Department of Mathematics Course Descriptions
 Vector Calculus Students learn about differentiation of a function with several variables, method of Lagrange's multiplier, integral calculus, Green’s theorem, divergence theorem, and Stokes’ theorem. Linear Algebra (1), (2) Deals with space vector, basis, dimension, matrix, determinant, linear change, eigenvalue, matrix diagonalization and the Jordan form of matrix. Set Theory Deals with numbers and sets, relations, functions, semi-ordered sets, axiom of choice, supplementary theorem, well-ordering theorem, the finite set of natural numbers, infinite sets, cardinal numbers, ordinal numbers and the transfinite cyclic method. Introduction to Mathematical Analysis (1) Students learn about the strict definitions of the limit of sequences, infinite series, and continuity of function, based on which they learn various characteristics related to continuity of function and series. Introduction to Mathematical Analysis (2) Students learn about the definitions and characteristics of derivatives of function and integral function; as well as the limits of series of function. Introduction to Mathematical Analysis (3) (Planned to be closed down in 2010) This course covers series, infinite series, limit of a function, continuous, differentiation, series of functions, series, and integrals of Riemann-Stieltjes. Metric Space Based on the set theory, the course focuses on metric space in the dimension of phase space. Number Theory Deals with denominators and prime numbers, greatest common denominators, least common multiples, congruence on module, polynomial and primitive elements, residue formula, the quadratic reciprocal rule and the continued fraction. Multivariable Calculus Deals with implicit function theorem, factorization theorem, Jacodians Simplexes and Stokes’ theorem. Theory of Differential Equations Based on the basic theories of linear algebra and analysis, the course systematically studies solutions to differential equations that determine the various mathematical models in natural science and engineering. Topology (1), (2) Main topics include metric space, topological space, continuous mapping, relative topology, completeness, separated space, connectivity, relativity and Tychonoff’s theorem. Computer & Mathematics Focuses on programming using Mathematica or Matlab. Modern Algebra (1), (2) This course covers groups, quotient groups, Sylow theorem, rings, quotient rings, polynomial rings, and isomorphism. Differential Geometry (1), (2) Deals with curvature of curves, torsion, geometry on surface and differentiable manifold. Complex Analysis Deals with complex number fields, analytic functions, power series, line integral, Cauchy’s Theorem, Laurent series and series and residue integrals. Applied Analysis Covers calculus, linear algebra, and differential equations using computer software such as Mathematica. Topics in Algebra In the course, topics include Sylow Subgroups, free commutative groups, automorphism, meronts, separable extension, and the Galois theory. Mathematical Finance Measures the value of derivatives through mathematics. Main topics include futures, options, hedging, strategy, Black-Scholes analysis and numerical procedures. Futures, Options, Hedging strategy, Black-Scholes Analysis, Numerical Procedures. Actuarial Mathematics Main topics include survival distributions and table, life insurance, life annuities, amortization schedules, yield rates and bonds. History of Mathematics Covers mathematics of Babylonia and Egypt, Pythagorean mathematics, the three construction problems, Euclidean principles, Greek, Chinese, Arabic mathematics, European mathematics from the 6th to the 16th century, mathematics in Germany, Great Britain and France, 18th century calculus, the initial developments in geometry and algebra, 19th century mathematics and 20th century abstracts. Real Analysis Deals with the general features of measure. Based on this, the course will cover Lebesque integral.