MATH 19:
Calculus
Introduction to differential calculus of functions of one variable. Topics: review of elementary functions including exponentials and logarithms, limits, rates of change, the derivative, and applications. Math 19, 20, and 21 cover the same material as Math 41 and 42, but in three quarters rather than two. Prerequisites: precalculus, including trigonometry, advanced algebra, and analysis of elementary functions.
Terms: Aut, Win, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
MATH 41:
Calculus (accelerated)
Introduction to differential and integral calculus of functions of one variable. Topics: limits, rates of change, the derivative and applications, introduction to the definite integral and integration. Math 41 and 42 cover the same material as Math 19-20-21, but in two quarters rather than three. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions, including exponentials and logarithms.
Terms: Aut
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
MATH 41A:
Calculus ACE
Students attend MATH 41 lectures with different recitation sessions, four hours instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR
MATH 42:
Calculus (Accelerated)
Continuation of 41. Methods of symbolic and numerical integration, applications of the definite integral, introduction to differential equations, infinite series. Prerequisite: 41 or equivalent.
Terms: Aut, Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
MATH 42A:
Calculus ACE
Students attend MATH 42 lectures with different recitation sessions, four hours instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut, Win
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR
MATH 51:
Linear Algebra and Differential Calculus of Several Variables
Geometry and algebra of vectors, systems of linear equations, matrices and linear transformations, diagonalization and eigenvectors, vector valued functions and functions of several variables, parametric curves, partial derivatives and gradients, the derivative as a matrix, chain rule in several variables, constrained and unconstrained optimization. Prerequisite: 21, or 42, or a score of 4 on the BC Advanced Placement exam or 5 on the AB Advanced Placement exam, or consent of instructor.
Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors: ;
Goodman, E. (PI);
Hasson, H. (PI);
Hicks, A. (PI);
Ionel, E. (PI);
Lucianovic, M. (PI);
Maximo, D. (PI);
Moore, K. (PI);
Wang, Y. (PI);
Wieczorek, W. (PI);
Yang, T. (PI);
Yun, Z. (PI);
Zheng, T. (PI);
Lucianovic, M. (GP)
MATH 51A:
Linear Algebra and Differential Calculus of Several Variables, ACE
Students attend MATH 51 lectures with different recitation sessions: four hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see http://soe.stanford.edu/edp/programs/ace.html.
Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR
MATH 51H:
Honors Multivariable Mathematics
For prospective Mathematics majors in the honors program and students from other areas of science or engineering who have a strong mathematics background. Three quarter sequence covers the material of 51, 52, 53, and additional advanced calculus and ordinary and partial differential equations. Unified treatment of multivariable calculus, linear algebra, and differential equations with a different order of topics and emphasis from standard courses. Students should know one-variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on BC Advanced Placement exam, or consent of instructor.
Terms: Aut
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
MATH 51M:
Introduction to MATLAB for Multivariable Mathematics
Corequisite: MATH 51.
Terms: Aut
| Units: 1
MATH 52:
Integral Calculus of Several Variables
Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations. Divergence theorem and the theorems of Green, Gauss, and Stokes. Prerequisite: 51 and 42 or equivalents.
Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
MATH 53:
Ordinary Differential Equations with Linear Algebra
Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 and 42 or equivalents.
Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
MATH 113:
Linear Algebra and Matrix Theory
Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization.
Terms: Aut, Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
MATH 115:
Functions of a Real Variable
The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Honors math majors and students who intend to do graduate work in mathematics should take 171. Prerequisite: 51.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math
MATH 118:
Mathematics of Computation
Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites: MATH 51 and 53.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
MATH 120:
Groups and Rings
Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
MATH 131P:
Partial Differential Equations I
An introduction to PDE; particularly suitable for non-Math majors. Topics include physical examples of PDE's, method of characteristics, D'Alembert's formula, maximum principles, heat kernel, Duhamel's principle, separation of variables, Fourier series, Harmonic functions, Bessel functions, spherical harmonics. Students who have taken MATH 171 should consider taking MATH 173 rather than 131p. Prerequisite: 53.
