| MATH101 | Math Discovery Lab | MDL is a discovery-based project course in mathematics. Students work independently in small groups to explore open-ended mathematical problems and discover original mathematics. Students formulate conjectures and hypotheses; test predictions by comp... |
| MATH104 | Applied Matrix Theory | Linear algebra for applications in science and engineering. The course introduces the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and nearly all quantitative fields o... |
| MATH106 | Functions of a Complex Variable | Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (Math 116 offers a more theoretical treatment.) Prerequisite: 52. |
| MATH107 | Graph Theory | An introductory course in graph theory establishing fundamental concepts and results in variety of topics. Topics include: basic notions, connectivity, cycles, matchings, planar graphs, graph coloring, matrix-tree theorem, conditions for hamiltonicit... |
| MATH108 | Introduction to Combinatorics and Its Applications | Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent. |
| MATH109 | Groups and Symmetry | Applications of the theory of groups. Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing. Applications: rotational symmetry groups, the study of the Platonic solids, c... |
| MATH110 | Number Theory for Cryptography | Number theory and its applications to modern cryptography. Topics include: congruences, primality testing and factorization, public key cryptography, and elliptic curves, emphasizing algorithms. Includes an introduction to proof-writing. This course... |
| MATH113 | 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... |
| MATH115 | Functions of a Real Variable | The development of 1-dimensional real analysis (the logical framework for why calculus works): sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Includes introduction to proof-writing. Prerequisite:... |
| MATH116 | Complex Analysis | Analytic functions, Cauchy integral formula, power series and Laurent series, calculus of residues and applications, conformal mapping, analytic continuation, introduction to Riemann surfaces, Fourier series and integrals. (Math 106 offers a less the... |
| MATH118 | 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 discretizati... |
| MATH120 | Groups and Rings | Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced treatment of group theory than in Math 109, also including ring theory. Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simpl... |
| MATH121 | Galois Theory | Field of fractions, splitting fields, separability, finite fields. Galois groups, Galois correspondence, examples and applications. Prerequisite: Math 120 and (also recommended) 113. |
| MATH122 | Modules and Group Representations | Modules over PID. Tensor products over fields. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite: Math 120. Also recommended: 113. |
| MATH131P | Partial Differential Equations | 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 seri... |
| MATH136 | Stochastic Processes | 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, sam... |
| MATH137 | Mathematical Methods of Classical Mechanics | Newtonian mechanics. Lagrangian formalism. E. Noether's theorem. Oscillations. Rigid bodies. Introduction to symplectic geometry. Hamiltonian formalism. Legendre transform. Variational principles. Geometric optics. Introduction to the theory of integ... |
| MATH138 | Celestial Mechanics | Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variationa... |
| MATH142 | Hyperbolic Geometry | An introductory course in hyperbolic geometry. Topics may include: different models of hyperbolic geometry, hyperbolic area and geodesics, Isometries and Mobius transformations, conformal maps, Fuchsian groups, Farey tessellation, hyperbolic structur... |
| MATH143 | Differential Geometry | Geometry of curves and surfaces in three-space. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces. Prerequisite: Math 53. |
| MATH144 | Introduction to Topology and Geometry | Point set topology, including connectedness, compactness, countability and separation axioms. The inverse and implicit function theorems. Smooth manifolds, immersions and submersions, embedding theorems. Prerequisites: Math 61CM or both Math 113 and... |
| MATH145 | Algebraic Geometry | An introduction to the methods and concepts of algebraic geometry. The point of view and content will vary over time, but include: affine varieties, Hilbert basis theorem and Nullstellensatz, projective varieties, algebraic curves. Required: 120.... |
| MATH147 | Differential Topology | Introduction to smooth methods in topology including tranvsersality, intersection number, fixed point theorems, as well as differential forms and integration. Prerequisites: Math 144 or equivalent. |
| MATH148 | Algebraic Topology | Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120. |
