MATH 111: Computational Commutative Algebra
Introduction to the theory of commutative rings, ideals, and modules. Systems of polynomial equations in several variables from the algorithmic viewpoint. Groebner bases, Buchberger's algorithm, elimination theory. Applications to algebraic geometry and to geometric problems.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 114: Introduction to Scientific Computing (CME 108)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint 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.nImplementation of numerical methods in MATLAB programming assignments.nPrerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum

Units: 34

Grading: Letter or Credit/No Credit
Instructors:
Sing Long Collao, C. (PI)
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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Maximo, D. (PI)
;
Yang, T. (PI)
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 nonPID. Unique factorization domains. WIM.
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Li, Z. (PI)
;
Luu, M. (PI)
MATH 131P: Partial Differential Equations I
An introduction to PDE; particularly suitable for nonMath 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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Ignatova, M. (PI)
;
Menz, G. (PI)
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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
;
Zheng, T. (PI)
MATH 16: Mathematics and Statistics in the Real World (STATS 90)
Introduction to noncalculus applications of mathematical ideas and principles in realworld problems. Topics include probability and counting, basic statistical concepts, geometric series. Applications include insurance, gambler's ruin, false positives in disease testing, present value of money, and mortgages. No knowledge of calculus required. Enrollment limited to students who do not have Stanford credit for a high school or college course in calculus or statistics.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and settheoretical operations. The ZermeloFraenkel axiom system and the special role of the axiom of choice and its various equivalents. Wellorderings 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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
MATH 163: The Greek Invention of Mathematics
How was mathematics invented? A survey of the main creative ideas of ancient Greek mathematics. Among the issues explored are the axiomatic system of Euclid's Elements, the origins of the calculus in Greek measurements of solids and surfaces, and Archimedes' creation of mathematical physics. We will provide proofs of ancient theorems, and also learn how such theorems are even known today thanks to the recovery of ancient manuscripts.
Terms: not given this year

Units: 35

UG Reqs: GER:DBHum

Grading: Letter or Credit/No Credit
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