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.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Soundararajan, K. (PI)
MATH 16: Mathematics and Statistics in the Real World (STATS 90)
Introduction to noncalculus applications of mathematical ideas and principles in realworld problems. Topics include probability and counting, basic statistical concepts, geometric series. Applications include insurance, gambler's ruin, false positives in disease testing, present value of money, and mortgages. No knowledge of calculus required. Enrollment limited to students who do not have Stanford credit for a high school or college course in calculus or statistics.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and settheoretical operations. The ZermeloFraenkel axiom system and the special role of the axiom of choice and its various equivalents. Wellorderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Terms: Aut

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
MATH 163: The Greek Invention of Mathematics
How was mathematics invented? A survey of the main creative ideas of ancient Greek mathematics. Among the issues explored are the axiomatic system of Euclid's Elements, the origins of the calculus in Greek measurements of solids and surfaces, and Archimedes' creation of mathematical physics. We will provide proofs of ancient theorems, and also learn how such theorems are even known today thanks to the recovery of ancient manuscripts.
Terms: not given this year

Units: 35

UG Reqs: GER:DBHum

Grading: Letter or Credit/No Credit
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 51H or 115 or consent of the instructor. WIM
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Schoen, R. (PI)
;
Soundararajan, K. (PI)
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.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ignatova, M. (PI)
MATH 175: Elementary Functional Analysis
Linear operators on Hilbert space. Spectral theory of compact operators; applications to integral equations. Elements of Banach space theory. Prerequisite: 115 or 171.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Menz, G. (PI)
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 for credit

Grading: Satisfactory/No Credit
Instructors:
Soundararajan, K. (PI)
MATH 199: Independent Work
Undergraduates pursue a reading program; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for math majors. Approval of Undergraduate Affairs Committee is required to use credit for honors majors area requirement. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum

Units: 13

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Brendle, S. (PI)
;
Brumfiel, G. (PI)
;
Bump, D. (PI)
...
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Instructors:
Brendle, S. (PI)
;
Brumfiel, G. (PI)
;
Bump, D. (PI)
;
Camilier, I. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Church, T. (PI)
;
Cohen, R. (PI)
;
Conrad, B. (PI)
;
Dembo, A. (PI)
;
Diaconis, P. (PI)
;
Duffie, D. (PI)
;
Eliashberg, Y. (PI)
;
Feferman, S. (PI)
;
Finn, R. (PI)
;
Galatius, S. (PI)
;
Ionel, E. (PI)
;
Katznelson, Y. (PI)
;
Keller, J. (PI)
;
Kerckhoff, S. (PI)
;
Li, J. (PI)
;
Liu, T. (PI)
;
Lucianovic, M. (PI)
;
Mazzeo, R. (PI)
;
Milgram, R. (PI)
;
Mirzakhani, M. (PI)
;
Ornstein, D. (PI)
;
Osserman, R. (PI)
;
Papanicolaou, G. (PI)
;
Ryzhik, L. (PI)
;
Schoen, R. (PI)
;
Simon, L. (PI)
;
Soundararajan, K. (PI)
;
Toussaint, A. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
Venkatesh, A. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Ying, L. (PI)
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