We study the Theory of Mathematical Analysis
We study the theory of Differential Manifolds.
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 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.
In this course, students will learn to apply the concepts and theories in matrix algebra and linear programming. Appropriate methods will be determined to solve various optimization problems. The students will also learn to interpret the solution and sensitivity of a
linear programming problem from the output in excel.
This course covers mathematics which are useful to solve physics problems. The first two chapters covers some fundamental algebra of complex analysis which including complex functions and derivatives, Taylor and Laurent series, and contour integrations. Fourier series and power series method which are essentials tools to solve partial differential equations will also be discussed. Most of the physics problems require one to solve partial differential equations hence the last part of the course covers methods to solving partial differential equations.
This course introduces methods of discrete mathematics to students. Topics covered include: logic, arguments, sets, functions, matrices, number theory, counting techniques, pigeonhole principle, permutations and combinations, relations, graphs, Euler paths, Hamiltonian paths, trees, spanning trees and Boolean algebras.
This course introduces methods of discrete mathematics to students. Topics covered include: logic, arguments, sets, functions, matrices, number theory, counting techniques, pigeonhole principle, permutations and combinations, relations, graphs, Euler paths, Hamiltonian paths, trees, spanning trees, Boolean algebra.
This course introduces students to single variable calculus, including 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, applications of integrals, area, volume, techniques of integration, improper integrals.
Course Code: MAT519
Credit Value: 04
This course introduces students to optimization. Topics covered include: unconstrained optimization, gradient methods, convergence analysis, rate of convergence, Newton and Gauss-Newton methods, conjugate direction methods, quasi-Newton methods, incremental methods, convex optimization, feasible direction methods, gradient projection method and its alternatives, Lagrange multipliers, Karush-Kuhn-Tucker conditions, duality, interior point methods, penalty methods, augmented Lagrangian methods, discrete optimization, dual computational methods.
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 the mathematical theory of interest. Topics covered include: interest rate measurement, valuations of annuities, loan repayment, bond valuation, rate of return of an investment, term structure of interest rates, cashflow duration and immunization, fixed income investments.
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.