Terms: Aut, Win
| Units: 3
| UG Reqs: GER:DB-Math
MATH 136:
Stochastic Processes (STATS 219)
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite: STATS 116 or MATH 151 or equivalent. Recommended: MATH 115 or equivalent.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
MATH 146:
Analysis on Manifolds
Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 52 or 52H.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
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: students should be comfortable doing proofs.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
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: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
5 times
(up to 5 units total)
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.
Terms: Aut, Win, Spr
| Units: 1
| Repeatable
3 times
(up to 3 units total)
MATH 197:
Senior Honors Thesis
(Staff) May be repeated 3 times for a max of 9 units.
Terms: Aut, Win, Spr
| Units: 1-6
| Repeatable
3 times
(up to 9 units total)
Instructors: ;
Brendle, S. (PI);
Brumfiel, G. (PI);
Bump, D. (PI);
Candes, E. (PI);
Cantarero Lopez, J. (PI);
Carlsson, G. (PI);
Cohen, R. (PI);
Conrad, B. (PI);
Demanet, L. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Eliashberg, Y. (PI);
Feferman, S. (PI);
Finn, R. (PI);
Galatius, S. (PI);
Holmes, S. (PI);
Ionel, E. (PI);
Kahle, M. (PI);
Katznelson, Y. (PI);
Keller, J. (PI);
Kerckhoff, S. (PI);
Kojima, F. (PI);
Li, J. (PI);
Liu, T. (PI);
Lucianovic, M. (PI);
Mazzeo, R. (PI);
Milgram, R. (PI);
Milgrom, P. (PI);
Mints, G. (PI);
Ornstein, D. (PI);
Osserman, R. (PI);
Papanicolaou, G. (PI);
Ryzhik, L. (PI);
Schoen, R. (PI);
Simon, L. (PI);
Soundararajan, K. (PI);
Vakil, R. (PI);
Vasy, A. (PI);
Venkatesh, A. (PI);
White, B. (PI);
Wieczorek, W. (PI)
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 instructor. 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.
Terms: Aut, Win, Spr, Sum
| Units: 1
| Repeatable
3 times
(up to 3 units total)
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: 1-3
| Repeatable
3 times
(up to 9 units total)
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)
MATH 205A:
Real Analysis
Basic measure theory and the theory of Lebesgue integration. Prerequisite: 171 or equivalent.
Terms: Aut
| Units: 3
MATH 210A:
Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, introduction to representation theory. Prerequisite: 122 or equivalent.
Terms: Aut
| Units: 3
MATH 215A:
Complex Analysis, Geometry, and Topology
Analytic functions, complex integration, Cauchy's theorem, residue theorem, argument principle, conformal mappings, Riemann mapping theorem, Picard's theorem, elliptic functions, analytic continuation and Riemann surfaces.
Terms: Aut
| Units: 3
MATH 216A:
Introduction to Algebraic Geometry
Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.
Terms: Aut
| Units: 3
| Repeatable
for credit
MATH 220:
Partial Differential Equations of Applied Mathematics (CME 303)
First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut
| Units: 3
MATH 230A:
Theory of Probability (STATS 310A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116, MATH 171.
Terms: Aut
| Units: 2-4
MATH 249A:
Topics in number theory
Terms: Aut
| Units: 3
| Repeatable
3 times
(up to 9 units total)
MATH 280:
Evolution Equations in Differential Geometry
Terms: Aut, Win
| Units: 3
| Repeatable
for credit
MATH 290B:
Model Theory B (PHIL 350B)
Decidable theories. Model-theoretic background. Dense linear orders, arithmetic of addition, real closed and algebraically closed fields, o-minimal theories.
Terms: Aut
| Units: 1-3
| Repeatable
for credit
MATH 310:
Top Ten Algorithms of the 20th Century (CME 329)
A high-level survey course covering one algorithm per week: metropolis, simplex method, conjugate gradient, QR, quicksort, fast fourier transform, maxcut, fast multipole method, integer relation detection, and convex/semi-definite programming.
