MATH 143: Differential Geometry
Geometry of curves and surfaces in three-space. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces. Prerequisite:
Math 52.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Lai, Y. (PI)
;
Cua, M. (TA)
MATH 155: Analytic Number Theory
Introduction to Dirichlet series and Dirichlet characters, Poisson summation, Gauss sums, analytic continuation for Dirichlet L-functions, applications to prime numbers (e.g., prime number theorem, Dirichlet's theorem). Prerequisites: Complex analysis (
Math 106 or 116),
Math 152 (or comparable familiarity with the Euclidean algorithm, multiplicative group modulo n, and quadratic reciprocity), and experience with basic analysis arguments.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Conrad, B. (PI)
;
Rizk, K. (TA)
MATH 159: Discrete Probabilistic Methods
Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent. Typically in alternating years.
Terms: Aut
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Borga, J. (PI)
;
Rajasekaran, F. (TA)
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced and general version of
Math 115, introducing and using metric spaces. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite:
Math 61CM, or 61DM, or
Math 51 and
Math 115. WIM
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 193: Polya Problem Solving Seminar
Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition. Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability. Students present solutions to the class. Open to anyone with an interest in mathematics.
Terms: Aut
| Units: 1
| Repeatable
4 times
(up to 4 units total)
Instructors:
Manolescu, C. (PI)
MATH 193X: Polya Problem Solving Seminar
Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition. Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability. Open to anyone with an interest in mathematics. Taught concurrently with
Math 193, but students who sign up for
Math 193X are given homework and exams. Students cannot enroll in both 193 and 193X during the same quarter. Math majors may use
Math 193X towards their elective requirements.
Terms: Aut
| Units: 3
Instructors:
Manolescu, C. (PI)
MATH 197: Senior Honors Thesis
Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable
3 times
(up to 9 units total)
Instructors:
Abouzaid, M. (PI)
;
Barrett, C. (PI)
;
Borga, J. (PI)
...
more instructors for MATH 197 »
Instructors:
Abouzaid, M. (PI)
;
Barrett, C. (PI)
;
Borga, J. (PI)
;
Charikar, M. (PI)
;
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Icard, T. (PI)
;
Linderman, S. (PI)
;
Manolescu, C. (PI)
;
Montanari, A. (PI)
;
Reingold, O. (PI)
;
Rotskoff, G. (PI)
;
Ryzhik, L. (PI)
;
Schramm, T. (PI)
;
Schwarz, K. (PI)
;
Soundararajan, K. (PI)
;
Vondrak, J. (PI)
MATH 199: Reading Topics
For Math majors only. Undergraduates pursue a reading program under the direction of a Math faculty member; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for Math majors. Departmental approval required; please contact the Student Services Specialist for the enrollment proposal form at least 2 weeks before the final study list deadline. May be repeated for credit. Enrollment beyond a third section requires additional approval.
Terms: Aut, Win, Spr, Sum
| Units: 3
| Repeatable
for credit
Instructors:
Borga, J. (PI)
;
Bump, D. (PI)
;
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Ionel, E. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Taylor, R. (PI)
MATH 205A: Real Analysis
Basic measure theory and the theory of Lebesgue integration. Prerequisite:
Math 171.
Math 172 is also recommended.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Aut
| Units: 3
Instructors:
White, B. (PI)
;
Wu, Y. (TA)
MATH 210A: Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, canonical forms and Jordan decomposition. Prerequisite:
Math 121. It is also recommended to have taken at least one of
Math 122,
Math 145, or
Math 154.nNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Aut
| Units: 3
Instructors:
Conrad, B. (PI)
;
KAZANIN, S. (TA)
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