printer friendly pageMATH 109: Applied Group Theory
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, crystallographic groups and their applications in chemistry and physics.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Licata, J. (PI)
MATH 110: Applied Number Theory and Field Theory
Number theory and its applications to modern cryptography. Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kahle, M. (PI)
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: Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Licata, J. (PI)
;
Ryzhik, L. (PI)
MATH 113V: Linear Algebra
Topics: matrices, linear equations, vector spaces, linear dependence, bases and coordinates, linear transformations, similarity, eigenvectors and eigenvalues, and diagonalization. Prerequisites: two quarters of single variable calculus, or consent of instructor.
Terms: Sum
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Sanders, M. (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, Win, Sum
| Units: 3
| UG Reqs: GER:DB-Math
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:DB-Math
Instructors:
Katznelson, Y. (PI)
MATH 120: Modern Algebra
Groups acting on sets, examples of ¿nite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a ¿eld; PID and non-PID. Unique factorization domains.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kahle, M. (PI)
;
Vakil, R. (PI)
MATH 121: Modern Algebra II
Continuation of 120. Field of fractions, ¿eld theory and Galois theory. Modules over a PID, quotient modules, non-free modules. Canonical forms, generalized eigenspaces, quotients and duality for vector spaces. Prerequisite:
Math 120.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Venkatesh, A. (PI)
MATH 122: GROUP REPRESENTATIONS
Group representations and group rings, tensor algebra, character theory. Bilinear and quadratic forms, semisimplicity. Induced representations. Classi¿cation of representations, applications. Prerequisite:
Math 120, and either
Math 121 or permission of instructor.
Terms: Spr
| Units: 3
Instructors:
Venkatesh, A. (PI)
MATH 131P: Partial Differential Equations I
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 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:DB-Math
Instructors:
Garapon, P. (PI)
;
Liu, T. (PI)
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