Mathematics Major

A mathematics degree from Harvey Mudd College will prepare students for a variety of careers in business, industry or academics. Mathematical methods are increasingly employed in fields as diverse as finance, biomedical research, management science, the computer industry and most technical and scientific disciplines. To support the academic and professional goals of our majors, we offer a wide selection of courses in both pure and applied mathematics. This selection is enhanced by courses offered in cooperation with the other Claremont Colleges, including graduate courses at the Claremont Graduate University.

Students will have many opportunities to do mathematical research with faculty through independent study, a summer research experience, or their senior capstone experience. Active areas of mathematical research at HMC and The Claremont Colleges include algebra, algebraic geometry, algorithms and computational complexity, combinatorics, differential geometry, dynamical systems, fluid mechanics, graph theory, number theory, numerical analysis, mathematical biology, mathematics education, operations research, partial differential equations, real and complex analysis, statistical methods and analysis, and topology.

The culmination of the degree is the senior capstone research experience: every student experiences a taste of the life of a professional mathematician as part of a team in the Mathematics Clinic Program or by working individually on a Senior Thesis.

The Mathematics Clinic program extends the academic experience of our majors. An educational innovation of HMC, our Clinic Program brings together teams of students to work on a research problem sponsored by business, industry or government. Teams work closely with a faculty advisor and a liaison provided by the sponsoring organization to solve complex real-world problems using mathematical and computational methods. Clinic teams present their results in bound final reports to the sponsors and give several formal presentations on the progress of the work during the academic year.

Our Senior Thesis program provides students with the opportunity to work independently on a problem of their choosing. Advisors and readers may be chosen from the HMC faculty and the other mathematicians at The Claremont Colleges, providing students with a wealth of research opportunities. As with Clinic, the end product of a thesis is a bound volume as well as presentations made at a professional conference or other venue, during the college-wide Presentations Days and throughout the year.

The course of study for a mathematics degree has five components: The Major Core, Computational Mathematics, Clinic or Thesis, Mathematics Forum and Mathematics Colloquium, and the Elective Program. Each of these components to the major program is described below.

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Through the Major Core requirement, every major will have a foundation course in several important areas: discrete mathematics, analysis, algebra, differential equations and probability. In addition, every major will have a course relating to computational aspects of mathematics. The Major Core positions each student to move in any of several directions in the design of their elective program. There is a wide range of options to finish the major, supporting a variety of career goals and interests. It is expected that most students will take MATH055 HM – Discrete Mathematics and MATH131 HM – Mathematical Analysis I by the end of the sophomore year, MATH157 HM – Intermediate Probability, MATH171 HM – Abstract Algebra I, MATH180 HM – Introduction to Partial Differential Equations, MATH198 HM – Undergraduate Mathematics Forum, and MATH199 HM – Mathematics Colloquium by the end of the junior year, and MATH193 HM – Mathematics Clinic or MATH197 HM – Senior Thesis in Mathematics during the senior year.

Two semesters of Clinic or thesis are required of each major. All students must declare their intentions by the end of their junior year. Students who wish to take Clinic should inform the Mathematics Clinic Director, and preregister for MATH193 HM – Mathematics Clinic. Students choosing thesis must arrange to have a thesis advisor by the end of the spring semester of their junior year. In consultation with their advisor, the student must prepare a research proposal describing a suitable thesis problem, and submit the proposal to the mathematics department for approval. We expect that students will begin work on their theses immediately in the fall of the senior year. Thesis students will meet weekly as a group, to discuss their progress, make presentations, and exchange ideas. Students enrolled in Clinic who also wish to do thesis will be able to do a one-semester thesis, if desired. They may arrange their thesis in the fall of the senior year.

The faculty in the mathematics department works closely with each student to develop a coherent program of elective courses that meets the student’s professional and academic goals. The entire department meets once each term to discuss and compare all student programs and to discuss student progress.