Course Descriptions

Undergraduate Courses

Mathematics Section

S0325 Calculus (4/4) Limits, differentiation and integration of functions of one variable, infinite series, functions of several variables, partial derivatives, multiple integrals.

S0252 Fundamentals of Mathematics (2/2) Introduction to basic notion of set theory: topics include axioms of set, relations, partially ordered sets, natural numbers, finite and infinite sets and logic.

S0439 Linear Algebra (3/3) Vector spaces, linear transformations, matrices, eigenvalues and eigenvectors, Jordan and rational canonical forms, inner product spaces.

S0210 Advanced Calculus (4/4) The number systems, topological structures of Rⁿ, continuous functions, differentiable functions of one variable, Riemann-Stieltjes integrals, sequences and series of functions, differentiation on Rⁿ, inverse and implicit function theorems, integration on Rⁿ.

S0051 Algebra (3/3) Basic algebra structures, including groups, rings and algebraic field extensions.

S0317 Differential Equations (3/0) Ordinary differential equations, first order differential equations, higher order linear differential equations, system of linear differential equations, Laplace transforms, series method.

S0090 Vector Analysis (0/3) Tangent, normal and binomial vector, curvature, orthogonal curvilinear coordinates, Laplacian, line integral, conservative fields, potential function, oriented surface, Green's theorem, divergence theorem, Stoke's theorem.

S0336 Computer Applications in Mathematics (3/3) The use of computer and software packages in solving problems in mathematics.

S0450 Probability Theory (3/0) Basic concepts in probability, discrete and continuous random variables, expectation, bivariate probability distributions and functions of random variables , sampling distributions.

M0517 Statistics (0/3) Fundamental concepts of statistics including estimation, testing of hypotheses and applications.

E0767 Numerical Analysis (3/3) Interpolating polynomials, Newton's method, fixed point iteration, numerical differentiation and integration, Euler's method, Runge-Kutta method, Gaussian elimination with pivoting, power method, Householder transformation, QR algorithm, least square approximation, orthogonal functions.

S0024 Analysis I (3/3) Various topics in real analysis, including measure, measurable functions, integrable functions, the Lebesque spaces, modes of convergence, decomposition of measures, and generation of measures.

S0132 Topology (3/3) Essentials in point set topology, including the concept of topological spaces, connectedness, compactness, countability axioms, separation axioms.

S0155 Modern Algebra (3/3) Further studies in the structures of groups, rings, fields and Galois theory.

S0277 Combinatorics (3/3) Enumeration, generating functions, recurrence relations, graph theory and networks.

S0579 Complex Analysis (3/3) Analytic functions, complex integration, Cauchy's theorem, sequence and series of analytic functions, conformal mappings, and analytic continuation.

S0284 Geometry (3/3) Study of curves and surfaces including first and second fundamental forms, Gaussian map, Gauss-Bonnet theorem, geodesics.

S0027 Analysis II (3/3) Further studies of various topics in real analysis.

S0616 Linear Algebra II (3/3) Further studies of various topics in linear algebra.

Data Science and Mathematical Statistics Section

S0325 Calculus (4/4) Limits, differentiation and integration of functions of one variable, infinite series, functions of several variables, partial derivatives, multiple integrals.

S0439 Linear Algebra (3/3) Vector spaces, linear transformations, matrices, eigenvalues and eigenvectors, Jordan and rational canonical forms, inner product spaces.

S0266 Introduction to Statistics (2/2) This is the first course in statistics which covers the basic concepts of statistics and its uses in daily life.

S0250 Applied Statistical Software (2/2) Introduction to data input, output and programming using SAS and S-plus.

S0364 Computer Applications in Statistics (3/3) Advanced programming of SAS including SAS/connect, SAS/graph, SAS/AF and SAS/insight.

S0487 Discrete Mathematics (3/3) Fundamental mathematics, generating functions, recurrence relations, graph theory, networks and Boolean algebra.

M0264 Time Series (0/3) Single variable time series models, estimation, ARIMA models, model building and forecasting, seasonal models.

S0295 Nonparametric Statistics (3/3)This course introduces nonparametric methods and related theories.

S0423 Mathematical statisticsI (4/4) Some probability concepts, random variables and their distribution, moments of random variables, characteristic function, moment generating functions. Stochastic independence, limit theorem, transformations of random variables and random vectors, order statistics, point estimation, testing bypothesis, confidence intervals, Quadratic forms.

S0458 Stochastic Process (3/0) Poisson process, Markov chains, and applications.

M0202 Quality Control (3/3) Importance of quality control, early history, Deming's philosophy, process thinking, improving a process, the seven basic tools, control charts for means, ranges, individuals, proportions and counts.

S0722 Clinical Trials (3/3) Planning and design, basic design consideration, randomization and blinding, sample size determination, efficacy and safety evaluations.

M1043 Survival Analysis (3/3) Special features of survival data, survival function, KM estimate, Cox’s PH model and its assumption, general stratified Cox procedure,

extension of Cox’s PH model.

M0153 Operation Research (3/3) Linear programming, the simplex algorithm, sensitivity analysis, transportation, assignment, transshipment problems, network models, integer programming, game theory, queuing theory, inventory models.

S0408 Experimental Design (3/3) One-way and two-way classification, Latin squares, factorial designs.

S0424 Mathematical Statistics II (3/3) Further studies of various topics in mathematical statistics.

S0061 Reliability Analysis (3/3) Reliability concepts, and statistical analysis of censored data, degradation data and accelerated life tests.

