Topics in the graph theory part of the course include (if time permits) trees, k-connectivity, Eulerian and Hamiltonian graphs, tournaments, graph coloring, planar graphs, Euler’s formula, the 5-Color theorem, Kuratowski’s theorem, and the matrix-tree theorem. The second part of the course will deal with topics in the theory of finite partially ordered sets. This will … Read more
Fundamental group, covering spaces, simplicial complexes, graphs and trees, applications to group theory, singular and simplicial homology, Eilenberg-Steenrod axioms, Brouwer’s and Lefschetz’ fixedpoint theorems, and other topics.
Finite dimensional linear spaces and matrix representations of linear transformations. Bases, subspaces, determinants, eigenvectors and canonical forms. Structure of solutions of systems of linear equations. Applications to differential and difference equations. Provides more depth and content than MATH 417. MATH 420 is the proper election for students contemplating research in mathematics.
This course is devoted to the use of Fours Series and Transforms in the solution of boundary-value problems for 2nd order linear partial differential equations. We study the heat and wave equations in one and higher dimension. We introduce the spherical and cylindrical Bessel functions, Legendre polynomials and analysis of data smoothing and filtering
An introduction to combinatorics, covering basic counting techniques (inclusion-exclusion, permutations and combinations, generating functions) and fundamentals of graph theory (paths and cycles, trees, graph coloring). Additional topics may include partially ordered sets, recurrence relations, partitions, matching theory, and combinatorial algorithms
This course is an introduction to applications and integration of dynamical systems and game theory to model population and ecological dynamics and evolutionary processes. Topics include Lotka-Volterra systems, non-cooperative games, replicator dynamics and genetic mechanisms of selection and mutation, and other adaptive systems.
Intended primarily for students of engineering and of other cognate subjects. Doctoral students in mathematics elect Mathematics 596. Complex numbers, continuity, derivative, conformal representation, integration, Cauchy theorems, power series, singularities, and applications to engineering and mathematical physics.
This is an introduction to methods of applied functional analysis. Students are expected to master both the proofs and applications of major results. The prerequisites include linear algebra, undergraduate analysis, advanced calculus and complex variables. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program.