printer friendly pageMATH 53H: Honors Multivariable Mathematics
Continuation of 52H. Prerequisite: 52H.
Terms: Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Eliashberg, Y. (PI)
;
Carlotto, A. (TA)
MATH 104: Applied Matrix Theory
Linear algebra for applications in science and engineering: orthogonality, projections, the four fundamental subspaces of a matrix, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. Prerequisites:
MATH 51 and
MATH 52 or 53.
Terms: Win, Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math
MATH 106: Functions of a Complex Variable
Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. Prerequisite: 52.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Yang, T. (PI)
MATH 108: Introduction to Combinatorics and Its Applications
Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Hicks, A. (PI)
MATH 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. WIM.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Bump, D. (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. WIM.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kane, D. (PI)
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.
| UG Reqs: GER:DB-Math
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:DB-Math, WAY-FR
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:DB-Math
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:DB-Math
Instructors:
Li, J. (PI)
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