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Undergraduate math research

I believe this is the right place to ask this, so I was wondering if anyone could give me advice on research at the undergraduate level.

I was recently accepted into the McNair Scholars program . It is a preparatory program for students who want to go on to graduate school. I am expected to submit a research topic proposal in the middle of the spring semester and study it during the summer with a mentor.

Since I am currently in the B.S. Mathematics program and I want to get my Masters later. I figured that while my topic can be in any area, it should be in math since it is my main interest as well.

I am a junior at the moment and taking: One-Dimensional Real Analysis, Intro to Numerical Methods, and Abstract Algebra. I frequently search MathWorld and Wikipedia for topics that interest me, although I don't consider myself a brilliant student or particularly strong. I have begun speaking with professors about their research also.

I have not met any other students doing undergraduate math research and my current feeling is that many or all the problems in math are far beyond my ability to research them. This may seem a little defeatist but it seems mathematics is progressively becoming more specialized. I know that there are many areas emerging in Applied mathematics but they seem to be using much higher mathematics as well.

My current interest is Abstract Algebra and Game Theory and I have been considering if there are possibilities to apply the former to the latter.

So my questions are: 1) Are my beliefs about the possibilities of undergraduate research unfounded? 2) Where can I find online math journals? 3) How can I go about finding what has been explored in areas of interest. Should I search through Wikipedia and MathWorld bibliographies and or look in the library for research?

Thanks I hope someone can help to clarify and guide me.

• soft-question
• 4 $\begingroup$ All of the papers published in the journal Involve have a significant student contribution. You can read the abstracts at their website (involvemath.org). I am not saying this is the place to go to find a research topic (or that you should attempt to find a topic on your own via the internet). But I know from experience that it can be fun and inspirational to see that your peers are researching and publishing in a variety of areas. $\endgroup$ –  user4977 Nov 13, 2010 at 2:25
• 7 $\begingroup$ Note to the advice-givers: there is also a user Metahominid at the math.SE site who has asked a few questions about basic abstract algebra and real analysis. Reading over them gives some information (far from definitive, of course) about the student and his current level, which might result in more personalized advice. $\endgroup$ –  Pete L. Clark Nov 13, 2010 at 19:26
• 3 $\begingroup$ That is me. They are basic because I am in the class. I am not trying to give the impression I can do any significant research. There have been almost no math McNair students, and I suspect this because of the difficulty. The point of the program from what I have been told so far is to look into a topic of interest, and pursue it. There is only the expectation to submit, and not that it be good or profound. Mainly it is to prepare students for the research experience. The only other math McNair students have done math education, I would prefer not to. Thank you to everyone. $\endgroup$ –  user7504 Nov 14, 2010 at 0:22
• 5 $\begingroup$ Congratulations for making it into the program. There are already tons of answers, so I won't add much to them, except to say first that undergraduate research can be extremely valuable for your development (to help you appreciate the difference between solving exercises and tackling real questions, even if someone already knows the answer btw). Ans second, a point that has already been made but cannot be stressed enough, that a successful UG research experience requires a good mentor , so find her or him first, and then worry about the topic. $\endgroup$ –  Thierry Zell Nov 16, 2010 at 18:14
• $\begingroup$ I want to say good luck! I sympathize with the challenge. I'm trying to catch up on research-level math while no longer being in school, and if I could give my younger, enrolled self one piece of advice it would be to seek out anyone who studies what you want to study and take advantage of the fact that they're enthusiastic nerds who generally want to share their fascination with the subject. $\endgroup$ –  Malice Vidrine Aug 27, 2013 at 1:02

16 Answers 16

Since you are a student who's already interested in going on to graduate school and is specifically asking about finding a topic to study at your undergraduate level program at McNair, please disregard the negative nattering nabobs whose answers and comments suggest that undergraduates have no place or business in trying to perform research, whether it's research as defined for all scientists or the "research experience" that is put together for undergraduates and for advanced high-school students. Undergraduates can definitely perform research, or even benefit from going through a structured and well-administered "research experience".

I agree with Peter Shor about finding a mentor, or multiple mentors, as soon as possible. There's no reason you have to be limited to getting advice from just one professor or teacher.

I agree with Ben Webster, specifically about speaking with professors in order to get a reasonable idea about the level of work that would be needed for you to perform useful research at an undergraduate level. A few other suggestions come to mind:

if you are at an institution that offers Masters and Ph.D. level degrees in mathematics, then your institution's library should have multiple research journals in hard-copy . I have found that it is much easier to go to the stacks in the library and browse through one or two year's worth of Tables of Contents and Abstracts in one journal in an afternoon or evening. This will familiarize you with the types of research papers being published currently, and make you aware of what "quanta" of research is enough to be a single research article.

make sure to attend Seminars, Colloquia, and (if your school's graduate students have one) any graduate research seminar courses that you can find time for. This will allow you to become more familiar with various subtopics within the topics of your interests, and to see what the current areas of interest are for local and visiting faculty members.

Colloquia are great as they often start by including a brief history of the topic by an expert in that field.

Seminars are great because they allow students to see the social aspect of math, including the give-and-take and the critical comments and requests for more detail and explanation, even by tenured faculty who don't follow a speaker's thought processes.

Graduate student seminar presentations are great because a student observes how graduate students can falter during presentations, how they are quizzed/coached/criticized/mentored/assisted by faculty during their presentations.

I'll admit that I'm not sure attending dissertation defenses would be of any serious benefit to the undergraduate student, other than observing the interaction level (animosity level?) between faculty and graduate students.

absolutely make sure to schedule some time to meet with mathematics professors who specialize in the fields of your interest, and communicate your desire to do research while you are an undergraduate, and communicate your desire to go on to graduate studies in mathematics.

look on the internet and search for undergraduate opportunities for research in mathematics. I guarantee you will find quite a number of web sites that can give you more information. MIT has an undergraduate research opportunity program that many of their students take advantage of. Your institution may have professors who can speak with you and give you advice.

Also, make sure to speak with more than one professor, and do not take any single person's advice as being the final word. Mathematicians are human beings too, and subject to the foibles and inclinations and disinclinations that all human beings have. If you run into disgruntled and critical individuals, do not let that dissuade you from going on into mathematics or decrease your desires. If you run into overly optimistic individuals who praise you too much and are too eager to take you on to do "scut work" computer programming, thank them for their time and let them know you'll come back to speak with them after you've spoken with other professors and weighed your options. Don't turn anyone down immediately. Always be polite in speaking with professors and teachers. Ask them how they chose their topics for their degrees, and you'll learn a lot.

• 29 $\begingroup$ I'm sorry, but this seems totally unrealistic. Anyone who, as an undergraduate taking real analysis and abstract algebra, can follow research-level seminars, either A) should expect the Fields Medal within a few years, or B) doesn't exist. Most of the WORDS in most seminars would be literally meaningless! For a student who already seems discouraged about their ability, this is a recipe for crushing disappointment. My advice: don't worry so much about research as an undergraduate. Find a problem you are interested in, open or not, and a professor at your school you feel you can talk to. $\endgroup$ –  Tom Church Nov 12, 2010 at 13:34
• 29 $\begingroup$ @Tom-Church, much like pre-med students who can volunteer and observe at hospitals without being able to participate (or understand all of the details) at the level of medical doctors, it is possible for students to attend research-level seminars to get an idea of the type of topics which are being discussed and are at the fore-front of research currently. How is the student going to find a problem to be interested in without at a minimum glancing at the field, reading abstracts, and seeing if the topics tickle his/her fancy? This isn't unrealistic. I, and many others, published as undergrads. $\endgroup$ –  sleepless in beantown Nov 12, 2010 at 14:06
• 26 $\begingroup$ I would encourage enthusiastic undergraduates to attend colloquia (meant for general audiences of mathematicians), not necessarily just to follow research trends, but also to watch interactions between mathematicians. Eavesdropping on mathematicians at tea can be interesting too. The point is that mathematics is intensely social, and it's good to see what mathematics and mathematicians are like away from books, articles, and lectures. If OP maintains a healthy balance between "I've got a lot to learn" and "this looks like fun, and something I want to do", where's the harm in it? $\endgroup$ –  Todd Trimble ♦ Nov 12, 2010 at 16:36
• $\begingroup$ Colloquia are great as they often start by including a brief history of the topic by an expert in that field. Seminars are great because they allow students to see the social aspect of math, including the give-and-take and the critical comments and requests for more detail and explanation, even by tenured faculty who don't follow a speaker's thought processes. Graduate student seminar presentations are great because a student observes how graduate students can falter during presentations, how they are quizzed/coached/criticized/mentored by faculty during their presentations. $\endgroup$ –  sleepless in beantown Nov 13, 2010 at 0:20
• 9 $\begingroup$ sleepless: your advice is the essence of good common sense, and I am sure that the OP will benefit from it if they take it at heart. When I was an undergrad, we attended talks made for us, but the faculty would attend too and the questions at the end could get serious (this is where I heard the term "gauge theory" for the first time). We were also encouraged to attend regular seminars with no expectations that we would understand anything , but, as one person said, for the music . You get the music first, then you add in the lyrics. $\endgroup$ –  Thierry Zell Nov 16, 2010 at 18:29

As an undergraduate in the US with some research experience, let me offer my take on the situation.

1) I think it's important not to have a finished product (that is, a piece of original research) as the end goal. This past summer I did some research through MIT's SPUR program, and this is their definition of success:

Significant progress, relative to one's own background and experience, in developing interests, satisfaction, skill, and ideas, rather than getting the complete solution to a problem.

I think this is a really nice sentiment. The goal is not for you to start making serious contributions to mathematics but to prepare you in several ways for a graduate experience. (If you're curious, I blogged a little about my research here and for several posts afterwards. I did not prove a new result, but I learned a lot and thought it was a valuable experience.)

