from different perspectives and from different cultures, I think that’s something that I really built here at Princeton.

JB:  Is there anything else that I didn’t ask you that you wanted to talk about?

AM:  I don’t think so. 

JB:  Well Aleksa, congratulations again on all that you’ve achieved and thanks for speaking with me today.

PAWcast is a monthly interview podcast produced by the Princeton Alumni Weekly. If you enjoyed this episode, please subscribe. You can find us on Apple Podcasts, Google Podcasts, Spotify, and Soundcloud. You can read transcripts of every episode on our website, paw.princeton.edu. Music for this podcast is licensed from Universal Production Music.

Paw in print

Sheikh Nawaf al-Sabah ’94 in Kuwait; Tiger Travels; Why the graduate student union vote failed.

How is the distance calculated?

To calculate the distance between Bucharest and Tyumen, the place names are converted into coordinates (latitude and longitude). The respective geographic centre is used for cities, regions and countries. To calculate the distance the Haversine formula is applied.

Graduate School

Standard Requirements for All Advanced Degree Candidates

By design, Princeton emphasizes short, intensive programs of doctoral study. The Graduate School therefore has few central requirements for doctoral candidates.

To qualify for the Ph.D., students are required by the Graduate School to: 

• Pass the general examination in their subject; 
• Present an acceptable dissertation ; and
• After receiving approval of the advanced degree application from the department and the Graduate School, to pass the final public oral examination

Any additional requirements are set at the level of the department or program.

In addition to the above, the Graduate School tracks standard degree requirements that all students must meet to continue their work in good academic standing with the University. These include the major milestones that all Ph.D. students must meet in order to successfully obtain their degrees.

Administrative Standing Requirement

Students are to be in good administrative standing with the University to be awarded an advanced degree. They must be enrolled or, if enrollment has ended, continue to hold degree candidacy, and their accounts with various offices and departments must be settled.

All enrolled candidates for an advanced degree are required to complete semester sign-in and must also participate in the annual reenrollment process in the spring in order to be continued in an enrolled status in the next academic year.

Residence Requirement

The Graduate School is a community of scholars engaged in ongoing research, discussion, and scholarly exchange. Accordingly, except as approved by their departments and the Graduate School to be enrolled in absentia , candidates for advanced degrees are expected to be present on campus a majority of days per week for each academic term in order to use University resources to fulfill degree requirements and objectives. 

• All candidates for advanced degrees must spend at least one year in residence in Princeton or the vicinity. 
• Ph.D. candidates must be in residence for at least one academic year before standing for the general examination, and are expected to be in residence through the duration of their enrollment except when approved to be enrolled in absentia.

Full-time Study Requirement

Graduate study at Princeton is a full-time commitment. Graduate students are expected to pursue degree-related work and make use of University resources throughout the year, including the summer months.

Program Requirements

Program requirements vary by department and may include coursework, proficiency in foreign language(s), and exercises or preliminary exams. Address inquiries about departmental requirements to the appropriate director of graduate studies (DGS). Subject to departmental rules, Ph.D. students who have not fulfilled program requirements ordinarily will not be admitted to the third year (fifth term) of enrollment and may not sustain the general examination.

Satisfactory Academic Progress

The Graduate School and academic departments expect enrolled students to meet certain standards, as evidence of their successful engagement with graduate work and to continue to receive their stipends and other benefits of enrollment. View the Satisfactory Academic Progress Policy .

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Wie wird die Entfernung berechnet?

Um die Distanz zwischen Duisburg und Tyumen zu berechnen, werden die Ortsnamen in Koordinaten (Latitude und Longitude) umgewandelt. Hierbei werden bei Städten, Regionen und Ländern die jeweilige geografische Mitte verwendet. Zur Berechnung der Distanz wird dann die Haversine Formel angewendet.