MATH 158: Probability and Stochastic Differential Equations for Applications (CME 298)
Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with some applications in science and/or engineering. Prerequisites:
Math 53 and either
Math 151,
Stats 117 or equivalent level of probability knowledge.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Papanicolaou, G. (PI)
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:
Math 151,
Stats 117 or equivalent level of probability knowledge.
Terms: Win, Spr
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Abrishami, T. (PI)
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite:
Math 56 or comfort with proof-writing.
Last offered: Spring 2025
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
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. Fulfills WIM requirement. For more information on WIM guidance, please visit:
https://mathematics.stanford.edu/wim-guidance.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 172: Lebesgue Integration and Fourier Analysis
Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines. Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite:
Math 171 or consent of instructor.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Dembo, A. (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:
Math 171 or equivalent.
Terms: Win
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Franceschini, F. (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:
Math 115 or 171.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Franceschini, F. (PI)
;
Nowak, V. (TA)
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 195: Senior Exploration and Synthesis
This capstone course offers senior mathematics majors the opportunity to synthesize and apply their mathematical knowledge through collaborative, project-based learning. Students will be assigned to small groups to explore topics ranging from real-world applications to open-ended problems in mathematics. Through a combination of guided research, skill-building workshops, and peer collaboration, students will develop both professional and academic skill sets, supporting their transition into industry roles or graduate study in quantitative fields. Enrollment is by application.
Terms: Aut, Win
| Units: 4