2) It depends on what your institution has subscriptions to. Click around on scholar.google.com to see what you can access without paying for. Many institutions, for example, have access to JSTOR or SpringerLink .

3) Find someone who knows the subject and ask them to mentor you. Or, find a mentor and ask them for a subject. This is hard to do without guidance.

Let me also give you some advice you didn't ask for. If you are seriously planning on graduate studies, I think you should expand your mathematical worldview as much as possible beforehand. The easiest way to do that, in my opinion, is to read math blogs. I recommend starting with Terence Tao's and Tim Gowers' and working from there, and I also recommend John Baez's This Week's Finds (actually, read the rest of his stuff too). Math blogs are a valuable source of insight into mathematics and how mathematicians work, and these three are particularly interesting and well-written. Terence Tao's blog also contains his career advice, which is worth a read.

• 1 $\begingroup$ @Qiaochu-Yuan, excellent answer,+1. Also, the mathematics department may have its own internal library room/area, with hardcopy issues of journals that may not be in the main library or in the Barker engineering library. I still find that quickly skimming through the table of contents and abstracts is a good way to get an overview of what's going on in a particular field, and then being able to drill down into a topic by reading an article if the abstract catches my interest. The blogs you pointed out are excellent, particularly for the career advice. $\endgroup$ –  sleepless in beantown Nov 13, 2010 at 0:36
• 1 $\begingroup$ Yes, very good. The "problem-solving" model is invidious, as is the "no-previous-experience-required" idea. Awareness (not "originality", not fussiness over small, long-done details) is perhaps the most important goal for a beginning grad student. All the sadder that some REU's and other potentially encouraging, uplifting experiences give people the idea that they're "already done" in terms of knowledge, awareness, etc. $\endgroup$ –  paul garrett Aug 27, 2013 at 1:18
• $\begingroup$ The link to SpringerLink is broken; the site can now be found at link.springer.com . The link to MIT's SPUR program is also broken. The current website does not appear to contain the mentioned quote, but that can be seen in a snapshot preserved at the Wayback Machine. $\endgroup$ –  The Amplitwist May 3, 2023 at 19:13

There are quite a few undergrads who have done significant research in mathematics at your level. Even if you don't end up with a published paper (you shouldn't expect this, although it probably happens more often than you might expect), you will gain significant experience into what doing original research in mathematics means. However, I think expecting to find a problem to work on yourself, rather than have a mentor suggest one (or several) to you, is absolutely unrealistic . Maybe it's realistic for other fields, but in my opinion not mathematics.

Find a mentor who is willing to suggest a problem that you can tackle at your level, and (hopefully) give you ideas during the summer if you get stuck. Finding the right problems to work on is a major component of doing mathematical research, and sometimes the hardest one. If you find it on your own (rather than a mentor suggesting it), your mentor is likely not going to have any good ideas of how to attack it, it may end up a harder problem than is realistic for you to solve, and your mentor will be less motivated to help you. So my advice is to start looking for mentors now.

• $\begingroup$ Pity if the faculty in the environment are less able to think new thoughts than the student... though I suppose it happens all too often, given various dynamics. But, "srsly", one doesn't want a mentor to feel superior-to, in any case, indeed, for sure. $\endgroup$ –  paul garrett Aug 27, 2013 at 1:15

So on the one hand I have a very strong cultural bias against undergraduate research programs. I don't think trying to emphasize originality is a good idea. I think it would be much better to give people problems to work on that have already been solved and so you know lead to good and interesting mathematics. By forcing people to work on "new" questions I think you are often forcing them to work on bad math.

On the other hand, just because I think it would be better for people to do other sorts of programs, REU-style programs are what exist and they seem to work reasonably well for a lot of people. Furthermore, they're certainly valuable as an alternative to classroom learning. Real math research is not like what happens at most REUs, but it's also not like what happens in a classroom, so doing an REU is still going to help you get closer to understanding the scope of what a graduate student does.

So yes it's certainly possible and somewhat valuable for undergraduates to try to do "research," but you shouldn't expect that research to be the same sort of research that mathematicians are really doing.

• 3 $\begingroup$ What's "bad math"? $\endgroup$ –  Igor Belegradek Nov 13, 2010 at 3:25
• 13 $\begingroup$ Bad math may mean problems which are open because they seem uninteresting, or not clearly connected to anything. Working on odd, tedious but open problems may allow a student to do original work, but might be worse than a course for learning or for stimulating interest. $\endgroup$ –  Douglas Zare Nov 13, 2010 at 4:00
• 3 $\begingroup$ Of course, I solved this issue during my REU experience by working on a problem that had been solved 40 years previously (and was actually easy, when viewed correctly), though neither my mentor or I knew this. $\endgroup$ –  Ben Webster ♦ Nov 13, 2010 at 7:17
• 2 $\begingroup$ Several points: "bad" math includes artificial problems, and problems posed as though they were mysteries, when they are not. Also, is it always about "problems"? This, too, is corruptive. I'd not tell people to work to understand something by_prescribed_means , but to understand it however they can. And that surely many important things are already understood (by hard-working, able people), but everyone has to get themselves caught up to the present. The "standard" that genuinely worthwhile new contributions be made by people who don't know anything is both a vicious fiction... $\endgroup$ –  paul garrett Aug 27, 2013 at 1:12
• 1 $\begingroup$ @PaulGarrett: I think some of your points are overstated. It is true that most REU's address questions that don't really matter to mathematics, but there are exceptions. For instance, your colleague Vic Reiner has a good record of getting interesting research out of undergrads. My own approach to running REU's is based on the observation that many serious research papers have two parts: a reduction via sophisticated techniques to a concrete question of combinatorics, linear algebra, or calculus, and then an ad hoc treatment of that concrete question. Undergraduates can solve these concrete... $\endgroup$ –  Michael Zieve Aug 30, 2013 at 14:44

Your beliefs are somewhat unfounded; lots of people (for example, me) do research in various fora as undergrads, and in fact, the NSF is pushing undergrad research quite hard nowadays.

On the other hand, it's not something that's easy to do on your own. While you may get some other reasonable suggestions from people, there's an obvious first step here, which is talking to a professor (possibly several). Decide on the mentor, and then have them help you prepare the research proposal. As an undergraduate, trying to go out and find articles on your own without any direction is like searching for a needle in a haystack. You might find something cool, but I wouldn't recommend it as a first approach.

• 21 $\begingroup$ You say "lots of people (for example, me) do research in various fora as undergrads..." Interesting, but extremely unusual in my experience. To my knowledge, almost no undergrads at my university ( or any subsequent places I went to as a graduate and teacher ) did ( or would have been capable of ) any proper research at all (apart from small little "projects" and "investigations"). Still, that was back in the nineties in England, so maybe it doesn't apply here. The NSF sounds totally crazy to me, but I admit I'm not qualified to judge. $\endgroup$ –  Zen Harper Nov 12, 2010 at 10:07
• 3 $\begingroup$ In my (limited but recent) experience, undergrad research is encouraged much more in the US than the UK, and thought of as more achievable. In the UK (my own undergrad was Cambridge, early 2000’s) we weren’t for the most part encouraged to think of research as something accessible to us at all as undergraduates, like Zen Harper says. In the US (my own grad school, and what I've seen at other schools) it's widely encouraged (though not ubiquitous or essential); and it turns out that undergrads, with good mentoring, can often reach some non-trivial original work. (ct’d) $\endgroup$ –  Peter LeFanu Lumsdaine Nov 12, 2010 at 17:30
• 4 $\begingroup$ …so I think there may be a bit of “if you don’t believe you can do it, then you can’t”: in the UK, we don’t have expectations that it’s achievable, and we don't have much of a model or experience of how to do it, without which our expectations of impossiblity are pretty much correct! (I don’t mean to disparage the teachers I had in the UK, by the way: they were excellent, and encouraged us in many useful directions; undergraduate research just wasn’t one of them.) $\endgroup$ –  Peter LeFanu Lumsdaine Nov 12, 2010 at 17:36
• 4 $\begingroup$ Felipe- I (obviously) don't think this advice is over-optimistic at all. Maybe the McNair Scholars program is too optimistic, but that's an issue you should take up with them. I'm not sure "over-optimistic" is really the right characterization of the problem in MO advice; I still think its more of an issue of getting advice from people who don't really understand your situation, as Zen as demonstrated. There are so many details necessary for getting good advice on these professional issues that "Go talk to someone who actually knows you" is essentially always the right advice. $\endgroup$ –  Ben Webster ♦ Nov 12, 2010 at 19:48
• 8 $\begingroup$ Qiaochu: while I hope you are enjoying Cambridge, I suggest you try the sentence "the structure of the UK system means that students are all at fairly similar levels of mathematical maturity and knowledge as they progress" out on some people and see what their reaction is ;-) Let me just say that Cambridge is not a representative sample of UK tertiary maths education... $\endgroup$ –  Yemon Choi Nov 13, 2010 at 0:23

" I am a junior at the moment and taking: One Dimensional Real Analysis, Intro to Numerical Methods, and Abstract Algebra ".

Based on this information, I think it is a complete waste of your time even to consider research seriously at this stage; you need several more years of study as a minimum. Right now, you are still learning the basic language of mathematics. It's similar to, say, a student who wants to begin reading classical German literature, but only knows 100 words -- premature, to say the least. The maths you know right now is probably less than 1% of what you will need. Even after my Ph.D., I feel that my knowledge is very limited in comparison to most good researchers.

But do you really mean "research", i.e. new, original, nontrivial and interesting, and publishable in a good quality journal, i.e. one which your professors would publish in?

Or do you mean a kind of "investigation" or "project" instead? These are not required or expected to contain anything new or original. This would be highly worthwhile -- but only for your personal interest and satisfaction.

The question is, what do you expect to get out of it? If you're at a good university, their lecture courses should already provide you with all you need.

