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 …
Studies selected analysis topics accessible to undergraduates sufficiently advanced in the math major curriculum. Prerequisite: courses in real analysis (MATH 3310 or equivalent) and linear algebra (MATH 3351 or equivalent).
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., …