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, firstorder ordinary differential equations, existence, uniqueness, and longterm behavior of solutions; bifurcations; approximate solutions; secondorder ordinary differential equations and their properties, applications; firstorder 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, ZinnBrooks
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 centrallimit 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, ZinnBrooks
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; SturmLiouville theory and orthogonal expansions; Bessel functions.
Prerequisites: MATH082 HM and MATH131 HM

MATH198 HM Undergraduate Mathematics Forum
Credit: 1
Instructors: Castro, Jacobsen, Orrison, Williams, ZinnBrooks
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 CSmath 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, onedimensional and threedimensional 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 laboratorylecture 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 leastsquares 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 fastFourier 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 nonlinear 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 GPUbased ), 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: 13
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, solidstate and lowtemperature 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, realworld 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):
 MATH136 HM – Complex Variables and Integral Transforms
 MATH142 HM – Differential Geometry
 MATH181 HM – Dynamical Systems
 PHYS161 HM – Topics in Quantum Theory
Study Abroad Considerations
The following applies only to students who will be studying abroad for a semester in their junior or senior year:
 Sophomores may enroll in MATH198 HM – Undergraduate Mathematics Forum.
 Mathematics Colloquium requirement will not be waived.
 At most one semester of Physics Colloquium may be waived.