Please don't take offense, and apologies if I've formed the wrong impression, but it sounds to me ( from your statement "I have begun speaking with professors about their research also" ) like you might be the kind of student that irritates professors, always bugging them and asking them questions about their own research, but lacking the knowledge to understand the answers. ( But it's not your fault you lack knowledge - that's what you're at university to learn! ) As an analogy, imagine a ten-year-old, knowing nothing more than how to add fractions, constantly harrassing you to teach them about calculus; my response (unless I were in a very good mood that day) would be: " go back to school and stop bothering me, for at least another 3 years! " Unless you're an exceptionally good, enthusiastic student, or your professors are far more patient than me, that might be what they're thinking also, but are too polite to tell you.

But just my opinion, don't take my word for it; why don't you ask them directly if that's what they're thinking?!

• 13 $\begingroup$ +1: Why was this answer down-voted? Are you suggesting that juniors are ready to do research? $\endgroup$ –  Douglas S. Stones Nov 12, 2010 at 12:38
• 30 $\begingroup$ I think it is possible to find a suitable project for a math-interested student at any level. For example, I would be happy to discuss calculus with any ten-year-old who was interested enough to learn about it; it would be an excuse to talk about graphs and rates of change and the concept of limits and the effect of minute changes. One can explain a part of these ideas even to someone with little background. Similarly, one can find an interesting suitable project for an undergraduate. The surreal numbers, for example, would be an attractive topic at the boundary of algebra and game theory. $\endgroup$ –  Joel David Hamkins Nov 12, 2010 at 14:20
• 40 $\begingroup$ The down vote might have been because the same thoughts could have been conveyed in a much more polite manner (just a guess). $\endgroup$ –  BCnrd Nov 12, 2010 at 14:20
• 17 $\begingroup$ Agree with BCnrd. "like you might be the kind of student that irritates professors, always bugging them and asking them questions about their own research, but lacking the knowledge to understand the answers" - isn't that reading a bit much into it? OP said "research at the undergraduate level", which I take to mean investigations into subjects he finds attractive, not publishing in the Annals as an undergraduate. Also, "their lecture courses should already provide you with all you need" - are books and papers all that pros need? One-on-one conversation is something we all benefit from. $\endgroup$ –  Todd Trimble ♦ Nov 12, 2010 at 14:56
• 28 $\begingroup$ -1: This answer latches on to one fact about the student while ignoring another big one: the OP is in a structured program, not just doing this on a lark. You can, of course, doubt whether that program will produce very high quality research; I think most of us do. But that's not really the point of such programs. They're mainly aimed at grad school preparation/promotion. Frankly, students need to do something over the summer, and they may as well have a experience that shows them mathematics from another angle than just the classroom. $\endgroup$ –  Ben Webster ♦ Nov 12, 2010 at 17:46

Metahominid,

I am an undergraduate myself who was in a situation two years ago similar to the one you're in right now. As a sophomore (I'm a senior now), I wanted to do some sort of research but I hadn't taken that many courses. I was just taking real analysis and abstract algebra at the time. However, I asked around the math department for research opportunities algebra and game theory (yes, even my interests were similar!) and a professor recommended another professor to me who had just what I was looking for: an approach to combinatorial game theory using algebra (and a little bit of geometry). I have been working on this topic with him since the summer after my sophomore year. Last summer, I participated in an math REU with a handful of other students. Research in the REU was more independent, with the students doing pretty much all of the work while the mentors served more as helpful sounding boards than co-researchers. Here are the differences I have found between the two research experiences:

Research with professor

Since the problems I am working on are of direct interest to my professor as well, the topics I have to learn in order to even begin to approach the research tend to be more advanced, so I end up learning a lot of interesting theory (my research has led me into combinatorial commutative algebra and local cohomology)

Again, since the professor is working on this with me, I spend a great deal of time talking with him, bouncing ideas back and forth, and this creates a very strong mentor-student relationship that I feel is very beneficial. My mentor gives me advice not just on how to do math, but also on applying to graduate schools, writing good papers and abstracts, giving talks and presentations, etc.

As the students were expected to work independently of the professor, I was thrown into the deep end basically. What entailed were weeks of intensive reading and thinking. Although the mentor was there to help me make sure I was sane by letting me bounce ideas off him, I was still responsible for all of the original thinking and problem solving. The benefits of this are absurdly great: my problem solving skills have improved greatly and I find it far easier to follow lectures and do homework problems now. In fact, math classes feel like nothing now that I have done some research on my own.

We were free to work with other students, and I did collaborate with a few students, which I think is an invaluable experience. By talking to these students every day, I learned different ways of thinking about things, and different approaches to solving problems. Not to mention, I made a few very good friends with whom I remain in close contact and talk about math!

I got to do some nontrivial original work (although I wouldn't say the problems I solved were important) and wrote some publishable material. This needn't happen, though. The point is to get the experience.

The bottom line is this: if you're eager to do research, ask around for professors who are looking for motivated undergraduate students. Make sure they know that you are motivated and willing to learn and work hard. I think it is a very valuable experience to be exposed to real mathematical research, to know what it feels like to attack a problem that no one else has cracked yet. It's completely different from coursework. I never considered myself particularly talented at mathematics, but over the years I have realized that being good at doing math is much more about practice and experience rather than some "natural" talent. I also highly recommend one of the NSF sponsored REUs, as the mentors are usually very skilled at picking problems that are at an appropriate level for undergraduate students. I hope this helped.

The following might be more appropriate as a comment to sleepless in beantown's answer instead of an answer, but for some reason I am not able to comment.

The following website of the AMS contains numerous links to Research Experience for Undergraduates (REU) programs

http://www.ams.org/programs/students/undergrad/emp-reu

If I understand correctly, these REU programs are funded by the NSF to offer undergraduate students (not necessarily from the institution that is hosting the program) an opportunity to do research, under supervison, over the summer. (Since there was some debate what "research" should mean, I add that here "research" means, or at least can mean [and not only rarely], something that in the end is published in well-established mathematical research journals.)

Also, there is a somewhat recently founded journal Involve specifically dedicated to "showcasing and encouraging high quality mathematical research involving students (at all levels)"

http://pjm.math.berkeley.edu/involve/about/journal/about.html

• 1 $\begingroup$ Hi, unknown (you can register and add a name or nickname also), you couldn't add a comment because you don't have 50 reputation points yet. Thanks for the comment/reply. I hadn't head about the AMS REU program web site. $\endgroup$ –  sleepless in beantown Nov 12, 2010 at 14:19

The web site on the McNair Graduate Opportunity program gives no indication that mathematics students were in mind, and a quick survey of some past students' topics showed none in mathematics. I do not think the program was designed for mathematics students or the way mathematics research is done, even undergraduate mathematics research.

Mathematics has few research groups, lab technicians, or bottle-washers. We usually do mathematics with 1-2 people involved. In other areas, you can learn to run some tests, and collect data, and analyze it with the help of an advisor. You have a very high chance of accomplishing something, and meanwhile you can try to learn how your work fits into a larger picture. Most mathematical projects are more risky. It takes a lot of work as an advisor to create a project approachable by an above average mathematics major which has a good chance to produce new results the student can write up. Much of mathematics does not involve programming, but many projects designed for short-term results are programming exercises which may give a distorted picture of mathematics.

This is not to say that undergraduate research is not worth the attempt. It is one way to see that mathematics is alive and exciting, which may be hard to see from courses. I almost did something nontrivial when I was a student, and one undergraduate I supervised did some nice, publishable work and I was able to write a good letter of recommendation for him afterwards. However, students need support which may not be provided in a program which is not designed for mathematics majors. You need an advisor who will put a lot of effort in (even in choosing the topic) beyond what is needed in other areas. You should be aware that failing to solve the problem is often not a surprise, and that you may be severely handicapped with only one year of solid mathematics courses.

I think you should look at alternatives such as mathematics Research Experiences for Undergraduates (REUs) or setting up a reading course in which the goal is not to produce new research, but to understand some recent result or paper, perhaps to create a more accessible exposition of that topic.

• 7 $\begingroup$ After looking over the McNair website, I agree completely. I didn't see anything oriented towards math specifically, and this makes me skeptical -- the way math is done is quite different from that of other academic endeavors. I was especially concerned by something on the website that said that creation of a paper of "publishable quality" was a requirement of the program. In my opinion this is not a realistic goal for undergrad summer research. If I were the OP, I would consider either doing the summer research in something else, or, if math is truly of interest, applying for an REU. $\endgroup$ –  Pete L. Clark Nov 13, 2010 at 7:08
• 4 $\begingroup$ I ran out of space in my last comment, but let me give one reason an REU is a better bet for summer math study than this McNair Program: in REUs there is a guaranteed cohort of other students to interact with and derive support from. $\endgroup$ –  Pete L. Clark Nov 13, 2010 at 7:11
• $\begingroup$ Sorry I didn't mention that. It is pretty much an REU. It is a TRIO program and I do have a cohort, although they are not in my field. I will be living with them in the summer as well as students from other universities. $\endgroup$ –  user7504 Nov 14, 2010 at 3:08
• 3 $\begingroup$ @Metahominid: if the other students are not doing math, then they will be able to support you in some ways but not others -- for instance, you cannot ask them casual questions that you might not want to bother your mentor with. I think an REU would be better for this. $\endgroup$ –  Pete L. Clark Nov 14, 2010 at 7:41
• $\begingroup$ @Pete L. Clark I recognize this however I have already been accepted and I cannot do both this summer and I am not sure if I will be able to my senior year's summer. $\endgroup$ –  user7504 Nov 14, 2010 at 9:34

I think the earlier one starts doing research the better, even if it is a research in plane geometry.

I directed a few REU's and it was great fun; the only problem is that it is hard to do anything significant in 8 weeks. I am confident that many US undergrads can produce a publishable work after focusing on a problem for 1-2 years.