S0487 Discrete Mathematics (3/3) Counting, logic, mathematical induction, relations, finite state machines, generating functions, recurrence relations and graph theory.

M0115 Multivariate analysis (3/3) Multivariate normal distribution, Hotelling’s test, MANOVA, Factor analysis.

S0733 Queuing theory (3/3) Birth-death models, M/M/1 system, M/M/2 systems, M/G/1 system, G/M/1 system, networks of queues, transient solutions.

Master’s Program

Mathematics

S0046 Algebraic Topology (3/3) Singular homology theory, cohomology ring and duality in manifolds.

S0051 Algebra (3/3) Groups and rings; free, projective and injective modules; Hom and tensor product, field extensions and Galois Theory.

S0024Analysis (3/3) Measure, Lebesgue measure, Lebesgue integral, L^P-spaces, integration on product spaces, complex measure.

S0277 Combinatorial Mathematics (3/3) Introduction to enumerative combinatorics, graph theory and combinatorial designs.

S0320 Differential Geometry (3/3) Euclidean geometry, geometry of surfaces in Euclidean space, Riemannian geometry.

S0238 Partial Differential Equations (3/3) First-order equations, principles for higher-order equations, Fourier methods, the differential equations of physics and engineering

S0566 Ordinary Differential Equation (3/3) Existence and uniqueness, continuation. autonomous and nonautonomous system. Poincaré-Bendixson theorem, linear and linearization, Poincaré map, stability near equilibia and periodic orbit, bifurcation diagram, congugacy, structurally stable.

S0187 Matrix Theory (3/3) Similarity, diagonalization, unitary equivalence, normal matrices, Jordan canonical forms, variational characterizations of eigenvalues of Hermitian matrices, matrix norms, location of eigenvalues, nonnegative matrices.

S0631 Fractal Geometry (3/3) Hausdoff measure and dimension, alternative definitions of dimension, techniques for calculating dimensions.

S0632 Hyperspace Theory (3/3) Various topologies on spaces whose elements are certain subsets of a given underlying space are studied.

S0686 Commutative Algebra (3/3) Various topics in commutative rings, including Noetherian, Artinian rings and modules, localization, primary decomposition, Hilbert Nullstellensatz, integral extensions and valuations, analysis of Dedekind domains.

S0079 Abelian Groups (3/3) Ulm's Theorem and various structure theorems, homological methods and recent results.

S0602 Topics in Algebra (3/3) Various topics in algebra, such as homological algebra, representations of finite groups and characters.

S0402 Graph Theory (3/3) Planar graphs, graphs coloring domination, independence, chromatic numbers and networks.

S0598 Combinatorial Design (3/3) Orthogonal Latin squares, symmetric designs, Steiner systems and tournament designs.

S0573 Topics in Analysis (2/2) Selected special topics in mathematical analysis.

Mathematical Statistics

S0231 Advanced Mathematical Statistics (3/3) Probability theory, transformations and expectations, common families of distributions, multiple random variables, properties of a random sample, principles of data reduction, point estimation, hypothesis testing, interval estimation, decision theory.

S0233 Advanced Probability (3/3) Topics includes random walks, probability theory, random variables independence, expectation, convergence, limit theorems, conditional expectation, Martingales.

S0075 Statistical Application in Biology (3/3) Generalized linear model, categorical data analysis, survival analysis, nonparametric methods, with applications in various areas of biostatistics.

S0269 Statistical Methods (3/3) Regression analysis, analysis of frequencies variable, introduction to time series data, CR and RCB designs, nest design, factorial experiment.

S0441 Linear Statistical Models (3/3) This course covers general linear model, generalized linear model, with basic concepts, theorems, and applications.

S0295 Nonparametric Statistics (3/3) This course introduces the important theoretical foundations of nonparametric statistics, both classical and current.

S0408 Experimental Designs (3/3) Factorial treatment designs, random and mixed models, complete block designs. incomplete block designs, fractional factorial designs, split-plot designs, repeated measure designs, cross-over designs.

M0115 Multivariate Analysis (3/3) Multivariate normal distribution, inferences about multivariate means and linear models, principal components, factor analysis, discrimination and classification, clustering.

S0061 Reliability Analysis (3/3) Censoring and statistical methods, life table and graphs, inference procedures for distributions of exponential, Weibull, extreme-value and other models, parametric regression models, proportional hazards and related regression models, nonparametric methods, goodness-of-fit tests.

S0264 Time Series (3/3) Autocorrelation function, stationary models, nonstationary models, seasonal models, transfer function models, intervention models.

Ph.D. Program

S0137 Functional Analysis (3/3) Topological vector spaces, local convexity, completeness, convexity, duality, Banach algebras, Gelfand-Naimark theory, the spectral theorem.

S0427 Number Theory (3/3) Algebraic integers, quadratic and cyclotomic fields, class-group and class-number, p-adic numbers, Zeta and L-functions.

E1197 Dynamic Systems (3/3) Diffeomorphisms and flows, stable manifold, center manifold, normal form, versal deformation.

S0593 Smooth Dynamic Systems (3/3) Diffeomorphisms, flows, invariant manifold, transversality, generic properties, structural stability.

S0590 Nonlinear Functional Analysis (3/3) Basic problems of the theory of non-expansive mappings in Banach spaces, fixed point theorems and convergence of successive approximations.

S0591 Linear Integral Equations (3/3) Basic existence theorem, integral equations with L₂ kernels, applications to partial differential equations, Fourier transforms, the Fredholm theory.

S0594 Nonparametric Regression (3/3) Theorems, methods, and applications of kernel regression procedure.