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 116: 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. Prerequisites: 52, and 115 or 171.
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Li, J. (PI)
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 initialvalue and boundaryvalue ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.
Terms: Aut

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Ying, L. (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 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: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Conrad, B. (PI)
MATH 122: Modules and Group Representations
Modules over PID. Tensor algebra. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite:
Math 120. Also recommended: 113.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Venkatesh, A. (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)
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