In the place where I went in college (Novosibirk, Russia, mid 80s) students went through abstract algebra and real analysis in the first two years and the best of them them could do nontrivial work in the 3rd year. Quite a few people were going to research seminars in 3-4th year, which they had to be doing since a (master) thesis with original research was expected at the end of 5th year. As it happens for many students this thesis was largely expository, but those who later become professional mathematicians usually got something publishable in the 5th year. My own research in the 4th year went nowhere, but in the 5th year I proved something I am not ashamed of.

• $\begingroup$ Although the OP is in his 3rd year, it doesn't sound like he would fit into the third year of the college you describe by the courses he is currently taking. In many US colleges, mathematics majors spend a lot of their first two years taking classes outside mathematics. $\endgroup$ –  Douglas Zare Nov 13, 2010 at 4:14
• 1 $\begingroup$ Douglas, I am fully aware that US system is different (having taught here for many years). My points are (a) those who want to become mathmaticians should try research long before they pass comprehensive and oral exams in grad school (b) with proper mentoring math research is quite doable. $\endgroup$ –  Igor Belegradek Nov 13, 2010 at 12:13
• $\begingroup$ Thank you Igor. One of my good friends in my math classes is from Russia. From what he has told me and I have read both the secondary and post-secondary schooling emphasizes math more and introduces many things earlier. I wish that were the case here. I also wish the culture for chess were the same. $\endgroup$ –  user7504 Nov 14, 2010 at 3:06
• $\begingroup$ @Metahominid, the system in Russia is different and I cannot say it is better, but it does prove that original research by undergraduates is quite possible. Some in this thread seem to argue that a student is better off by delaying research till grad school, and I disagree. $\endgroup$ –  Igor Belegradek Nov 14, 2010 at 12:32
• 1 $\begingroup$ There are two different issues being confounded throughout, for unfortunate semantic reasons. If "research" means "thinking" (as opposed to obeying, conforming, guessing what's on the final), well, yes, this is a fundamental scientific/intellectual trait. But if "research" means to do better than all existing professionals on an issue meaningful and interesting to them... well, let's think... maybe this is not something to be counted-on on a regular basis. Sometimes kids are in stark, low-energy situations, which is bad, but let's not deceive them about the larger world. Yes, thinking is good. $\endgroup$ –  paul garrett Aug 27, 2013 at 1:22

Most major topics have been covered in discussion, so just two remarks/experiences:

While director of graduate studies at Northwestern (2007-2010), I led a committee which valued undergraduate preparedness over research experience. So at least as far as Northwestern was concerned during that time frame, research (especially research for which an undergrad may not be fully prepared) did not help as much as you might have thought.

In trying to use RTG funds toward undergraduates, rather than try to simulate a research environment, I and my co-PI's created an "undergraduate conference" to try to offer a supplement to standard undergraduate curricula, without yet getting on toward research. Here is the link: http://www.math.northwestern.edu/summerconference/ Maybe we'll do it again next year?

• 1 $\begingroup$ I can see why research experience is not a good way to select grad students, and that good bases are fundamental. But its usefulness is upstream: a serious research experience is a very good way for a student to figure out if they want to go to graduate school in the first place. In that respect, I think it plays a very educational role (I wish all of our secondary-math majors did REU-like intensive research, if only to have teachers out there with an understanding of what professional math is like.) $\endgroup$ –  Thierry Zell Nov 16, 2010 at 18:33
• 1 $\begingroup$ We need a different name for "undergraduate mathematics research"... I am very enthusiastic about getting people out of textbook/school-math/artificial/adversarial settings, but "exploration" is not "research", or else the latter term has become meaningless. I rant endlessly to my students about the evils of "school-math", and also about accidentally believing that one's voyage of discovery is "research" that should be published... as necessary as this voyage is. Confounding substantially different things is not helpful. $\endgroup$ –  paul garrett Aug 27, 2013 at 1:03

Yesterday I proved a small fact and asked a follow-up question in this answer:

Algebras over the little disks operad

It's fairly elementary, I'd be interested to know more about it, and I have never seen anything like it in the literature (although I have not searched). So you could look at that if you wanted to. More generally, there are plenty of problems like this, but they are not always easy to find. If you just start reading books and looking for things to research there is a danger that you will just be led along the best-travelled paths where enormous amounts of work have already been done. So I would second the advice to ask several professors for suggestions before deciding on a topic.

I have to disagree with the sentiment that undergraduate research (that is, research done by students who are actually at the undergraduate level in their studies, like the OP) is premature or somehow not worthwhile. A month into my first abstract algebra class, I approached my professor to talk about research and what I should do to get to that level. Luckily for me, this professor went a step further and actually gave me a choice of things to work on.

Now granted, I doubt this is the norm. My college did not have a graduate program, which made undergraduates more of the center of attention and moreover this particular professor has a keen interest in fostering undergraduate research. However, I think it is worthwhile to a student to pursue it (even if your professors aren't interested or don't have a problem at your level to give you, as has been mentioned there are always REUs) for the following reasons:

You see a different facet of mathematics then you typically see in a course or textbook. Those are realms of proven things (generally speaking; I am sure there are exceptions, but the usual undergraduate topics tend to be fully developed in my experience). On the other hand, research is messy, with missteps and "mathematicians block" and the thrill of showing something new. I think the potential mathematician should see that as soon as possible!

You gain a wealth of valuable insight and skills. At least for me, I grew very comfortable with TeX, got a good deal of experience with presenting mathematics, and learned a lot about effectively explaining mathematics on paper as well.

If you are lucky like I was, this initial collaboration can lead to more research, hence more time honing your intuition, research habits, and paper-writing skills.

In other words, sure, you are probably not going to see an undergraduate solve a particularly interesting problem, but surely it is worthwhile to promote growth of these skills as well (not to mention that, frankly, in the competitive world we live in it wouldn't hurt to have your name on some papers and some professors seeing you talk at workshops and things). On a personal note, I have to say I found that there was feedback between positive research and my courses: the more I learned, the more tools I had to attack problems obviously but the research aspect really improved my ability to see the solutions to exercises and grasp the larger picture of the courses I took.

Bottom line, for an aspiring mathematician there is nothing to lose and everything to gain, so you should definitely see what is out there and try to get involved with some research.

You might want to start looking for a mentor before you get too deeply involved in developing your project. It's great to have some broad ideas, but it isn't a good idea to box yourself in so far that your project isn't a good fit for those on the faculty who might be interested in mentoring you over the summer. Also, potential mentors might have some ideas for projects that would be a good fit for both you and the mentor.

Before you start approaching potential mentors, be sure to check with your McNair program to find out what the program expects of the mentor (for example, the mentor might be expected to write a brief biweekly status report commenting on your progress, as well as validating that you have met milestones for your project). You might want to develop your project proposal with your mentor and to start working together on a realistic set of milestones. The McNair program here tied a large chunk of the summer stipend to meeting milestones.

Have there been other McNair scholars in math at your school in previous years? You might check with your school's McNair program, your department head, and/or your coursework advisor about this. If there have been others, you might also get some tips about potential mentors. You might also check with your coursework advisor or your department head about which faculty members have mentored undergraduate research students. Did you submit letters of recommendation as part of your application? If so, you might want to share your good news with your letter writers and ask their advice concerning potential mentors.

Please don't worry about finding a big result. This is an opportunity to get a taste of research and to learn about some new topics. You will probably be expected to write up what you learned at the end of the summer and present at a conference for McNair scholars. Good luck!

I cannot speak from the point of view of a Math major in US since I never was one. I completed my undergraduate studies in engineering and currently pursuing a Ph.D. in pure mathematics. In my opinion, applied mathematics (though admittedly this quite a generic term) would be more accessible to an undergraduate considering research than pure Mathematics. I ended up publishing two single author papers in respected journals while in my senior year. I had started working on both these problems during my junior and both of them were picked by me. When I though I had a good insight into the problems, I approached the faculty within my university for suggestions. I think it is safe to say that a lot of problems in applied mathematics require less sophisticated machinery than is used by most pure mathematicians. Many of my engineering friends started working on their Ph.D. thesis problems fresh out of a Bachelors in areas which could be termed as applied mathematics. This contrasts with most pure math grad students I know who usually spend between 1 to 3 years of coursework before starting to work on a concrete research problem. So it seems that "undergraduate level coursework" would be sufficient in handling a good number of applied math problems. So if you are advanced undergraduate student with a good background in one such allied area, I think it might be worthwhile to explore this possibility. After all you can gain valuable experience doing research even if you do decide to pursue some other area of math in your graduate life.

• 8 $\begingroup$ I was not implying that anyone who wishes to become a pure math researcher should consider applied mathematics research as an undergrad. This was specifically directed to the OP since the OP mentioned taking a class in numerical methods, an interest in game theory and having considered applied mathematics as a research option. $\endgroup$ –  Timothy Wagner Nov 12, 2010 at 22:52
• 1 $\begingroup$ It is also worth considering that part of the purpose of summer REU's is to discover what sort of research one might or might not want to do later. Besides, knowing some applied math is almost certainly bound to help even the most "pure" mathematician, since the origins of much of the best mathematics lie in very real problems. (I spent two summers trying to learn quantum field theory under the ultimately mistaken impression I wanted to do physics, and I would not say the time was wasted.) $\endgroup$ –  Dave Anderson Nov 13, 2010 at 4:47
• 1 $\begingroup$ I cannot agree more. To add to that, the number of first rate pure mathematicians who have made significant progress in applied math areas keeps increasing. For e.g. Tao (Compressed sensing), Mumford (computer vision, pattern theory) and those with a non math background, Raoull Bott (Electrical Network theory), Harish Chandra (theoretical physics) come to mind. $\endgroup$ –  Timothy Wagner Nov 13, 2010 at 5:11
• 10 $\begingroup$ Harry- That's a fairly ridiculous position; intellectual development and careers do not proceed in an entirely linear manner. I'm not sure I would strongly recommend applied math research to someone who ultimately was planning on going into pure math, but it can surely still be a valuable experience for them. But more to the point, no undergrad should proceed with their life as though it was absolutely certain that they would end up in a particular career. Given the job situation at the moment, I bet a lot of people trained in pure mathematics would be happy to go back in time and (cont'd) $\endgroup$ –  Ben Webster ♦ Nov 14, 2010 at 8:45
• 4 $\begingroup$ spend more time getting experience with applied mathematics as an undergrad. $\endgroup$ –  Ben Webster ♦ Nov 14, 2010 at 8:46

Since you are interested in game theory, one area you could consider is "Algorithmic Game Theory" (basically Algorithm Design + Game Theory) It is a now a fairly hot area in theoretical computer science but still seems relatively approachable to an undergraduate with knowledge of game theory. If you can find someone willing/able to mentor you in this area I think there is good potential for a productive experience.

