Here is some important information about mathematics at Brown.

The Math Concentration

Beginning in 2019, we have three faculty advisors for the math concentration: Professor Benoit Pausader; Professor Rich Schwartz; and Professor Jeffrey Hoffstein.

Professor Rich Schwartz previously spent several years as sole Director of Undergraduate Studies. His website is equipped with a lot of useful stuff, such as a list of scholarships and prizes, how to apply for transfer credit, and how to declare the math concentration.

For more information on concentration requirements please visit the following pages...

- Requirements for A.B. and Sc.B. in Mathematics
- Requirements for Sc.B. in Mathematics - Computer Science
- Requirements for the A.B. in Mathematics - Economics

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Writing Requirement

Any piece of expository writing about mathematics which includes the complete proof of at least one nontrivial theorem may be submitted in lieu of a second writing designated course between semesters 5-7 (or the penultimate semester).

For questions related to the concentration, you can talk to the department staff in Kassar House, Room 109.

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Math Courses

**Which Calculus Course to Take?**

Here is a page describing three simple steps that will help you to determine which calculus class is appropriate for you. If you're still not sure, you can email any of the faculty advisors listed above, or email the DUG officers, for more personalized advice. Also, remember that you can shop multiple calculus courses, or different sections of the same course, to see which instructor and which material is right for you.

**Transition to Proofs (MATH 420, 540, 1010, 1530)**

Proofs form the foundation for all of mathematics. However, the math you've seen so far might not have included any formal proofs, but instead relied on intuitive explanations. An essential part of your mathematics education is gaining the ability to read and understand a rigorous mathematical argument, and even more importantly, the ability to create your own proofs and arguments.

The courses MATH 420 (Introduction to Number Theory), MATH 540 (Honors Linear Algebra), MATH 1010 (Analysis: Functions of One Variable), and MATH 1530 (Abstract Algebra) not only introduce you to core areas of mathematics, they are designed to give you excellent practice working with rigorous mathematics that will help you succeed in, and fully appreciate, subsequent upper-level math courses.

**Upper-Level Courses**

The standard high school mathematics curriculum doesn't demonstrate the true diversity or the true nature of mathematics. Exploring the mathematical landscape beyond calculus, you'll find number theory, complex analysis, algebraic topology, and many other fields that investigate the deep questions raised by seemingly simple ideas. You might encounter situations where multiplication isn't commutative, where a number can have more than one prime factorization, or where a sequence can have more than one limit. Studying these generalizations and abstractions, in addition to being great fun in its own right, helps to shed a surprising amount of light on the "usual" mathematics you know and love.

Here is a list of math courses, and a collection of course descriptions.

**Independent Study (MATH 1970)**

In keeping with Brown's principle of educational self-determination, the Brown math department offers an "independent study" or "honors conference" course. This course allows you to study material that may not be offered in a standard course, at your own pace. A professor of your choice will advise you and grade your work.

Ideally, you should approach the professor you'd like to advise your independent study the semester before you want to take the course. You should discuss your goals for the course, what material or textbooks you'd like to use, and what the professor's expectations are for a good grade.

Note that it requires a lot of self-discipline to get the full benefit of an independent study course. You should be confident that a standard course won't fit your needs before you decide to engage in an independent study.

**Honors Theses**

The math concentration includes the option of completing an honors thesis, which can either be expository or consist of new research. While it's not necessary for the purpose of getting your degree with honors, you should consider signing up for MATH 1970 with the professor who is advising your honors thesis - this will give you course credit for the work you're doing.

You might already have in mind a specific topic you want to learn about, or a specific problem you want to tackle, but you can always ask your professor for suggestions. Especially if you are interested in doing research on a problem for your thesis, you should get input from a professor - they'll know whether or not the problem you want to solve is too difficult or too easy for you.

Here are some honors theses from recent years.

**Tutoring & The Math Resource Center**

The Math Resource Center (MRC) is a walk-in help center designed for students taking calculus courses at Brown University. The MRC is staffed by 1-2 graduate students and 2-3 undergraduates per night who help students on an individual or small group basis.

Brown offers tutoring for several math courses; for more info, see here. If you need a tutor for a math course that doesn't have tutoring offered through Brown, e.g. one of the upper-level courses, email the DUG officers and we'll try to find someone who can work with you.

**Math Competitions**

Hartshorne-Hypatia Prize Examination (Brown first-years only) - For more information on this examination contact Professor Alan Landman.

H.P. Manning Prize Examination (Brown juniors only)

William Lowell Putnam Mathematical Competition

Brain Power Hour, a math competition held annually by the Applied Math DUG