| MATH151 | Introduction to Probability Theory | A proof-oriented development of basic probability theory. Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; Centr... |
| MATH152 | Elementary Theory of Numbers | Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quad... |
| MATH154 | Algebraic Number Theory | Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations. Prerequisites: 120 and 121, especially modules over principal ideal domains and Galois theory of finite fields. |
| MATH155 | 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 analys... |
| MATH158 | Basic Probability and Stochastic Processes with Engineering Applications | 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 motio... |
| MATH159 | 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 15... |
| MATH161 | 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... |
| MATH171 | 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... |
| MATH172 | 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 Lebe... |
| MATH173 | 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. Metho... |
| MATH175 | 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. |
| MATH177 | Geometric Methods in the Theory of Ordinary Differential Equations | Hamiltonian systems and their geometry. First order PDE and Hamilton-Jacobi equation. Structural stability and hyperbolic dynamical systems. Completely integrable systems. Perturbation theory. |
| MATH18 | Foundations for Calculus | This course develops and enriches fundamental skills in foundational math to prepare students for success in calculus and other courses at Stanford that rely on quantitative methods (such as in biology, chemistry, computer science, economics, enginee... |
| MATH19 | Calculus | Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites:... |
| MATH193 | 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 th... |
| MATH193X | 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... |
| MATH197 | 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 m... |
| MATH198 | Practical Training | Only for undergraduate 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... |
| MATH199 | 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... |
| MATH19ACE | Calculus, ACE | Additional problem solving session for Math 19 guided by a course assistant. Concurrent enrollment in Math 19 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH20 | Calculus | The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus. Integration by substitution and by parts. Area between curves, and volume by slices, washers, and shells. Initial-value problems, exponential and logistic m... |
| MATH205A | Real Analysis | Basic measure theory and the theory of Lebesgue integration. Prerequisite: Math 171. Math 172 is also recommended.
NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instru... |
| MATH205B | Real Analysis | Point set topology, basic functional analysis, Fourier series, and Fourier transform. Prerequisites: 171 and 205A or equivalent.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contac... |
| MATH205C | Topics in Harmonic Analysis | Topics of contemporary interest in Fourier, harmonic, and/or microlocal analysis. Prerequisite: Math 205B.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for p... |
| MATH20ACE | Calculus, ACE | Additional problem solving session for Math 20 guided by a course assistant. Concurrent enrollment in Math 20 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH21 | Calculus | This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all leve... |
| MATH210A | 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... |
| MATH210B | Modern Algebra II | Continuation of 210A. Topics in field theory, commutative algebra, algebraic geometry, and finite group representations. Prerequisites: 210A, and 121 or equivalent.
NOTE: Undergraduates require instructor permission to enroll. Undergraduates inter... |
| MATH210C | Lie Theory | Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite: Math 210A and familiarity with the basics of finite group representations. When the course is on Lie groups, familiarity with tangent spaces and integration on manifolds... |
| MATH215A | Algebraic Topology | Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Prerequisites: 120 and 144.
NOTE: Un... |
| MATH215B | Differential Topology | Topics: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes' Theorem, deRham cohomology, intersection theory via Poincare duality, Morse the... |
| MATH215C | Differential Geometry | This course will be an introduction to Riemannian Geometry. Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison... |
| MATH216A | Introduction to Algebraic Geometry | Algebraic varieties, and introduction to schemes, morphisms, sheaves, and the functorial viewpoint. May be repeated for credit. Prerequisites: 210AB or equivalent.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested... |
| MATH216B | Introduction to Algebraic Geometry | Continuation of 216A. May be repeated for credit.
NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant backgro... |
| MATH216C | Introduction to Algebraic Geometry | Continuation of 216B. May be repeated for credit.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant backgroun... |
| MATH217C | Complex Differential Geometry | Complex structures, almost complex manifolds and integrability, Hermitian and Kahler metrics, connections on complex vector bundles, Chern classes and Chern-Weil theory, Hodge and Dolbeault theory, vanishing theorems, Calabi-Yau manifolds, deformat... |
| MATH21A | Calculus, ACE | Students attend one of the regular MATH 21 lectures with a longer discussion section of two hours per week instead of one. Active mode: students in small groups discuss and work on problems, with a TA providing guidance and answering questions. Appli... |
| MATH21ACE | Calculus, ACE | Additional problem solving session for Math 21 guided by a course assistant. Concurrent enrollment in Math 21 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH220 | Partial Differential Equations of Applied Mathematics | First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus... |
| MATH226 | Numerical Solution of Partial Differential Equations | Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation... |
| MATH228 | Stochastic Methods in Engineering | The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to paramete... |
| MATH230A | Theory of Probability I | 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 num... |
| MATH230B | Theory of Probability II | Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory,... |
| MATH230C | Theory of Probability III | Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infini... |
| MATH231 | Mathematics and Statistics of Gambling | Probability and statistics are founded on the study of games of chance. Nowadays, gambling (in casinos, sports and the Internet) is a huge business. This course addresses practical and theoretical aspects. Topics covered: mathematics of basic random... |
| MATH232 | Topics in Probability: Percolation Theory | An introduction to first passage percolation and related general tools and models. Topics include early results on shape theorems and fluctuations, more modern development using hyper-contractivity, recent breakthrough regarding scaling exponents, an... |
| MATH233A | Topics in Combinatorics | A topics course in combinatorics and related areas. The topic will be announced by the instructor.
NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permiss... |
| MATH233B | Topics in Combinatorics | A topics course in combinatorics and related areas. The topic will be announced by the instructor.
NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permiss... |
| MATH233C | Topics in Combinatorics | A topics course in combinatorics and related areas. The topic will be announced by the instructor. |
| MATH234 | Large Deviations Theory | Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistica... |
| MATH235A | Topics in combinatorics | This advanced course in extremal combinatorics covers several major themes in the area. These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods. |
| MATH235B | Modern Markov Chain Theory | This is a graduate-level course on the use and analysis of Markov chains. Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics. Topics covered: basic constructions (metropolis, Gibb... |
| MATH235C | Topics in Markov Chains | Classical functional inequalities (Nash, Faber-Krahn, log-Sobolev inequalities), comparison of Dirichlet forms. Random walks and isoperimetry of amenable groups (with a focus on solvable groups). Entropy, harmonic functions, and Poisson boundary (fol... |
| MATH236 | Introduction to Stochastic Differential Equations | Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Introduction to stoc... |
| MATH237A | Topics in Financial Math: Market microstructure and trading algorithms | Introduction to market microstructure theory, including optimal limit order and market trading models. Random matrix theory covariance models and their application to portfolio theory. Statistical arbitrage algorithms. |
| MATH238 | Mathematical Finance | Stochastic models of financial markets. Risk neutral pricing for derivatives, hedging strategies and management of risk. Multidimensional portfolio theory and introduction to statistical arbitrage. Prerequisite: Math 136 or equivalent. NOTE: Undergra... |
| MATH243 | Functions of Several Complex Variables | Holomorphic functions in several variables, Hartogs phenomenon, d-bar complex, Cousin problem. Domains of holomorphy. Plurisubharmonic functions and pseudo-convexity. Stein manifolds. Coherent sheaves, Cartan Theorems A&B. Levi problem and its solut... |
| MATH244 | Riemann Surfaces | Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. Riemann-Hurwitz formula. Riemann-Roch theorem, Abel-Jacobi map. Uniformization theorem. Hyperbolic sur... |
| MATH245A | Topics in Algebraic Geometry | Topics of contemporary interest in algebraic geometry. May be repeated for credit.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing inf... |
| MATH245B | Topics in Algebraic Geometry | Topics of contemporary interest in algebraic geometry. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing in... |
| MATH245C | Topics in Algebraic Geometry | Topics of contemporary interest in algebraic geometry. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing in... |
