Joint Major in Mathematics and Physics

Professor Levy in lab

The fields of physics and mathematics have been closely intertwined, with significant influences on each other, for hundreds of years. Numerous courses and research programs at Harvey Mudd draw heavily on both disciplines.  The Joint Major in Mathematics and Physics highlights the intersections between physics and mathematics while preparing a student with solid foundations in both fields. Graduates of this program should be well positioned for further study in physics or mathematics, or for immediate employment.

The major is cooperatively administered by the Mathematics and Physics departments, and students have faculty advisors in both departments. Students complete courses from the mathematics and physics major sequences, as well as a required course in computational techniques relevant to the field. Each student must complete a capstone (thesis or clinic), which may be chosen from either department's offerings. 

Mathematics Courses

  • Credits: 3

    Instructors: Benjamin, Bernoff, Orrison, Pippenger

    Offered: Fall and Spring

    Description: Topics include combinatorics (clever ways of counting things), number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs. Possible applications include probability, analysis of algorithms, and cryptography.

    Corequisites: MATH073 HM 

and

  • Credits: 1.5

    Instructors: de Pillis, Omar, Orrison

    Offered: Spring, first half

    Description: This half course is a continuation of MATH065  HM and is designed to in­crease the depth and breadth of students' knowledge of linear algebra. Topics include: Vector spaces, linear transformations, eigenvalues, eigenvectors, inner-product spaces, spectral theorems, Jordan Canonical Form, singular value decomposition, and others as time permits.

    Prerequisites: MATH065  HM. May not be taken by students who have completed MATH073 HM.

or

  • Credits: 3

    Instructor: Staff

    Offered: Spring

    Description: Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization. General vector spaces and linear transformations; change of basis and similarity. Additional Topics.

    Prerequisites: MATH019 HM or equivalent

and

  • Credits: 1.5

    Instructors: Bernoff, Castro, de Pillis, Jacobsen

    Offered: Spring, second half

    Description: This half course is a continuation of MATH065  HM and is designed to increase the depth and breadth of students' knowledge of differential equations. Topics include Existence and Uniqueness, Power Series and Frobenius Series Methods, Laplace Transform, and additional topics as time permits.

    Prerequisites: MATH065  HM. May not be taken by students who have completed MATH082 HM.

or

  • Credits: 3

    Instructor: Staff

    Offered: Fall

    Description: Modeling physical systems, first-order ordinary differential equations, existence, uniqueness, and long-term behavior of solutions; bifurcations; approximate solutions; second-order ordinary differential equations and their properties, applications; first-order systems of ordinary differential equations. Applications to linear systems of ordinary differential equations, matrix exponential; nonlinear systems of differential equations; equilibrium points and their stability. Additional topics.

    Prerequisites: (MATH019 HM and MATH073 HM) or equivalent 

and

  • Credits: 3

    Instructors: Castro, de Pillis, Karp, Omar, Su, Zinn-Brooks H

    Offered: Jointly; Fall semester at HMC and Pomona, Spring semester at HMC and CMC

    Description: This course is a rigorous analysis of the real numbers and an introduction to writing and communicating mathematics well. Topics include properties of the rational and the real number fields, the least upper bound property, induction, countable sets, metric spaces, limit points, compactness, connectedness, careful treatment of sequences and series, functions, differentiation and the mean value theorem, and an introduction to sequences of functions. Additional topics as time permits.

    Prerequisites: MATH055 HM 

  • Credits: 1.5

    Instructors: Benjamin, Martonosi, Pippenger, Su, Williams

    Offered: Fall and Spring

    Description: Continuous random variables, distribution functions, joint density functions, marginal and conditional distributions, functions of random variables, conditional expectation, covariance and correlation, moment generating functions, law of large numbers, Chebyshev's theorem, and central-limit theorem. 

    Prerequisites: MATH019 HM 

  • Credits: 3

    Instructors: Karp, Lindo, Omar, Orrison, Staff (CMC), Staff (Pomona)

    Offered: Jointly; Fall semester at HMC and CMC, Spring semester at HMC and Pomona

    Description: Groups, rings, fields, and additional topics. Topics in group theory include groups, subgroups, quotient groups, Lagrange's theorem, symmetry groups, and the isomorphism theorems. Topics in Ring theory include Euclidean domains, PIDs, UFDs, fields, polynomial rings, ideal theory, and the isomorphism theorems. In recent years, additional topics have included the Sylow theorems, group actions, modules, representations, and introductory category theory.

