Topics will include systems of linear equations, matrix operations and inverses, vector spaces and subspaces, determinants, eigenvalues and eigenvectors, matrix factorizations, inner products and orthogonality, and linear transformations. Emphasis will …
Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Emphasis will …
Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra …
Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. …
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisites: MATH 3100 …
This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets …
This course covers linear algebra/complex analysis/vector differential & integral calculus. Thus it is a compressed version of MATH 3351 & MATH 3340 and a review of some of the material …
This course is a beginning course in partial differential equations/Fourier analysis/special functions (such as spherical harmonics and Bessel functions). The discussion of partial differential equations will include the Laplace and …
A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; …
Includes Taylor's theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or least-square approximation. Prerequisite: MATH …
This course covers the basic topology of metric spaces/continuity and differentiation of functions of a single variable/Riemann-Stieltjes integration/convergence of sequences and series. Prerequisite: MATH 3310 or permission of instructor.
Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: multivariable calculus, basic real analysis, linear algebra and one of the following: …
Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, Reed-Muller …
This course provides the opportunity to offer a new topic in the subject of mathematics.
Review of topics from Math 3351: vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth and generality. The course continues with more …
Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and …
Combinatorics of counting using basic tools from calculus, linear algebra, and occasionally group theory. Topics include: tableaux, symmetric polynomials, Catalan numbers, quantum binomial theorem, q-exponentials, partition and q-series identities. Bijective …
Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry …
Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also …
Topics include abstract topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., …