This course introduces students to essential concepts and techniques in algebraic topology that are required for the advanced studies of mathematics. Topics covered include: fundamental group, van Kampen theorem, covering spaces, deck transformations, simplicial homology, singular homology, exact sequences, Mayer-Vietoris sequences, cohomology, Künneth formula, Poincarĕ duality, homotopy group, Whitehead’s theorem, fibre bundles.
This course introduces students to single variable calculus. Topics covered include: functions, limits, continuity, derivative, mean value theorem for derivative, indefinite integral, definite integral, fundamental theorem of calculus, applications of derivatives, maximum and minimum, rate of change, mean value theorem for integrals, approximations of the integrals, applications of integrals, area, volume, transcendental functions, techniques of integration, improper integrals, first order differential equations.
This course introduces students to basic techniques in solving partial differential equations. Topics covered include: first order linear PDE, quasilinear PDE, characteristic method, classification of second order linear PDE, parabolic equations, hyperbolic equations, elliptic equations, canonical forms, heat equation, wave equation, Laplace equation, Laplace transform method, Fourier transform method, Sturm-Liouville eigenvalue problems, PDE’s with more than two independent variables, Green’s function method.
This course introduces students to fundamental knowledge of regression analysis. Topics covered include: simple and multiple linear regression, model adequacy checking, ways to correct model inadequacies, indicator variables as predictors, the problem of multicollinearity in predictors, variable selection in model building and validation of the regression models.
This course introduces students to the methods in statistics required for data analysis. Topics covered include: descriptive statistics, exploratory data analysis, sampling methods, point estimation, confidence intervals, hypothesis testing, chi-squared tests, single factor analysis of variance, simple linear regression, and some distribution free procedures.
This course introduces students to basic concepts and methods in quantitative methods and data analysis. Topics covered include: matrix algebra, determinants, eigenvalues and eigenvectors, functions, limits, derivatives, maxima and minima, integration, Taylor series, partial derivatives, Lagrange multiplier method.
This course introduces students to complex function theory and partial differential equations.