    Prerequisites: MATH073 HM and MATH055 HM 

and

  • Credits: 3

    Instructors: Bernoff, Jacobsen, Weinburd, Zinn-Brooks H

    Offered: Fall

    Description: Partial Differential Equations (PDEs) including the heat equation, wave equation, and Laplace's equation; existence and uniqueness of solutions to PDEs via the maximum principle and energy methods; method of characteristics; Fourier series; Fourier transforms and Green's functions; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions.

    Prerequisites: MATH080 HM and MATH131 HM 

or

  • Credits: 3

    Instructors: Bernoff, Weinburd, Yong

    Offered: Spring

    Description: Complex variables and residue calculus; Laplace transforms; Fourier series and the Fourier transform; Partial Differential Equations including the heat equation, wave equation, and Laplace's equation; Separation of variables; Sturm-Liouville theory and orthogonal expansions; Bessel functions. May not be included in a mathematics major program. Students may not receive credit for both Mathematics 115 and MATH180 HM.

    Prerequisites: MATH073 HM and MATH082 HM 

and

  • Credit: 1

    Instructors: Castro, Jacobsen, Orrison, Weinburd, Zinn-Brooks H, Zinn-Brooks L

    Offered: Fall and Spring

    Description: The goal of this course is to improve students' ability to communicate mathematics, both to a general and technical audience. Students will present material on assigned topics and have their presentations evaluated by students and faculty. This format simultaneously exposes students to a broad range of topics from modern and classical mathematics. Required for all majors; recommended for all joint CS-math majors and mathematical biology majors, typically in the junior year.

  • Credit: 0.5

    Instructor: Staff

    Offered: Fall and Spring

    Description: Students will attend weekly Claremont Math Colloquium, offered through the cooperative efforts of the mathematics faculty at The Claremont Colleges. Most of the talks discuss current research in mathematical sciences and are accessible to under­graduates. No more than 2.0 credits can be earned for departmental seminars/col­loquia. 

Physics Courses

  • Credits: 3

    Instructor: Staff

    Offered: Spring

    Description: The development and formulation of quantum mechanics, and the application of quantum mechanics to topics in atomic, solid state, nuclear, and particle physics.

    Prerequisites: PHYS051 HM and MATH082 HM 

  • Credit: 1

    Instructors: Eckert, Staff

    Offered: Spring

    Description: Classical experiments of modern physics, including thermal radiation and Rutherford scattering. Nuclear physics experiments, including alpha, beta and gamma absorption, and gamma spectra by pulse height analysis. Analysis of the buildup and decay of radioactive nuclei.

    Corequisites: PHYS050 HM and PHYS052 HM 

  • Credits: 3

    Instructor: Shuve

    Offered: Fall

    Description: The application of mathematical methods to the study of particles and of systems of particles; Newton, Lagrange, and Hamilton equations of motion; conservation theorems; central force motion, collisions, damped oscillators, rigid body dynamics, systems with constraints, variational methods.

    Prerequisites: PHYS023 HM, PHYS024 HM, and MATH082 HM 

  • Credits: 3

    Instructor: Gallicchio

    Offered: Spring

    Description: The elements of nonrelativistic quantum mechanics. Topics include the general formalism, one-dimensional and three-dimensional problems, angular momentum states, perturbation theory and identical particles. Applications to atomic and nuclear systems.

    Prerequisites: PHYS052 HM 

  • Credits: 3

    Instructor: Esin

    Description: Classical and quantum statistical mechanics, including their connection with thermodynamics. Kinetic theory of gases. Applications of these concepts to various physical systems.

    Prerequisites: PHYS052 HM 

    Corequisites: PHYS111 HM 

  • Credits: 2

    Instructor: Staff

    Offered: Spring

    Description: A laboratory-lecture course on the techniques and theory of classical and modern optics. Topics of study include diffraction, interferometry, Fourier transform spectroscopy, grating spectroscopy, lasers, quantum mechanics and quantum optics, coherence of waves and least-squares fitting of data.

    Prerequisites: PHYS051 HM and PHYS054 HM 

and

  • Credits: 3

    Instructor: Eckert

    Offered: Fall

    Description: The theory of static and dynamic electromagnetic fields. Topics include multipole fields, Laplace's equation, the propagation of electromagnetic waves, radiation phenomena and the interaction of the electromagnetic field with matter.