There is a free textbook online and the blog of Noam Nisan (a leader in the field) is a good place to follow the latest developments.

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Research Experience for Undergraduates (REUs) are summer programs sponsored by the National Science Foundation (NSF). REUs usually consist of two parts: intensive study of topics through lecture and interaction, and student research on a question/questions. Travel costs are paid for as well as room and board. A stipend is given to participants. These are all available on a competitive basis. Students that participate in REUs often present their research at national meetings.

Finding and Applying for REUs

Both AMS and the NSF keep current lists of math REUs.  Most deadlines for the summer programs are in February and March.

AMS list of REU sites

NSF list of REU sites

More Information

Not sure what it would be like to participate in an REU? Take a look at this article from our archives:  Is an REU for you?

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Undergraduate Research

Where to start:.

A good starting point is the Harvard College Undergraduate Research and Fellowships page. The Office of Undergraduate Research and Fellowships administers research programs for Harvard College undergraduates. Check out the website . Another resource is OCS , the Harvard Office of Career Services. It offers help on preparing a CV or cover letters and gives advice on how to network, interview, etc. Their website is here . Other Sources that can provide additional information on Scholarships, awards, and other grants:

• Committee on General Scholarships: more …
• Office of International Programs: more …
• Student Employment Office: more …

Independent study in Mathematics

Students who would like to do some independent study or a reading class please read the pamphlet page . about Math 91r.

THE ANNUAL OCS SUMMER OPPORTUNITIES FAIR

The Office of Career Services hosts summer programs to help you begin your summer search. Programs are both Harvard affiliated and public or private sector and include internships, public service, funding, travel, and research (URAF staff will be there to answer your questions!). Check out the website.

Harvard-Amgen Scholars program in Biotechnology

Check out the Harvard-Amgen Scholars Program Learn about Harvard’s Amgen 10-week intensive summer research program, one of ten Amgen U.S. programs that support research in biotechnology. The Harvard program includes faculty projects in FAS science departments, SEAS, the Wyss Institute for Biologically-inspired Engineering, and the School of Medicine, open to rising juniors and seniors in biotechnology-related fields.

PRIMO program

The Program for research in Markets and Organizations (PRIMO) is a 10-week program for Harvard undergraduates who wish to work closely with Harvard Business School faculty on research projects.

Harvard Undergraduate Research Events

• Wednesday, October 10, 12:00-1: 20 PM – Fall Undergraduate Research Spotlight. Come and meet Harvard undergraduate peers who will showcase their research projects and share their experiences conducting research at Harvard and abroad, followed by reception and deserts. Event program and list of presentations can be found here: here (pizza and desserts while supplies last). Free for Harvard students. Cabot Library 1st floor Discovery Bar.
• Wednesday, October 17, 12:00-1: 00 PM – Undergraduate Science Research Workshop. Workshop facilitators Dr. Margaret A. Lynch, (Assoc. Director of Science #Education) and Dr. Anna Babakhanyan, (Undergraduate Research Advisor) will help Harvard students learn about science research landscape at Harvard. You will learn about what kind of research (basic science vs. clinical, various research areas) is available at Harvard, where you can conduct research, the types of undergraduate research appointments, how to find a lab that fits, interviewing and more. In addition, the workshop will provide strategies for students to prepare for the Annual HUROS Fair, see below. No registration is required for this event (pizza while supplies last). Free for all Harvard students. Cabot Library first floor Discover Bar. More.

Outside Programs

Caltech always announces two summer research opportunities available to continuing undergraduate students. Examples: WAVE Student-Faculty Programs The WAVE Fellows program provides support for talented undergraduates intent on pursuing a Ph.D. to conduct a 10-week summer research project at Caltech. And then there is the AMGEN Scholars program. See the website for more details.

Johns Hopkins Summer 2018 Opportunities

The Johns Hopkins University Center for Talented Youth (CTY) is seeking instructors and teaching assistants for our summer programs. CTY offers challenging academic programs for highly talented elementary, middle, and high school students from across the country and around the world. Positions are available at residential and day sites at colleges, universities, and schools on the East and West coasts, as well as internationally in Hong Kong. Website

Math REU list from AMS

Mellon Mays opportunities awareness

The Mellon Mays Undergraduate Fellowship Program ( MMUF ) selects ten students in their sophomore year to join a tightly-knit research community during junior and senior years to conduct independent research in close collaboration with a faculty mentor. Join us at this information session to find out more about the program. MMUF exists to counter the under-representation of minority groups on college and university faculties nationwide through activities designed to encourage the pursuit of the Ph.D. in the humanities and core sciences.

MIT Amgen and UROP

You may be familiar with the Amgen Scholars Program, a summer research program in science and biotechnology. The Massachusetts Institute of Technology is a participant in the Amgen-UROP Scholars Program for a ninth year. UROP is MIT’s Undergraduate Research Opportunities Program. The mission of the Amgen-UROP Scholars Program is to provide students with a strong science research experience that may be pivotal in their undergraduate career, cultivate a passion for science, encourage the pursuit of graduate studies in the sciences, and stimulate interest in research and scientific careers. MIT is delighted to invite undergraduate students from other colleges and universities to join our research enterprise. We value the knowledge, experience, and enthusiasm these young scholars will bring to our campus and appreciate this opportunity to build a relationship with your faculty and campus.

More REU's, not only math

The National Science Foundation Research Experiences for Undergraduates (REU) NSF funds a large number of research opportunities for undergraduate students through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific research project, where he/she works closely with the faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduate students supported with NSF funds must be citizens or permanent residents of the United States or its possessions. An REU Site may be at either the US or foreign location. By using the web page , search for an REU Site, you may examine opportunities in the subject areas supported by various NSF units. Also, you may search by keywords to identify sites in particular research areas or with certain features, such as a particular location. Students must contact the individual sites for information and application materials. NSF does not have application materials and does not select student participants. A contact person and contact information are listed for each site.

Here is a link with more information about summer programs for undergraduates at NSA: NSA The most math-related one is DSP, but those students who are more interested in computer science could also look at, say, CES SP. They are all paid with benefits and housing is covered. Note that application deadlines are pretty early (usually mid-October). The application process will involve usually a few interviews and a trip down to DC.

NSF Graduate Research Fellowships

US citizens and permanent residents who are planning to enter graduate school in the fall of 2019 are eligible (as are those in the first two years of such a graduate program, or who are returning to graduate school after being out for two or more years). The program solicitation contains full details. Information about the NSF Graduate Research Fellowship Program (GRFP) is here . The GRFP supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based Masters and doctoral degrees at accredited United States institutions. The program provides up to three years of graduate education support, including an annual, 000 stipend. Applications for Mathematical Sciences topics are due October 26, 2018.

Pathway to Science

summer research listings from pathways to science.

Perimeter Institute

Applications are now being accepted for Perimeter Institute’s Undergraduate Theoretical Physics Summer Program. The program consists of two parts:

• Fully-Funded Two Week Summer School (May 27 to June 7, 2019) Students are immersed in Perimeter’s dynamic research environment — attending courses on cutting-edge topics in physics, learning new techniques to solve interesting problems, working on group research projects, and potentially even publishing their work. All meals, accommodation, and transportation provided
• Paid Research Internship (May 1 to August 30, 2019, negotiable) Students will work on projects alongside Perimeter researchers. Students will have the opportunity to develop their research skills and absorb the rich variety of talks, conferences, and events at the Perimeter Institute. Applicants can apply for the two-week summer school or for both the summer school and the research internship. Summer school and internship positions will be awarded by February 28, 2019. Selected interns will be contacted with the research projects topics. All research interns must complete the two-week summer school.

Apply online at perimeterinstitute.ca/undergrad

Stanford resident counselors

Stanford Pre-Collegiate Institutes is hiring Residential Counselors for the summer to work with the following courses:

• Cryptography (grades 9-10)
• Knot Theory (grades 10-11)
• Logic and Problem Solving (grades 8-9)
• Number Theory (grades 9-11)
• Excursions in Probability (grades 8-9)
• Discrete Mathematics (grades 9-10)
• The Mathematics of Symmetry (grades 10-11)
• Mathematical Puzzles and Games (grades 8-9)

Stanford Pre-Collegiate Institutes offers three-week sessions for academically talented high school students during June and July. Interested candidates can learn more about our positions and apply by visiting our employment website .

Summer Research 2019 at Nebraska

We are now accepting applications for the University of Nebraska’s 2019 Summer Research Program, and we’d like to encourage your students to apply. Details.

Undergraduate Research and Reading Programs

Undergraduate students at MIT Mathematics Department have several opportunities to participate in mathematical research and directed reading. Four programs dedicated to cultivating research with the guidance of graduate students and faculty are:

• SPUR - Summer Program in Undergraduate Research
• DRP - Directed Reading Program during IAP in January
• UROP - Undergraduate Research Opportunities Program
• UROP+ - Supervised UROP Summer Program
• MSRP - MIT Summer Research Program

Undergraduates also have an opportunity to lead recitations, grade, and tutor in mathematics. For more information visit Math Academic Services .