Terms: Aut
| Units: 3
MATH 360:
Advanced Reading and Research
Terms: Aut, Win, Spr, Sum
| Units: 1-10
| Repeatable
for credit
Instructors: ;
Brendle, S. (PI);
Brumfiel, G. (PI);
Bump, D. (PI);
Candes, E. (PI);
Carlsson, G. (PI);
Chatterjee, S. (PI);
Cohen, R. (PI);
Conrad, B. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Durrleman, V. (PI);
Eliashberg, Y. (PI);
Feferman, S. (PI);
Fetecau, R. (PI);
Finn, R. (PI);
Galatius, S. (PI);
Ionel, E. (PI);
Iyer, G. (PI);
Kahle, M. (PI);
Katznelson, Y. (PI);
Kerckhoff, S. (PI);
Levy, D. (PI);
Li, J. (PI);
Li, T. (PI);
Liu, T. (PI);
Mazzeo, R. (PI);
Milgram, R. (PI);
Mints, G. (PI);
Mirzakhani, M. (PI);
Munson, B. (PI);
Ornstein, D. (PI);
Papanicolaou, G. (PI);
Papikian, M. (PI);
Rubin, K. (PI);
Rubinstein, Y. (PI);
Ryzhik, L. (PI);
Schoen, R. (PI);
Simon, L. (PI);
Soundararajan, K. (PI);
Storm, P. (PI);
Thiem, F. (PI);
Vakil, R. (PI);
Vasy, A. (PI);
Venkatesh, A. (PI);
White, B. (PI);
Ying, L. (PI);
Yun, Z. (PI)
MATH 361:
Research Seminar Participation
Participation in a faculty-led seminar which has no specific course number.
Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable
for credit
Instructors: ;
Brendle, S. (PI);
Brumfiel, G. (PI);
Bump, D. (PI);
Candes, E. (PI);
Carlsson, G. (PI);
Cohen, R. (PI);
Conrad, B. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Durrleman, V. (PI);
Eliashberg, Y. (PI);
Feferman, S. (PI);
Galatius, S. (PI);
Ionel, E. (PI);
Kahle, M. (PI);
Kerckhoff, S. (PI);
Levy, D. (PI);
Li, J. (PI);
Liu, T. (PI);
Mazzeo, R. (PI);
Mints, G. (PI);
Mirzakhani, M. (PI);
Papanicolaou, G. (PI);
Ryzhik, L. (PI);
Schoen, R. (PI);
Simon, L. (PI);
Soundararajan, K. (PI);
Vakil, R. (PI);
Vasy, A. (PI);
Venkatesh, A. (PI);
White, B. (PI)
MATH 391:
Research Seminar in Logic and the Foundations of Mathematics (PHIL 391)
Contemporary work. May be repeated a total of three times for credit. Math 391 students attend the logic colloquium in 380-381T.
Terms: Aut, Win, Spr
| Units: 1-3
| Repeatable
3 times
(up to 9 units total)
MATH 802:
TGR Dissertation
Terms: Aut, Win, Spr, Sum
| Units: 0
| Repeatable
for credit
Instructors: ;
Brendle, S. (PI);
Brumfiel, G. (PI);
Bump, D. (PI);
Candes, E. (PI);
Carlsson, G. (PI);
Cohen, R. (PI);
Conrad, B. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Eliashberg, Y. (PI);
Feferman, S. (PI);
Galatius, S. (PI);
Ionel, E. (PI);
Kerckhoff, S. (PI);
Levy, D. (PI);
Li, J. (PI);
Liu, T. (PI);
Mazzeo, R. (PI);
Mirzakhani, M. (PI);
Papanicolaou, G. (PI);
Ryzhik, L. (PI);
Schoen, R. (PI);
Simon, L. (PI);
Soundararajan, K. (PI);
Vakil, R. (PI);
Vasy, A. (PI);
Venkatesh, A. (PI);
White, B. (PI)
MATH 259:
mirror symmetry
| Units: 3
| Repeatable
3 times
(up to 9 units total)
