This course deals with various properties of real numbers, their topological aspects, limits of sequences and series, continuous functions, differentiation, the Riemann integral and their applications. 3 A survey of simplex methods, dual simplex methods, advanced methods, and methods of integer programming as algebraic solution methods of linear programming. Topics include probability random variable, discrete probability distribution, continuous probability distribution, change of variables, sampling distribution, and limiting distribution. Some applications to pure mathematics and applied sciences are also attempted. This course covers operations of vectors, differentiation and integration of vector functions, line and surface integrals, curvilinear coordinations, and multiple integrals.
Emphasis is placed on laboratory work using the computer in solving mathematical problems.
Topics also include topological space, continuous map, and homomorphisms. Basics in calculus, linear algebra, and vector analysis are required. This course deals with applications of Cauchy's theorem, harmonic functions, conformal mapping and the Riemann mapping theorem, univalent functions, and analytic continuation. Laboratory work will include computer use in solving problems. Normed spaces, Banach spaces, and fundamental theorems for normed and Banach spaces.