Department of Mathematics

Undergraduate math research.

Performing undergraduate research is one of the very best ways to make the most out of your college experience. It will empower you to take the tools you learn in the classroom and apply them to real-world problems, all while building invaluable mentoring relationships with faculty in a professional setting.

For more than 25 years, the mathematics department has been proud to partner with the National Science Foundation to host Research Experiences for Undergraduates (REU). Remember to explore the additional funding opportunities from OSU and the College of Science which can help you get paid while doing the research you love!

Research Experiences for Undergraduates

Learn more about the reu program here , summer undergraduate research experience, learn more about the sure science program and how to apply , undergraduate research, scholarship and the arts (ursa).

The URSA Engage program provides funding for undergraduate students to work alongside mathematics faculty on mathematical research projects. URSA Engage is designed to establish mentoring relationships for undergraduates early in their academic programs at OSU and provide students opportunities to pursue research under the guidance of an OSU faculty member.

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Going above and beyond in undergraduate research.

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Using mathematical biology to explore everything from ecological phenomenon to cancer cells

URSA Engage funds undergraduates to work on mathematics research

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Is it delusional to believe you can become a quant only with an undergrad degree?

• Thread starter Three_LIttle_Pigs
• Start date 2/6/22

Three_LIttle_Pigs

I am currently a sophomore undergraduate math major at a top 30 university. Ever since, junior year of highschool, I have always wanted to become a quant- I know quant encompasses many different roles, but my idea of a dream job involves a lot of math and is very lucrative. The more I research about this field on the internet, the more I realize that you either have to be an exceptional undergraduate student or have advanced degrees. What are the chances that I will be an exceptional undergraduate student? Probably not. I'm starting to think that I would have to pursue an MFE degree- but I keep thinking to myself, how can I try to prepare as an undergrad if I don't want to pursue an MFE degree and waste time? Are there specific courses that I should be taking? Should I do lots of relevant research projects? I notice that many of the quant trading interns at the top quant firms are cs majors and had multiple programming internships and research projects. Aside from math, I'm not really passionate about programming that I would want be a programmer and I never thought much until now of what other careers I could pursue if I can't become a quant.  

If you want to be a quant, you will almost certainly have to know how to code. Not necessarily C++ , but Python /R are almost taken for granted. You can get in by having good grades, good projects and good interview preparation; for projects, you will (again) need to know how to code...  

Daniel Duffy

C++ author, trainer.

Three_LIttle_Pigs said: I am currently a sophomore undergraduate math major at a top 30 university. Ever since, junior year of highschool, I have always wanted to become a quant- I know quant encompasses many different roles, but my idea of a dream job involves a lot of math and is very lucrative. The more I research about this field on the internet, the more I realize that you either have to be an exceptional undergraduate student or have advanced degrees. What are the chances that I will be an exceptional undergraduate student? Probably not. I'm starting to think that I would have to pursue an MFE degree- but I keep thinking to myself, how can I try to prepare as an undergrad if I don't want to pursue an MFE degree and waste time? Are there specific courses that I should be taking? Should I do lots of relevant research projects? I notice that many of the quant trading interns at the top quant firms are cs majors and had multiple programming internships and research projects. Aside from math, I'm not really passionate about programming that I would want be a programmer and I never thought much until now of what other careers I could pursue if I can't become a quant. Click to expand...

I think there are multiple paths to quant, so that brings flexibility. A vast majority of listings I have seen state a graduate degree requirement. With that being said, I have no idea how often they stick/do not stick to this requirement. Maybe with an impressive resume, undergraduates are considered. You are young, so maybe you can pronounce yourself early and get away with just a bachelors. Most graduate students do not look at their program as a waste of time, rather necessary. Graduate school is reserved for those looking to go deeper into their respective subjects. Fin math is diverse and complex, many think it is necessary to dedicate more time to study it. In my opinion, it would be naïve to expect to learn a credible amount of fin math in a bachelor's degree. Especially considering almost half of that time will be used completing more rudimentary coursework. I would focus heavily on probability, proofs, linear algebra. If you can take an analysis course or matrix analysis, do it. I may be wrong in saying this (also depends on what quant track), but I think experience is more important than research. Try to lock in an internship or two in quant/finance/data science.  

I've seen some undergrads from target programs getting quant developer, algo trading, and quant research roles. Most of them have double degrees in some combination of CS/Math/Stats/(maybe)Econ, some research experience, or have taken many masters/phd level courses. Winning top ranks in competitions sponsored by quant firms could also help you land interviews (e.g. Data Open, trading competitions, quant hackathons). It's also possible to start from trading or data science in finance and transition to quant roles in a few years once you've gained better quantitative skills and knowledge of financial instruments.  

Anthony Brockwell

If you have a good understanding of markets and probability, you are strong at coding, and you understand the methodological tools of regression/machine learning/data science, etc., then you are effectively a quant regardless of what degrees you have completed or who your employer is. As others have pointed out above, it's difficult to achieve the depth required in these fields without something more than an undergraduate degree. Not impossible, but it would require a lot of drive and time to do all the extra learning with only limited guidance. In terms of employability, the same applies. It's possible, but difficult, to get employed as a quant with only an undergraduate degree. As a starting point, you could set yourself the task of predicting each day's move in the markets (e.g. SP500 index) ahead of time. Record the results for a year or so and keep a log. The point is not to predict accurately, which is pretty much impossible, but to see the difficulty and reach the point where you can frame relevant (quantitative) questions for yourself.  

Daniel Duffy said: Probably not. It's a question of achieving intellectual maturity, like well-seasoned sherry. Being a maths student probably means your programming skillls are probably weak. It all takes time.. BTW what "kind" of math degree is it? Click to expand...

Three_LIttle_Pigs said: I am required to take a few cs classes like data structures, object oriented programming, analysis of algorithms. I would not say I enjoy computer science and am good at it since I barely scraped by with a B in data structures- I had programming assignments that took me the whole day to debug and I still could not figure out. For the class on analysis of algorithms, the median exam grade is often 7/100 or 4/100 For my math classes, I'm required to take linear algebra, analysis, complex analysis, ODE,PDE, probability, statistics, numerical analysis, math modelling, I could also take graduate math classes in stochastic processes if necessary. My university also offers financial math classes from their MFE program as electives I can take. Click to expand...

C++ Programming for Financial Engineering

MundaneMatters

You can be a good quant without undergrad degree.  

MundaneMatters said: You can be a good quant without undergrad degree. Click to expand...

I've known only one fully-fledged quant with only a bachelor's degree. I believe that's the exception that proves the rule.  

Daniel Duffy said: Even Galois had to do some study. Click to expand...

Ken Abbott said: I've known only one fully-fledged quant with only a bachelor's degree. I believe that's the exception that proves the rule. Click to expand...

Daniel Duffy said: Don't want to be too criitical, but progamming courses in universities are not good (and many are atrocious) in general. There are many reasons for this (believe me for the moment on this). We don't have the headaches you mention in the QN C++ course C++ Programming for Financial Engineering The best online C++ course designed for people interested in MFE (Financial Engineering) degrees and essential topics with applications to quantitative finance. quantnet.com In a sense, the best investment ever made. I would focus on hard maths and worry about finance after graduation. One thing at a time. Click to expand...

C++ is a skill and you learn much of what is needed in later life. And TAs who respond speedily to all your questions.  

Ok, so I'd say that a standard undergrad degree in applied math/statistics/computer science should be fine to get into a good MFE program. A good understanding of the technical skills in the most important thing for being a quant, and that's what you'll be hired on. The skill set required to get into a good MFE program is the same as the skill set needed to get into a good statistics/math grad program or STEM job if you don't want to do grad school. So, just get good grades and learn the material, and you should be fine. You can look at doing projects related to the field in order to familiarize yourself with the subject, but I'd say that a good understanding of the fundamental technical skills is much more important. Hell, almost all MFE programs expect that students have no familiarity with basic investment finance, so they just teach that to you as needed. Now, the core skills you need to focus on, in importance to this field, are: probability theory (and analysis), statistics, AI/machine learning, PDEs, numerical analysis, and coding. Now, if you decide to focus more on being a quant developer than being a trinational quant, then coding becomes much more important. However, it's really not that hard to learn to learn how to code, and you can probably learn the needed coding skills in a few months if you're smart. It's much harder to learn the math and stats needed for this job, so employers and grad schools focus on those skill sets over coding or financial knowledge.  

However, it's really not that hard to learn to learn how to code, and you can probably learn the needed coding skills in a few months if you're smart. It's much harder to learn the math and stats needed for this job, so employers and grad schools focus on those skill sets over coding or financial knowledge. Interesting. The word "coding" is in anno 2022 dumbing down programmer skills. Maths is 1d but programming has many semantic levels. But they don't teach you that in the ivory tower. The software crisis continues, 90% of software projects fail on a scale [1,5].  

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Undergraduate Research Assistantships in the Faculty of Mathematics

Undergraduate research assistantships in the faculty of mathematics, mathematics undergraduate research award (mura) program.

The Mathematics Undergraduate Research Award (MURA) Program is an undergraduate research award program sponsored by the Faculty of Mathematics.

This award provides research experience that nurtures an interest in research careers and mathematics experience for undergraduate students with financial support during a full-time, on-campus or remote position for 16 weeks.

Students should apply online using the MURA Program application form .

• UC Berkeley
• Letters & Science

Undergraduate Research & Scholarships

Nir elber l&s math & physical sciences, frobenius symmetries in motivic galois groups.

