Prerequisite: 136 or equivalent and differential equations.nnNOTE: Undergraduates require instructor permission to enroll. The course emphasizes computations alongside an intuitive understanding of key ideas. Prerequisites: 51 or equivalent. The widespread use of computers makes it important for users of math to understand concepts: novel users of quantitative tools in the future will be those who understand ideas and how they fit with examples and applications. Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; Central Limit Theorem and laws of large numbers. MATH 114. MATH 263B. MATH 245C. Proofs and Modern Mathematics. See the "Mathematical and Computational Science" section of this bulletin. are discussed in the "Graduate Degrees" section of this bulletin. May be repeated for credit up to 6 total units. Topics in Combinatorics. MATH 87Q. Differential Geometry. MATH 249C. Honors math majors and students who intend to do graduate work in mathematics should take 120. Prerequisite: 53. All MATH courses at Stanford University (Stanford) in Stanford, California. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. MATH 280. Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods. Fundamental concepts are presented in the context of their application to biological and physiological problems including cancer, cardiovascular disease, infectious disease, and systems biology. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Department of Mathematics Building 380, Stanford, California 94305 Phone: (650) 725-6284 Email Courses are available in subjects including computer science, math, creative writing, philosophy, engineering, and more. Modern Mathematics: Continuous Methods. Discrete time stochastic control and Bayesian filtering. 3 Units. Course work for the M.S. 3 Units. 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, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations, behavior of solutions near an equilibrium point, and Sturm-Liouville theory. Spectral theory of compact operators; applications to integral equations. This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. 3 Units. MATH 70SI. Preference to sophomores. You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course. Linear Algebra, Multivariable Calculus, and Modern Applications. Conformal Field Theory is a branch of physics with origins in solvable lattice models and string theory. Application required: This course is ideal for students who would like to learn about the reasoning underlying mathematical results, but at a pace and level of abstraction not as intense as MATH 61CM/DM, as a consequence benefiting from additional opportunity to explore the reasoning. Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates. Advanced Reading and Research. Momentum map and its properties. Submenu, Show MATH 155. This course is a series of case-studies in doing applied mathematics on surprising phenomena we notice in daily life. Same as: CME 321A. The Department of Mathematics participates with the departments of Computer Science, Management Science and Engineering, and Statistics in a program leading to a B.S. 3 Units. Includes introduction to proof-writing. degree: The following requirements refer to the Mathematics Bachelor’s degree with the Computer Science Theory/Discrete Mathematics Subplan. Partial Differential Equations of Applied Mathematics. Students who have taken MATH 171 should consider taking MATH 173 rather than 131P. Incompressible surfaces, irreducible manifolds, prime decomposition, Morse theory, Heegaard diagrams, Heegaard splittings, the Thurston norm, sutured manifold theory, Heegaard Floer homology, sutured Floer homology. These will not count against the limit of 6 CR/NC elective units that may be applied towards the major. The department offers 3 sequences in multivariable mathematics. 3 Units. 5 Units. Topics in field theory, commutative algebra, algebraic geometry, and finite group representations. 1 Unit. This subplan is intended for students wishing for a strong and deep background in the area of computer science theory and mathematics. Plurisubharmonic functions and pseudo-convexity. Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Hedging strategies and management of risk. The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research and analysis in Mathematics. Phone: (650) 725-6284Email, Promote and support the department and its mission. The mathematics requirements for departmental and School of Engineering majors are delineated by major in the detailed “Majors & Minors” section. See the the "Advanced Placement" section of this bulletin. Topics may include 1) subadditive and multiplicative ergodic theorems, 2) notions of mixing, weak mixing, spectral theory, 3) metric and topological entropy of dynamical systems, 4) measures of maximal entropy. No lecture component; in-class meetings reserved for student presentations, attendance mandatory. The University requires that the graduate advisor be assigned in the student’s first graduate quarter even though the undergraduate career may still be open. Same as: CME 306. MATH 232. Credit can fulfill the elective requirement for Math majors. (Suitable for advanced undergraduates.) Prerequisite: MATH 20 or equivalent. Similar to 115 but altered content and more theoretical orientation. This is achieved through completion of courses, in the primary field as well as related areas, and experience with independent work and specialization. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. Oscillations. (MATH 106 offers a less theoretical treatment.) Students with questions about the honors program should see the department's director of undergraduate studies. Topics covered: basic constructions (metropolis, Gibbs sampler, data augmentation, hybrid Monte Carlo); spectral techniques (explicit diagonalization, Poincaré, and Cheeger bounds); functional inequalities (Nash, Sobolev, Log Sobolev); probabilistic techniques (coupling, stationary times, Harris recurrence). WIM. Prerequisites: MATH 51. Majors interested in honors can apply in winter quarter of their junior year at the earliest, and no later than the last day of classes in the spring quarter of junior year. MATH 269. Meet Mykel Kochenderfer, Associate Professor of Aeronautics and Engineering at Stanford. MATH 104 and ENGR 108 cover complementary topics in applied linear algebra. Examples and problems from various applied areas. Possible topics: principal bundles, vector bundles, classifying spaces. 3 Units. Mathematics of Computation. If you are impacted by this, please contact our office to request an extension: Celestial Mechanics. The Mathematics Department courses must include at least 18 units numbered 200 or above. 3 Units. MATH 52. Markov and strong Markov property. 3 Units. Basic point set topology. 3 Units. 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. 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. May be repeated for credit.nnNOTE: Undergraduates require instructor permission to enroll. Graduate students are active contributors to the advising relationship, proactively seeking academic and professional guidance and taking responsibility for informing themselves of policies and degree requirements for their graduate program. The selection of courses for the 64 total units must contain the required courses listed in the chart below. Submenu, Stanford University Mathematical Organization (SUMO), Stanford University Mathematics Camp (SUMaC), Linear Algebra, Multivariable Calculus, and Modern Applications, Linear Algebra, Multivariable Calculus, and Modern Applications, ACE, Integral Calculus of Several Variables, ACE, Ordinary Differential Equations with Linear Algebra, ACE, Ordinary Differential Equations with Linear Algebra, Introduction to Combinatorics and Its Applications, Introduction to Scientific Computing (CME 108), Basic Probability and Stochastic Processes with Engineering Applications (CME 298), Lebesgue Integration and Fourier Analysis, Partial Differential Equations of Applied Mathematics (CME 303), Numerical Solution of Partial Differential Equations (CME 306), Stochastic Methods in Engineering (CME 308, MS&E 324), Mathematics and Statistics of Gambling (STATS 334), Introduction to Stochastic Differential Equations, Applied Fourier Analysis and Elements of Modern Signal Processing (CME 372), Topics in Representation Theory: Affine Lie Algebras and Modular Forms, Topics in Applied Mathematics: A World of Flows II. 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