| MATH249A | Topics in number theory | Topics of contemporary interest in number theory. May be repeated for credit.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing informat... |
| MATH249B | Topics in Number Theory | Topics of contemporary interest in number theory. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing informa... |
| MATH249C | Topics in Number Theory | Topics of contemporary interest in number theory. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing informa... |
| MATH256A | Partial Differential Equations | The theory of linear and nonlinear partial differential equations, beginning with linear theory involving use of Fourier transform and Sobolev spaces. Topics: Schauder and L2 estimates for elliptic and parabolic equations; De Giorgi-Nash-Moser theory... |
| MATH256B | Partial Differential Equations | Continuation of 256A. |
| MATH257A | Symplectic Geometry and Topology | Linear symplectic geometry and linear Hamiltonian systems. Symplectic manifolds and their Lagrangian submanifolds, local properties. Symplectic geometry and mechanics. Contact geometry and contact manifolds. Relations between symplectic and contact m... |
| MATH257B | Symplectic Geometry and Topology | Continuation of 257A. May be repeated for credit.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant backgroun... |
| MATH257C | Symplectic Geometry and Topology | Continuation of 257B. May be repeated for credit. |
| MATH258 | Topics in Geometric Analysis | May be repeated for credit.NOTE: 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... |
| MATH262 | Applied Fourier Analysis and Elements of Modern Signal Processing | Introduction to the mathematics of the Fourier transform and how it arises in a number of imaging problems. Mathematical topics include the Fourier transform, the Plancherel theorem, Fourier series, the Shannon sampling theorem, the discrete Fourier... |
| MATH263A | Topics in Representation Theory | Topics in Contemporary Representation Theory. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information... |
| MATH263B | Topics in Representation Theory | Topics in Contemporary Representation Theory. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information... |
| MATH263C | Topics in Representation Theory | Topics in Contemporary Representation Theory. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information... |
| MATH269 | Topics in symplectic geometry | May be repeated for credit. |
| MATH270 | Geometry and Topology of Complex Manifolds | Complex manifolds, Kahler manifolds, curvature, Hodge theory, Lefschetz theorem, Kahler-Einstein equation, Hermitian-Einstein equations, deformation of complex structures. May be repeated for credit. |
| MATH271 | The H-Principle | The language of jets. Thom transversality theorem. Holonomic approximation theorem. Applications: immersion theory and its generaliazations. Differential relations and Gromov's h-principle for open manifolds. Applications to symplectic geometry. Mic... |
| MATH272 | Topics in Partial Differential Equations | NOTE: 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, readin... |
| MATH273 | Topics in Mathematical Physics | Covers a list of topics in mathematical physics. The specific topics may vary from year to year, depending on the instructor's discretion. Background in graduate level probability theory and analysis is desirable. |
| MATH275A | Topics in Applied Math I | Topics in Applied Mathematics I. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about releva... |
| MATH275B | Topics in Applied Math II | Topics in Applied Mathematics II. May be repeated for credit. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relev... |
| MATH275C | Topics in Applied Mathematics III: The Mathematics of AI | This course introduces the mathematics knowledge involved in machine learning and artificial intelligence on two levels. In the first half of the quarter, we introduce math needed to understand machine learning practices, i.e. data, models, and algor... |
| MATH282A | Low Dimensional Topology | The theory of surfaces and 3-manifolds. Curves on surfaces, the classification of diffeomorphisms of surfaces, and Teichmuller space. The mapping class group and the braid group. Knot theory, including knot invariants. Decomposition of 3-manifolds: t... |
| MATH282B | Homotopy Theory | Homotopy groups, fibrations, spectral sequences, simplicial methods, Dold-Thom theorem, models for loop spaces, homotopy limits and colimits, stable homotopy theory. May be repeated for credit up to 6 total units. Prerequisite: Math 215A. NOTE: Under... |
| MATH282C | Fiber Bundles and Cobordism | Possible topics: principal bundles, vector bundles, classifying spaces. Connections on bundles, curvature. Topology of gauge groups and gauge equivalence classes of connections. Characteristic classes and K-theory, including Bott periodicity, algebra... |
| MATH283A | Topics in Topology | Topics of contemporary interest in topology. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background su... |
| MATH286 | Topics in Differential Geometry | Topics of contemporary interest in differential geometry. May be repeated for credit.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing... |
| MATH298 | Graduate Practical Training | Only for mathematics graduate students. 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 resul... |
| MATH305 | Applied mathematics through toys and magic | This course is a series of case-studies in doing applied mathematics on surprising phenomena we notice in daily life. Almost every class will show demos of these phenomena (toys and magic) and suggest open projects. The topics range over a great vari... |
| MATH355 | Graduate Teaching Seminar | Required of and limited to second year Mathematics graduate students. |
| MATH360 | Advanced Reading and Research | No Description Set |
| MATH382 | Qualifying Examination Seminar | No Description Set |
| MATH51 | Linear Algebra, Multivariable Calculus, and Modern Applications | This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computatio... |
| MATH51A | Linear Algebra, Multivariable Calculus, and Modern Applications, ACE | Students attend one of the regular MATH 51 lectures with a longer discussion section of four hours per week instead of two. Active mode: students in small groups discuss and work on problems from a worksheet distributed 2 or 3 days in advance, with a... |
| MATH51ACE | Linear Algebra, Multivariable Calculus, and Modern Applications, ACE | Additional problem solving session for Math 51 guided by a course assistant. Concurrent enrollment in Math 51 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH52 | 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: Math 21 an... |
| MATH52ACE | Integral Calculus of Several Variables, ACE | Additional problem solving session for Math 52 guided by a course assistant. Concurrent enrollment in Math 52 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH53 | Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications | Ordinary differential equations and initial value problems, linear systems of such equations with an emphasis on second-order constant-coefficient equations, stability analysis for non-linear systems (including phase portraits and the role of eigenva... |
| MATH53ACE | Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications, ACE | Additional problem solving session for Math 53 guided by a course assistant. Concurrent enrollment in Math 53 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/... |
| MATH56 | Proofs and Modern Mathematics | How do mathematicians think? Why are the mathematical facts learned in school true? In this course students will explore higher-level mathematical thinking and will gain familiarity with a crucial aspect of mathematics: achieving certainty via mathem... |
| MATH61CM | Modern Mathematics: Continuous Methods | This is the first part of a theoretical (i.e., proof-based) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces... |
| MATH61DM | Modern Mathematics: Discrete Methods | This is the first part of a theoretical (i.e., proof-based) sequence in discrete mathematics and linear algebra. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and line... |
| MATH62CM | Modern Mathematics: Continuous Methods | A proof-based introduction to manifolds and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space (with many examples), differential forms and their geometric interpretations,... |
| MATH62DM | Modern Mathematics: Discrete Methods | This is the second part of a theoretical (proof-based) sequence with a focus on discrete mathematics. The central objects discussed in this course are finite fields. These are beautiful structures in themselves, and very useful in large areas of mode... |
| MATH63CM | Modern Mathematics: Continuous Methods | A proof-based course on ordinary differential equations. Topics include the inverse and implicit function theorems, implicitly-defined submanifolds of Euclidean space, linear systems of differential equations and necessary tools from linear algebra,... |
| MATH63DM | Modern Mathematics: Discrete Methods | Third part of a proof-based sequence in discrete mathematics, though independent of the second part (62DM). The first half of the quarter gives a brisk-paced coverage of probability and random processes with an intensive use of generating functions a... |
| MATH75SI | Learn to Give a Math Talk | This class focuses on preparing and presenting math talks. The first few weeks introduce the main skills, learning from panels, guest lectures, and discussions. In the remaining weeks, participants practice presenting math topics to classmates that... |
| MATH77Q | Probability and gambling | One of the earliest probabilistic discussions was in 1654 between two French mathematicians, Pascal and Fermat, on the following question: 'If a pair of six-sided dice is thrown 24 times, should you bet even money on the occurrence of at least one `d... |
| MATH802 | TGR Dissertation | No Description Set |
| MATH87Q | Mathematics of Knots, Braids, Links, and Tangles | Preference to sophomores. Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants. The geometry and algebra of braids, including their relationships to knots. Topology of surfaces. Brief summa... |
| SOAR10MA | Preparation for Success in Mathematics at Stanford | This course will build on and enrich students' fundamental prerequisite skills in foundational mathematics to prepare students for success in Calculus and further mathematics courses at Stanford University. This course is intended for students that... |