Mathematics Major Requirements

A mathematics degree from HMC will prepare students for a variety of careers in business, industry or academics. Mathematical methods are increasingly employed in fields as diverse as finance, bio-medical research, actuarial science, banking, 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 cooperative courses offered at the other Claremont colleges and advanced mathematics courses at the Claremont Graduate University.

The Mathematics Clinic program extends the academic experience of our majors. An educational innovation of Harvey Mudd College, the Clinic program brings together teams of students to work on a year-long 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.

In addition to the Clinic program, students have many opportunities to work individually with faculty to do mathematical research. Active areas of mathematical research at HMC include real and complex analysis, topology, differential and hyperbolic geometry, probability theory, dynamical systems, partial differential equations, asymptotics, numerical analysis, combinatorics, graph theory, and mathematical modeling.

Course Requirements

Every HMC student, regardless of major, takes four semesters of mathematics (covering the topics of calculus, multivariable calculus, linear algebra, probability & statistics, and differential equations) as part of the general core curriculum. (Advanced placement is also possible.)

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

The Major Core

A set of core courses is required of each major. These courses cover a range of fundamental fields of mathematics, and position the student to pursue any one of a variety of elective programs to finish the degree.

Computational Mathematics

Computational techniques are essential to many fields of modern mathematics, and to most mathematical applications in business and industry. One course in computational mathematics is required of all majors, selected from the following list:

Senior Research Experience

One year of Mathematics Clinic (Math 193) or Senior Thesis (Math 197) is required, and is normally taken in the senior year.

Clinic and thesis are important capstone experiences for each major—they represent sustained efforts to solve a complex problem from industry or work on independent mathematical research.

Clinic teams are formed in the fall semester according to the requirements of the projects and student preferences.

For thesis, you must prepare a senior-research proposal with the help of your thesis advisor. Your proposal will describe the intended senior-research project and must be submitted to the department's Curriculum Committee for approval before the end of your junior year.

See the individual sites for each program for additional details about their requirements and procedures.

The Elective Program

To complete the degree, three elective mathematics courses (at least 8 units) are required. The student, in consultation with his or her advisor, will design their elective program. To assist students in this process, the Department has prepared a variety of sample programs. These sample programs are courses of study supporting a wide range of career goals in academics, business or industry. Several sample elective programs are listed below; course numbers in bold are strongly recommended (CS = Computer Science, CGU = Claremont Graduate University). Sample programs are advisory; students may follow a sample program, or design a program of their own.

Pure Mathematics: 132, 172, and at least one course from 104, 106, 123, 136, 142, 143, 147, 173, 175, 182, CGU 331, CGU 332, CGU 334.
Applied Mathematics: 136, 181 and at least one course from 118, 119, PO 120, 132, 164, 165, 173, 182, 185, 187, 189, CGU 362, CGU 368, CGU 382.
Probability and Statistics: 152, 156 and at least one course from 106, 132, 158, 159, 173, 187, CGU 351, CGU 355.
Operations Research: 156, 187 and at least one course from 104, 106, 132, 152, 155, 158, 159, 165, 168.
Actuarial or Financial Mathematics: CMC 109 156 and at least one course from 152, 158, 165, 187, CGU 355, Econometrics (CMC 125, 126; CGU 382, 383, 384; PO 167)
Scientific Computing: 164, 165 and at least one course from 136, 168, 173, 181, 182, 189, CS 156, CGU 362, CGU 368, CGU 382.
Theoretical Computer Science: CS 81, 168 and at least one course from 104, 106, 123, 165, 167, 172, 175, CS 151, CS 152, CS 156.; Students interested in this elective program may alternatively wish to consider the Joint Major in Computer Science and Mathematics.
Mathematical Biology: 118, 199, and at least one course from PO 120, 152, 156, 158, 159, 164, 168, 173, 181, 182, 185, 187.; Students interested in this elective program may alternatively wish to consider the Mathematical Biology major.

Comments

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 Math 55 and 131 by the end of the sophomore year, Math 157, 171, 180, 198, and 199 by the end of the junior year, and Math 193 or 197 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 Math 193. 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.