Joint Major in Mathematics and Physics

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

  • MATH055 HM Discrete Mathematics

    Credits: 3

    Instructors: Benjamin, Bernoff, Lindo, Martonosi, Orrison

    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

  • MATH082 HM Differential Equations

    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

  • MATH131 HM Mathematical Analysis I

    Credits: 3

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

    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

  • MATH157 HM Intermediate Probability

    Credits: 1.5

    Instructors: Benjamin, Haddock, Martonosi, Su, Williams

    Offered: Fall

    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: BIOL154 HM or MATH062 HM

  • MATH171 HM Abstract Algebra I

    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

  • MATH180 HM Introduction to Partial Differential Equations

    Credits: 3

    Instructors: Bernoff, Jacobsen, Zinn-Brooks

    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: MATH082 HM and MATH131 HM

  • MATH198 HM Undergraduate Mathematics Forum

    Credit: 1

    Instructors: Castro, Jacobsen, Orrison, Williams, Zinn-Brooks

    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.

  • MATH199 HM Mathematics Colloquium

    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

  • PHYS051 HM Electromagnetic Theory and Optics

    Credits: 3

    Instructors: Breznay, Donnelly, Eckert, Gerbode, Sahakian

    Offered: Fall

    Description: An introduction to electricity and magnetism leading to Maxwell’s elec­tromagnetic equations in differential and integral form. Selected topics in classical and quantum optics.

    Prerequisites: PHYS023 HM and PHYS024 HM

    Corequisites: MATH082 HM

  • PHYS052 HM Quantum Physics

    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

  • PHYS054 HM Modern Physics Laboratory

    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

  • PHYS111 HM Theoretical Mechanics

    Credits: 3

    Instructor: Ilton

    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

  • PHYS116 HM Quantum Mechanics

    Credits: 3

    Instructor: Gerbode

    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

  • PHYS117 HM Statistical Mechanics and Thermodynamics

    Credits: 3

    Instructors: Esin, Saeta

    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

  • PHYS134 HM Optics Laboratory

    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

  • PHYS151 HM Electromagnetic Fields

    Credits: 3

    Instructor: Sahakian

    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 (MATH180 HM or PHYS064 HM)

OR

  • PHYS154 HM Fields and Waves

    Credits: 3

    Instructor: Staff

    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: MATH180 HM or PHYS064 HM

OR

  • PHYS156 HM Foundations of Field Theory

    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 (MATH180 HM or PHYS064 HM)

AND

  • PHYS195 HM Physics Colloquium (taken twice)

    Credit: 0.5

    Instructor: Eckert

    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

  • MATH164 HM Scientific Computing

    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

  • MATH165 HM Numerical Analysis

    Credits: 3

    Instructors: Bernoff, Haddock, de Pillis, 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

  • PHYS170 HM Computational Methods in Physics

    Credits: 2

    Instructor: Sahakian

    Offered: Spring

    Description: Advanced techniques in computational physics including high performance computing using parallelization (both CPU- and GPU-based ), machine learning and neural networks, and metaprogramming.

    Prerequisites: PHYS052 HM, PHYS064 HM, and PHYS111 HM

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.

  • PHYS199 HM Senior Thesis in Physics (taken twice)

    Credits: 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

  • MATH197 HM Senior Thesis in Mathematics (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: Senior standing as a mathematics major and permission from the Mathematics Senior Thesis Coordinator.

OR

  • PHYS193 HM Physics Clinic

    Credits: 3

    Instructor: Staff

    Offered: Fall

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

    Prerequisites: Seniors only

AND

  • PHYS194 HM Physics Clinic

    Credits: 3

    Instructor: Staff

    Offered: Spring

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

    Prerequisites: Seniors only

OR

  • MATH193 HM Mathematics Clinic (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.

    Prerequisites: Senior standing as a mathematics major or permission of the Mathematics Clinic director.

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: