## MATH 143: Differential Geometry

Geometry of curves and surfaces in three-space and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.

| UG Reqs: GER:DB-Math

Instructors:
Schoen, R. (PI)

## MATH 144: Riemannian Geometry

Smooth manifolds, tensor fields, geometry of Riemannian and Lorentz metrics, the Levi-Civita connection and curvature tensor, Ricci curvature, scalar curvature, and Einstein manifolds, spaces of constant curvature. Prerequisites:
Math 51, 52, and 53.

## MATH 148: Algebraic Topology

Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.

| UG Reqs: GER:DB-Math

Instructors:
Berwick-Evans, D. (PI)

## MATH 149: Applied Algebraic Topology

Introduction to algebraic topology and its applications, in particular persistent homology as a tool for shape and pattern recognition from high dimensional data sets, with examples analyzed using state-of-the-art software. Prerequisite: linear algebra.

## MATH 155: Analytic Number Theory

Topics in analytic number theory such as the distribution of prime numbers, the prime number theorem, twin primes and Goldbach's conjecture, the theory of quadratic forms, Dirichlet's class number formula, Dirichlet's theorem on primes in arithmetic progressions, and the fifteen theorem. Prerequisite: 152, or familiarity with the Euclidean algorithm, congruences, residue classes and reduced residue classes, primitive roots, and quadratic reciprocity.

| UG Reqs: GER:DB-Math

## MATH 173: Theory of Partial Differential Equations

A rigorous introduction to PDE accessible to advanced undergraduates. Elliptic, parabolic, and hyperbolic equations in many space dimensions including basic properties of solutions such as maximum principles, causality, and conservation laws. Methods include the Fourier transform as well as more classical methods. The Lebesgue integral will be used throughout, but a summary of its properties will be provided to make the course accessible to students who have not had 172 or 205A. Prerequisite: 171 or equivalent.

Instructors:
Maximo, D. (PI)

## MATH 174: Calculus of Variations

An introductory course emphasizing the historical development of the theory, its connections to physics and mechanics, its independent mathematical interest, and its contacts with daily life experience. Applications to minimal surfaces and to capillary surface interfaces. Prerequisites:
Math 171 or equivalent.

## MATH 191: Research Project

Undergraduates pursue an individual or group research project under Math department faculty supervision. Math Department approval is required prior to enrolling. A maximum of 5 units of credit can be used towards the Math course requirement for the Math major. May be repeated for credit for up to 10 units per academic year.

| Repeatable for credit

Instructors:
Vakil, R. (PI)

## MATH 196: Undergraduate Colloquium

Weekly lectures by different experts on topics in pure and applied mathematics that go beyond the standard curriculum. May be repeated for credit for up to 3 units. Does not count toward the math major or minor.

| Repeatable for credit

## MATH 198: Practical Training

Only for students majoring in mathematics. Students obtain employment in a relevant industrial or research activity to enhance their professional experience. Students submit a concise report detailing work activities, problems worked on, and key results. May be repeated for credit up to 3 units. Prerequisite: qualified offer of employment and consent of department. Prior approval by Math Department is required; you must contact the Math Department's Student Services staff for instructions before being granted permission to enroll.

| Repeatable for credit

Instructors:
Conrad, B. (PI)

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