Is it possible to get into graduate school for math with a non-math undergraduate degree? [closed]

Question

I'm an undergraduate biology and chemical engineering dual major student. I recently got interested in pure math while I was researching patterns in biology which lead me down the rabbit hole of fractals and non-Euclidean geometry and eventually, lead me to number theory. I really enjoy the subjects. Is it possible for me to pursue my graduate studies in pure math? If so, what would be the necessary steps I should take to do the same? I am in my second year of studies and I do intend to take the GRE Math Subject test but I would really appreciate any other advice you could give me. Also, switching majors is not an option because my university doesn't have a good math program. If you are reading this, I hope you have a nice day ahead. Regards

Answer 1

This question was asked a few years ago, and I largely agree with what LSpice said in the comments, that it fits more with academia.SE than with MathOverflow. But, I'll try to answer anyway, so this doesn't linger on the unanswered queue. Since it's too late for this answer to help the OP, I'll aim it at a general undergrad student with a similar question.

General Thoughts: I get questions like this a lot from undergraduates at my university. Some feel like they need to stick with the plan they had when they started, e.g., to be a biology major, perhaps because that's what they told their family and friends back home that they'd be doing. But plenty of students change their major, and the general advice to undergrads in the USA (especially at a liberal arts college) is to follow their passion. If a student really likes the math they are seeing, then they should take more math. That might or might not lead to a math major. Students shouldn't feel like they need to have everything mapped out at every moment, especially as sophomores. It's also easy to see a bit of cool stuff (like fractals) and then think you want to be a mathematician, but it's essential to take math courses to determine whether or not that interest is really sustained, even in the face of math you find less interesting but that is still essential for success as a research mathematician.

For sure, if a student wants to go to math grad school, it's best to take a lot of math (even more than what is required to be a math major). You should look at the websites of PhD program you might be interested in, and see what they say about expectations for students who successfully get admitted. To be properly prepared for the first-year qualifying exams in a US-based PhD program, a student should have seen multivariable calculus, linear algebra, basic differential equations, real analysis, abstract algebra, and topology (including manifolds) at a minimum. Even better if they also took courses in complex analysis and differential geometry. This is important because math builds on itself and usually first-year grad courses assume students have already seen those subjects. For breadth, it's also good if they can get some exposure to graph theory, combinatorics, number theory, algebraic geometry, and whatever other electives they can take, because that can help them decide which PhD programs to apply for based on the research interests of the faculty there.

Sometimes, we get a student who has two or even three (not recommended) majors and can't take the specific math courses required to be a math major. In those cases, it's usually not the end of the world if the student's transcript doesn't say "math major." If they've had a sufficient exposure to high-level math, strong letters of recommendation from their math professors, and a good score on the GRE, then they can still get into good PhD programs. This is especially true if the second major is something like physics.

Specific thoughts for the OP: The OP was studying biology and chemistry and felt their math department wasn't good. Still, it would be wise to take as many math courses as possible, to learn as much math as you can, to show a legitimate interest in math, to get letters of recommendation from math professors, and to learn what you need to know for the math subject GRE (multivariable calculus, linear algebra, basic differential equations, a bit of complex analysis). If the department doesn't offer lots of upper-level math courses, then the student can try to do some directed studies with professors, to work through the core math curriculum.

Nowadays, mathematical biology is a major research area that the OP might be interested in. For example, Ohio State has the Mathematical Biosciences Institute and has a curriculum for math biology. For this kind of applied research, it's best to have undergraduate exposure to probability, statistics, differential equations (at a more advanced level), operations research, mathematical modeling, dynamical systems, and math biology. If a student was a biology major and took some math, they might be able to get accepted to a PhD program with a focus on math biology.

Lastly, sometimes an undergraduate-only institution just does not offer enough math to prepare a student for a career as a research mathematician. In such situations, it's wise to do a post baccalaureate program like this one at Smith College, or a master's degree in mathematics where you can get the courses you need as a foundation for a math PhD program. I echo LSpice's comment that it's wise to apply to a broad array of graduate programs, and emphasize your knowledge in biology and chemistry as a strength. Many programs may reject a candidate who does not seem to have the baseline math knowledge expected. But some programs, especially lower ranked ones, might take a chance on such a student. That said, the ranking of your PhD program does matter, so if you have the time, doing a master's degree at the best place you can get accepted, then applying to a PhD program after, is one way to fill in the missing math background and still get into a strong PhD program (hopefully one that has faculty interested in research in math biology).