This course introduces students to theories in Fourier analysis. Topics covered include: Fourier series, convergence of Fourier series, Cesaro and Abel summability, Plancherel formula, applications of Fourier series, Fourier transforms, inversion formula, Schwartz space, Poisson summation formula, applications of Fourier transform to partial differential equations, Fourier analysis on Z(N), Fourier analysis on finite abelian groups, Dirichlet’s theorem.
This course is an advanced course in discrete mathematics. It introduces students to advanced techniques in combinatorics. The course consist of two parts: graph theory and combinatorics. Topics in graph theory include planar graphs, Euler cycles, Hamilton circuits, graph coloring, trees, spanning trees, traveling salesperson problem, tree analysis of sorting algorithm, network algorithms (shortest paths, minimum spanning trees, ...). Topics in Combinatorics include counting principles, generating functions, partitions, recurrence relations, divide-and-conquer relations, inclusion-exclusion formula, Polya’s enumeration formula.
This course introduces students to probability theory and some probabilistic models.
In this course, we study the basic pre-calculus mathematical knowledges in the field of Algebra and Analytic Algebra
This course introduces students to complex function theory and partial differential equations.
This course introduces students to basics techniques in solving ordinary differential equations. Topics covered include: direction fields, first order linear equations, separable equations, exact equations, integrating factors, existence and uniqueness theorem, second order linear equations, homogeneous equations, inhomogeneous equations, method of underdetermined coefficients, variations of parameters, higher order linear equations, series solutions, Laplace transforms, Laplace transform methods in solving ordinary differential equations, systems of first order linear equations.
Building on the calculus learned in the first year, this course provides students with a rigorous foundation of single variable calculus. Topics covered include: completeness axiom, convergent sequences, limits, continuity, intermediate value theorem, uniform continuity, differentiation, mean value theorem for derivative, integration, Darboux sums, fundamental theorem of calculus, mean value theorem for integrals, approximations by Taylor polynomials, sequences and series of functions, uniform convergence of functions.
This course introduces students to fundamental concepts and theories in point set topology. Topics covered include: axiom of choice, topological spaces, open and closed sets, basis of topology, product topology, quotient topology, connectedness, path-connectedness, compactness, first and second countable, separable axiom, metrization theorem, complete metric spaces, pointwise and compact convergence.
Game Theory is a branch of mathematics concerned with decision-making. In this course we will learn how to make optimal decisions in business, sports, and other parts of life in a mathematically rigorous way.
This course introduces students to single variable calculus. Topics covered include limits and continuity, differentiation, chain rule, implicit differentiation, maximum and minimum, definite integral, area, volume, series, test of convergence, Taylor series.
This course includes the study of systems of linear equations, matrices, determinants, vectors, vector spaces, linear transformations, inner products, eigenvalues, eigenvectors, symmetric matrices and quadratic forms.