BSC136 Discrete Mathematics B (AIT) (DMT) (SWE) by Tam Kam Fai
BSC129 Discrete Mathematics (PHY) (CST-Group 2) by Tam Kam Fai
This course introduces students to infinite series, multivariable calculus and vector calculus including infinite series and convergence test, Taylor series and approximation, parametric equations and polar coordinates, geometry of space, vector functions, partial derivatives, application of partial derivatives, maxima and minima, multiple integrals, iterated integrals, applications of multiple integrals, line and surface integrals, Green’s Theorem, Gauss’s Divergence Theorem and Stokes’s Theorem, Fourier series.
This course introduces students to infinite series, multivariable calculus and vector calculus including infinite series and convergence test, Taylor series and approximation, parametric equations and polar coordinates, geometry of space, vector functions, partial derivatives, application of partial derivatives, maxima and minima, multiple integrals, iterated integrals, applications of multiple integrals, line and surface integrals, Green’s Theorem, Gauss’s Divergence Theorem and Stokes’s Theorem, Fourier series.
This course is a continuation of MAT 104 Linear Algebra I. Topics covered include: inner product spaces, Gram-Schmidt process, QRdecomposition, least squares, quadratic forms, orthogonal matrices, orthogonal diagonalization of symmetric matrices, linear transformations, isomorphism, similarity, LU-decomposition, singular value decomposition, applications of linear algebra.
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 the methods for analyzing time series. Topics covered include: time series, forecasting, stationary processes, AR. MA, ARMA, ARIMA, ARCH, GARCH models, spectral analysis, model fitting, long memory processes.
This course covers various topics on probability and statistics, including conditional probability, random variables and distributions, expectation, typical distributions, stochastic processes, estimation, testing hypotheses, categorical data and nonparametric methods, and linear statistical models
This course introduces students to infinite series, multivariable calculus, and vector calculus. Topics covered include: Infinite series and convergence test, Taylor series and approximation, vector functions, partial derivatives, application of partial derivatives, maxima and minima, multiple integrals, iterated integrals, line and surface integrals, Green’s Theorem, Gauss’s Divergence Theorem, and Stokes’s
Theorem.
This course covers the fundamentals of numerical methods. Topics include solutions of equations, polynomial approximation and interpolation, numerical differentiation and integration, ordinary differential equations, and matrix algebra.
This course introduces students to fundamental theories and basic techniques in complex analysis. Topics covered include: analytic
functions, Cauchy-Riemann equations, harmonic functions, reflection principle, elementary functions, entire functions, branches of
logarithms, zeros and singularities, contour integrals, Cauchy-Goursat theorem, Cauchy integral formula, fundamental theorem of algebra,
maximum modulus principle, Taylor series and Laurent series, residues and poles, Cauchy’s residue theorem, application of residues,
argument principle, Rouche’s theorem.
This course introduces methods of discrete mathematics to students. Topics covered include: logic, arguments, algorithms, well-ordering
principle, recursion, counting techniques, pigeonhole principle, permutations and combinations, divide-and-conquer algorithms, generating
functions, inclusion-exclusion, equivalence relation, partial orderings.
This course introduces students to essential concepts and techniques in algebraic geometry that are required for the advanced studies of mathematics. Topics covered include: algebraic varieties, quasiprojective varieties, singularities, divisors, Reimann-Roch theorem on curves, intersection numbers, Grassmanians, Hilbert polynomials and moduli spaces.