    Prerequisites: (PHYS111 HM or PHYS116 HM) and MATH115 HM 

or

  • Credits: 3

    Instructor: Lyzenga

    Offered: Spring

    Description: The theory of deformable media. Field equations for elastic and fluid media and for conducting fluids in electromagnetic fields. Particular emphasis on body and surface wave solutions of the field equations.

    Prerequisites: MATH115 HM 

or

  • Credits: 3

    Instructor: Sahakian

    Offered: Spring

    Description: This course explores concepts, methods, and applications of the classical theory of fields. On the physics side, we will learn about cosmological inflation, superconductivity, electroweak theory, solitons, the nuclear force, and magnetic monopoles. On the mathematics side, we will learn the basics of differential geometry and Lie algebras. Throughout the course, we will emphasize the unity of physical principles and techniques across a wide range of systems and disciplines.

    Prerequisites: PHYS111 HM and MATH115 HM 

and

  • (taken twice)

    Credit: 0.5

    Instructors: Eckert, Ilton

    Offered: Fall and Spring

    Description: Oral presentations and discussions of selected topics, including recent developments. Participants include physics majors, faculty members, and visiting speakers. Required for all junior and senior physics majors. No more than 2.0 credits can be earned for departmental seminars/col­loquia. 

Scientific Computation Requirement

  • Credits: 3

    Instructors: Bernoff, de Pillis, Yong

    Description: Computational techniques applied to problems in the sciences and engineering. Modeling of physical problems, computer implementation, analysis of results; use of mathematical software; numerical methods chosen from: solutions of linear and nonlinear algebraic equations, solutions of ordinary and partial differential equations, finite elements, linear programming, optimization algorithms, and fast-Fourier transforms.

    Prerequisites: MATH073 HM, MATH082 HM, and CSCI060 HM 

or

  • Credits: 3

    Instructors: Bernoff, de Pillis, Pippenger, Yong

    Offered: Fall

    Description: An introduction to the analysis and computer implementation of basic numerical techniques. Solution of linear equations, eigenvalue prob­lems, local and global methods for non-linear equations, interpolation, approximate integra­tion (quadrature), and numerical solutions to ordinary differential equations.

    Prerequisites: MATH073 HM and MATH082 HM 

or

  • Credits: 2

    Instructor: Sahakian

    Offered: Spring

    Description: Typical numerical methods for solving a wide range of problems of current interest in physics. Examples are drawn from mechanics, electromagnetism, quantum mechanics, statistical mechanics, solid state and chemical physics.

    Prerequisites: PHYS052 HM and the ability to program

Capstone

Two semesters of capstone, either thesis or clinic (2 semesters x 3 units). Students completing a thesis follow the practices and guidelines of the thesis advisor's department.

  • (taken twice)

    Credit: 1-3

    Instructor: Staff

    Offered: Fall and Spring

    Description: Original experimental or theoretical investigations in physics undertaken in consultation with a faculty member. Projects may be initiated by the student or by a faculty member. Present faculty research areas include astrophysics, biophysics, optics, solid-state and low-temperature physics, general relativity, quantum mechanics, particle physics, geophysics, and soft matter physics. Students are responsible for an oral presentation on progress and plans in the first half of the thesis research.

    Prerequisites: Permission of department. Senior standing.  

or

  • (taken twice)

    Credits: 3

    Instructor: Staff

    Offered: Fall and Spring

    Description: Senior thesis offers the student, guided by the faculty advisor, a chance to experience a taste of the life of a professional research mathematician. The work is largely independent with guidance from the research advisor. The principal objective of the senior thesis program is to help you develop intellectually and improve your written and verbal communication skills. Students are expected to present their work orally and to produce a thesis conforming to the publication standards of a professional mathematician.

    Prerequisites: Permission of department

or

  • Credits: 3

    Instructor: Staff

    Offered: Fall

    Description: Team projects in applied physics, with corporate affiliation.

    Prerequisites: Seniors only

and

  • Credits: 3

    Instructor: Staff

    Offered: Spring

    Description: Team projects in applied physics, with corporate affiliation.

    Prerequisites: Seniors only

or

  • (taken twice)

    Credits: 3

    Instructor: Staff

    Offered: Fall and Spring

    Description: The 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. Students are expected to present their work orally and to produce a final report conforming to the publication standards of a professional mathematician. Students are expected to take the two semesters of Clinic within a single academic year.

Electives

Suggested math and physics electives of interest (not part of the major):

Study Abroad Considerations

The following applies only to students who will be studying abroad for a semester in their junior or senior year: