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; dual space and dual basis; eigenvectors and eigenvalues; diagonalization. Includes an introduction to proof-writing. (
Math 104 offers a more application-oriented treatment.) Prerequisites:
Math 51
Terms: Aut, Win, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Malinnikova, E. (PI)
;
Swaminathan, M. (PI)
;
Vondrak, J. (PI)
...
more instructors for MATH 113 »
Instructors:
Malinnikova, E. (PI)
;
Swaminathan, M. (PI)
;
Vondrak, J. (PI)
;
Amar, S. (TA)
;
Niu, J. (TA)
MATH 115: 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:
Math 51 or
Math 56.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 116: Complex Analysis
Holomorphic and analytic functions, power series, Cauchy integral and Cauchy integral formula, meromorphic functions and differential forms, calculus of residues and applications, analytic continuation, conformal mappings, Riemann mapping theorem, Laurent series and conformal classification of annuli, harmonic functions and Dirichlet problem, introduction to Riemann surfaces, theory of elliptic functions and integrals. (
Math 106 offers a less theoretical treatment). Prerequisites: 51,52 and 171, or 61cm and 62cm.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Eliashberg, Y. (PI)
;
Chen, Y. (TA)
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: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Cortinovis, A. (PI)
MATH 120: 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 simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM course. Prerequisite:
Math 51 and some prior proof-writing experience.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 121: Galois Theory
Field of fractions, splitting fields, separability, finite fields. Galois groups, Galois correspondence, examples and applications. Prerequisite:
Math 120 and (also recommended) 113.
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Bump, D. (PI)
;
Lopez, A. (TA)
MATH 131P: Partial Differential Equations
An introduction to techniques for solving PDE's. Topics include physical examples (such as the heat equation, wave equation, and Laplace's equation in 2 and 3 dimensions) and separation of variables with various coordinate systems to relate them to Sturm-Liouville problems using Fourier, Bessel, and Legendre series. Prerequisite:
Math 53.
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
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.
http://statweb.stanford.edu/~adembo/math-136/
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 137: 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 integrable systems. Prerequisites:
Math 53 and 147 or
Math 62CM and 63CM.
Last offered: Spring 2019
| UG Reqs: GER:DB-Math, WAY-FR
MATH 138: 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; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.
Last offered: Autumn 2014
| UG Reqs: GER:DB-Math
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