One goal of arithmetic geometry is to enumerate the points on geometric surfaces with rational coordinates. Over the past century, it has been profitable to study the geometry of the surface directly. For example, a “cohomology theory” is a way to assign a sequence of geometric invariants to the surface; it turns out that one can use cohomology in order to count points. Given a surface, there tend to be many reasonable cohomology theories. This project is interested in the symmetries of a cohomology theory. Given a cohomology theory, it turns out that there is a canonical symmetry attached to the theory. However, it is a conjecture of Serre that these canonical symmetries (on the different cohomology theories) are essentially the same! The goal of the project is to further what is known about this conjecture. Explicitly, it is known that these symmetries are the same when they are small in some sense, so it remains to understand what occurs without this smallness assumption.

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Four from MIT named 2024 Knight-Hennessy Scholars

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MIT senior Owen Dugan, graduate student Vittorio Colicci ’22, predoctoral research fellow Carine You ’22, and recent alumna Carina Letong Hong ’22 are recipients of this year’s Knight-Hennessy Scholarships. The competitive fellowship, now in its seventh year, funds up to three years of graduate studies in any field at Stanford University. To date, 22 MIT students and alumni have been awarded Knight-Hennessy Scholarships.

“We are excited for these students to continue their education at Stanford with the generous support of the Knight Hennessy Scholarship,” says Kim Benard, associate dean of distinguished fellowships in Career Advising and Professional Development. “They have all demonstrated extraordinary dedication, intellect, and leadership, and this opportunity will allow them to further hone their skills to make real-world change.”

Vittorio Colicci ’22

Vittorio Colicci, from Trumbull, Connecticut, graduated from MIT in May 2022 with a BS in aerospace engineering and physics. He will receive his master’s degree in planetary sciences this spring. At Stanford, Colicci will pursue a PhD in earth and planetary sciences at the Stanford Doerr School of Sustainability. He hopes to investigate how surface processes on Earth and Mars have evolved through time alongside changes in habitability. Colicci has worked largely on spacecraft engineering projects, developing a monodisperse silica ceramic for electrospray thrusters and fabricating high-energy diffraction gratings for space telescopes. As a Presidential Graduate Fellow at MIT, he examined the influence of root geometry on soil cohesion for early terrestrial plants using 3D-printed reconstructions. Outside of research, Colicci served as co-director of TEDxMIT and propulsion lead for the MIT Rocket Team. He is also passionate about STEM engagement and outreach, having taught educational workshops in Zambia and India.

Owen Dugan, from Sleepy Hollow, New York, is a senior majoring in physics. As a Knight-Hennessy Scholar, he will pursue a PhD in computer science at the Stanford School of Engineering. Dugan aspires to combine artificial intelligence and physics, developing AI that enables breakthroughs in physics and using physics techniques to design more capable and safe AI systems. He has collaborated with researchers from Harvard University, the University of Chicago, and DeepMind, and has presented his first-author research at venues including the International Conference on Machine Learning, the MIT Mechanistic Interpretability Conference, and the American Physical Society March Meeting. Among other awards, Dugan is a Hertz Finalist, a U.S. Presidential Scholar, an MIT Outstanding Undergraduate Research Awardee, a Research Science Institute Scholar, and a Neo Scholar. He is also a co-founder of VeriLens, a funded startup enabling trust on the internet by cryptographically verifying digital media.

Carina Letong Hong ’22

Carina Letong Hong, from Canton, China, is currently pursuing a JD/PhD in mathematics at Stanford. A first-generation college student, Hong graduated from MIT in May 2022 with a double major in mathematics and physics and was inducted into Sigma Pi Sigma, the physics honor society. She then earned a neuroscience master’s degree with dissertation distinctions from the University of Oxford, where she conducted artificial intelligence and machine learning research at Sainsbury Wellcome Center’s Gatsby Unit. At Stanford Law School, Hong provides legal aid to low-income workers and uses economic analysis to push for law enforcement reform. She has published numerous papers in peer-reviewed journals, served as an expert referee for journals and conferences, and spoken at summits in the United States, Germany, France, the U.K., and China. She was the recipient of the AMS-MAA-SIAM Morgan Prize for Outstanding Research, the highest honor for an undergraduate in mathematics in North America; the AWM Alice T. Schafer Prize for Mathematical Excellence, given annually to an undergraduate woman in the United States; the Maryam Mirzakhani Fellowship; and a Rhodes Scholarship.

Carine You ’22

Carine You, from San Diego, California, graduated from MIT in May 2022 with bachelor’s degrees in electrical engineering and computer science and in mathematics. Since graduating, You has worked as a predoctoral research assistant with Professor Amy Finkelstein in the MIT Department of Economics, where she has studied the quality of Medicare nursing home care and the targeting of medical screening technologies. This fall, You will embark on a PhD in economic analysis and policy at the Stanford Graduate School of Business. She wishes to address pressing issues in environmental and health-care markets, with a particular focus on economic efficiency and equity. You previously developed audio signal processing algorithms at Bose, refined mechanistic models to inform respiratory monitoring at the MIT Research Laboratory of Electronics, and analyzed corruption in developmental projects in India at the World Bank. Through Middle East Entrepreneurs of Tomorrow, she taught computer science to Israeli and Palestinian students in Jerusalem and spearheaded an online pilot expansion for the organization. At MIT, she was named a Burchard Scholar.

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RIT graduate pursues Ph.D. across time zones

Nastaran Nagshineh, center, defended her Ph.D. thesis at RIT in April. Faculty from RIT’s Rochester and Dubai campuses served on her thesis committee and include, from left to right, Kathleen Lamkin-Kennard, Steven Weinstein, Nathaniel Barlow, and David Kofke (a professor at the University at Buffalo). Mohamed Samaha participated remotely and appears on the video screen behind the group and alongside Nagshineh’s picture.

Nastaran Nagshineh is one of the first Ph.D. candidates to bridge RIT’s Rochester and Dubai campuses. Her accomplishment creates a path for future students at the university’s international campuses.

Nagshineh completed her Ph.D. in mathematical modeling while working full time as a mathematics lecturer at RIT Dubai in the United Arab Emirates, teaching as many as five classes a semester. She described her Ph.D. journey as “an exercise in perseverance” due to competing demands and long days. Rochester is eight hours behind Dubai, and the time difference meant many late-night classes and meetings.

“I saw this collaboration as an opportunity, rather than as a challenge, because my primary adviser, Dr. Steven Weinstein (RIT professor of chemical engineering), and my co-adviser, Dr. Mohamed Samaha (RIT Dubai associate professor of mechanical engineering), both have the same area of research interest,” she said. “They both worked toward my success.”

Nagshineh is one of 67 RIT Ph.D. students who defended their thesis this academic year and who will earn their doctorate. RIT awarded 63 Ph.D. degrees in 2023.

In 2020-2021, RIT’s Graduate School met and surpassed the university’s goal of conferring 50 Ph.D. degrees during an academic year. That number will continue to grow as students cycle through the seven new Ph.D. programs that RIT has added since 2017, said Diane Slusarski , dean of RIT’s Graduate School.

Meeting these goals puts RIT on a path toward achieving an “R1,” or research-intensive designation, from the Carnegie Classification of Institutions of Higher Learning. RIT is currently ranked as an R2 institution . Many factors go into changing a university’s status, including research investment and maintaining a three-year average of 70 Ph.D. degrees awarded per year, according to Slusarski.

“We have met the goals of the strategic plan, and now we look forward to contributing to the research innovation in the future,” Slusarski said. “We want to help the new programs thrive and win national research awards.”

RIT’s emphasis on high-level research is seen in Nagshineh’s Ph.D. work. She applies mathematical modeling to the field of fluid dynamics. Her research has been published in top-tier journals and has gained notice, said Weinstein, her thesis adviser.

Weinstein describes Nagshineh’s accomplishments as “a testament to a fantastic work ethic and commitment” and is inspirational to younger students at Rochester and Dubai.

“The collaboration between RIT Dubai/Rochester has continued,” he said. “Another paper was submitted a few weeks ago with Mohamed Samaha and Nate Barlow (RIT associate professor in the School of Mathematics and Statistics) as co-authors, as well as Cade Reinberger, a younger Ph.D. student in my research group.”

Mathematical modeling is one of RIT’s newer Ph.D. degree programs, and Nagshineh is among its earliest graduates. The program has doubled in size since it began accepting students in 2017, Slusarski said. This past fall, the mathematical modeling program had 35 students, with two graduating this year.

Altogether, RIT has 13 Ph.D. degree programs currently enrolling 438 students, with computing and information sciences accounting for the largest with 117 students. RIT’s other Ph.D. programs include astrophysical sciences and technology , biomedical and chemical engineering , business administration , color science , electrical and computer engineering, imaging science , mechanical and industrial engineering , microsystems engineering , and sustainability .

New programs in cognitive science and physics will launch in the fall.

The growth in RIT graduate education—with more than 3,000 master’s and doctoral students—reflects a demographic change in the student population, Slusarski said. “We have a higher percentage of women in the graduate programs than we have for RIT undergraduate programs.”

RIT’s graduate programs enroll 42 percent women, according to Christie Leone , assistant dean for the Graduate School.

Nagshineh, who also holds an MS in electrical engineering from RIT Dubai, welcomes her role as a mentor to other women students on both campuses.

“As a young woman in an Arabic country, the power of women is often underestimated and undervalued, and I hope to serve as a role model to female students, especially those that question their path,” Nagshineh said.

She plans to continue in her career as a professor and a researcher. “I would like to pursue a research program where I can advise my own students and teach them more deeply.”

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Trig Identities: A Crash Course in Complex Math Concepts

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Fundamental trigonometric identities, aka trig identities or trigo identities, are equations involving trigonometric functions that hold true for any value you substitute into their variables.

These identities are essential tools if you want to solve trigonometric equations and perform complex calculations in mathematics, physics or engineering . Understanding all the trigonometric identities can help you simplify seemingly complicated problems, especially in geometry and calculus.

The Foundation of Trigonometry

Fundamental trigonometric identities, double angle trigonometric identities, triple angle trigonometric identities, half angle identities, sum and difference identities.

Trigonometry is a branch of mathematics . At the heart of trigonometry lie the trigonometric functions, which relate the angles of a triangle to the ratios of its sides.

The most basic trigonometric functions are sine, cosine and tangent, which instructors often teach using the mnemonic SOH-CAH-TOA in right-angled triangles.

From these basic trig functions, we derive other crucial functions, such as secant, cosecant and cotangent, all of which play vital roles in further developing trigonometric theory.

You might hear people refer to sine, cosine, tangent, secant, cosecant and cotangent as the six trigonometric ratios , or trig ratios.

Trigonometric identities form a cornerstone of higher mathematics. They encapsulate all the trigonometric ratios and relationships in a framework that enhances the solving of equations and understanding of geometric and algebraic concepts.

Trigonometric identities encompass a wide range of formulas, but people generally group them into categories based on their specific applications and forms.

There are three main categories comprising eight fundamental trigonometric identities. These categories include reciprocal identities, Pythagorean identities and quotient identities.

Reciprocal Identities

These identities express the basic trigonometric functions in terms of their reciprocal functions:

• Sine and cosecant : csc( θ ) = 1/sin( θ )
• Cosine and secant : sec( θ ) = 1/cos( θ )
• Tangent and cotangent : cot( θ ) = 1/tan( θ )

Pythagorean Identities

The Pythagorean trigonometric identities stem from the Pythagorean theorem , also known as the Pythagoras theorem, after the Greek scholar who came up with the mathematical statement.

The trig identities based on the Pythagorean theorem are fundamental to connecting the squares of the primary trigonometric functions:

• Basic Pythagorean identity : sin 2 ( θ ) + cos 2 ( θ ) = 1
• Derived for tangent : 1 + tan 2 ( θ ) = sec 2 ( θ )
• Derived for cotangent : cot 2 ( θ ) + 1 = csc 2 ( θ )

Quotient Identities

These identities relate the functions through division:

• Tangent as a quotient : tan( θ ) = sin( θ )/cos( θ )
• Cotangent as a quotient : cot( θ ) = cos( θ )/sin( θ )

Of course, there are many more trigonometric identities beyond just these core identities that have applications in specific scenarios, such as double angle, triple angle, half angle and sum and difference identities.

The double angle formulas are trigonometric identities that express trigonometric functions of double angles — that is, angles of the form 2 θ — in terms of trigonometric functions of single angles ( θ ).

These formulas are crucial in various mathematical computations and transformations, particularly in calculus, geometry and solving trigonometric equations.

The primary double angle formulas include those for sine, cosine and tangent.

Cosine Double Angle Formula

The cosine double angle formula is:

cos(2 θ ) = cos 2 ( θ ) – sin 2 ( θ )

You can also represent this in two alternative forms using the Pythagorean identity sin 2 ( θ ) + cos 2 ( θ ) = 1 :

Sine Double Angle Formula

The sine double angle formula is:

This formula is derived from the sum identities and is useful for solving problems involving products of sine and cosine.

Tangent Double Angle Formula

The tangent double angle formula is:

This expression arises from dividing the sine double angle formula by the cosine double angle formula and simplifying using the definition of tangent.

Triple angle formulas, while less commonly used, offer shortcuts in specific scenarios, such as in certain integrals and polynomial equations. These are identities that allow the calculation of the sine, cosine and tangent of three times a given angle (3θ) using the trigonometric functions of the angle itself (θ).

For example, the sine triple angle formula is:

This formula is derived by using the sine double angle formula and the angle sum identity.

Triple angle formulas can be derived from double angle and sum identities and are useful in specific mathematical and engineering contexts, such as simplifying complex trigonometric expressions or solving higher-degree trigonometric equations.

Half angle identities are trigonometric formulas that allow you to prove trigonometric identities for the sine, cosine and tangent of half of a given angle.

Half angle formulas are particularly useful in solving trigonometric equations, integrating trigonometric functions, and simplifying expressions when the angle involved is halved. Half angle formulas are derived from the double angle identities and other fundamental trigonometric identities.

The half angle identities for sine, cosine and tangent use the following half angle formulas:

• Sine half angle identity : sin⁡( θ /2) = ±√((1 – cos θ )/2)
• Cosine half angle identity : cos⁡( θ /2) = ±√((1 + cos θ ​​)/2)
• Tangent half angle identity : tan( θ /2) = sin( θ )/(1 + cos( θ )) = 1 – (cos( θ )/sin( θ ))

In the case of the sine and cosine half angle formulas, the sign depends on the quadrant in which θ /2​ resides. The tangent half angle formula you can also express in terms of sine and cosine directly.

These identities are derived by manipulating the double angle identities. For example, the cosine double angle identity cos(2 θ ) = 2cos 2 ( θ ) can be rearranged to express cos 2 ( θ ) in terms of cos(2 θ ) , and then taking the square root (and adjusting for sign based on the angle's quadrant) gives the half angle formula for cosine.

Half angle identities are crucial for simplifying the integration of trigonometric functions, particularly when integral limits involve pi (π) or when integrating periodic functions. They also play a vital role in various fields of science and engineering where wave functions and oscillations are analyzed.

Sum identities in trigonometry are essential formulas that allow for the calculation of the sine, cosine and tangent of the sum of two angles. Conversely, difference formulas allow you to calculate the sine, cosine and tangent of the difference between two angles.

These identities are incredibly useful for simplifying expressions, solving trigonometric equations and performing complex calculations.

We created this article in conjunction with AI technology, then made sure it was fact-checked and edited by a HowStuffWorks editor.

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College of Biological Sciences

Cbs students receive prestigious goldwater scholarships.

Three UC Davis students were awarded the scholarships this year, two from CBS

• by Isabella Beristain
• May 14, 2024

Three UC Davis students, including two from the College of Biological Sciences, have won the highly prestigious and competitive Barry Goldwater Scholarship. 

Every year, the Barry Goldwater Scholarship and Excellence in Education Foundation honors fewer than 500 undergraduate second- and third-year students from across the country with scholarships recognizing their science, technology, engineering and mathematics research accomplishments and future potential.

The 2024 UC Davis Goldwater Scholars are: Avantika Gokulnatha, a third-year genetics and genomics major, Madeleine Rose, a second-year cognitive science major, and Shih-Na Liu, an evolution, ecology and biodiversity major. Each of them submitted research spanning multiple STEM fields and topics.

Gokulnatha, who is from San Jose, California, investigates the cellular mechanisms of the human aging process. Rose, who is from Foster City, California, conducts research at the intersection of neuroendocrinology, chronic pain and artificial intelligence. And Liu, from Taoyuan, Taiwan, explores the effects of diet on the body shape evolution of reef fishes.

All three winners intend to continue their research at a graduate level. In the meantime, they’ll work on their ongoing endeavors here at UC Davis, where they began their journeys pursuing research excellence.

Goldwater dynasty

UC Davis has had 35 recipients earn the Goldwater Scholarship throughout the program’s 30-year history. This is the seventh consecutive year that one or more UC Davis students received the coveted Goldwater Scholar title. Only one other UC had more awardees than UC Davis for the 2024-25 scholarship cycle.

Scott Palmer, UC Davis prestigious scholarship advisor, said this number speaks not just to the caliber of students that UC Davis admits but also to the multitude of research opportunities available for undergraduates to pursue.

“At Davis, there are so many ways to get involved with research and the labs conducting it,” Palmer said. “We have a reputation for being collaborative, which not a lot of incoming students are necessarily aware about.” 

From seminar to scholar

Gokulnatha first learned about the scholarship at one of Palmer’s honors program advising seminars during her first quarter at UC Davis.

“In the past, I benefitted significantly from applying to scholarships — not just financially, but also through the doors that these awards open,” Gokulnatha said. “I knew I would need to start exploring research opportunities and immediately the one thing I grasped was that everyone seemed accessible and really invested in us undergraduates learning everything we can both inside and outside the classroom. People really do see themselves in you as a budding researcher.”

Bold actions, rich returns

Rose began her Goldwater journey cold emailing professors, looking for opportunities that best fit her personal research goals.

“The worst response you can get is a no and a no is not the end of the world. You never know what will happen if you do not hit send,” Rose said. “Reaching out to prospective mentors across disciplines is a great way to expand your options and diversify research interests, it’s how I now work with top researchers and clinicians across academic institutions.” 

Opportunities to rethink the way things work

Liu noted there are also many ways to get your research funded.

“Last year, I participated in the EVE Scholars Program . Through the Department of Evolution and Ecology, I was able to make a lot of progress on my research that I then submitted for the Goldwater Scholarship,” she said. “It is a really cool program because they fund you for the whole summer, then you take a research presentation class the following quarter and they even provide you with funding to go to conferences to learn more. It’s the whole research package.”

Gaining invaluable experience

According to Palmer, applying to a prestigious scholarship application, alone, is a huge win for most undergraduate students. “You get the opportunity to write about yourself, clarify your vision and show others why they should invest in you. This is a great skill to practice going into graduate school or for jobs after college,” he said.

Rose put herself through this experience to do exactly that: gain valuable experience to aid her future research endeavors.

“You miss 100% of the shots you do not take. The odds of receiving an award like this are slim and I was aware of this when I first decided to apply,” she said. “The application process was challenging but encouraged me to think critically about the research projects I am leading. Applying for this scholarship strengthened my skills both as a researcher and writer.”

Media Resources

• To learn more about the Goldwater Scholarship and how to apply, visit the Barry M. Goldwater webpage located on the UC Davis Financial Aid and Scholarships webpage.  
• Isabella Beristain is a communications specialist in UC Davis Enrollment Management.

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