Introduction to Mathematical Analysis

6 credits · Undergraduate

(3 hrs Lecture) This course provides a careful treatment of the basic concepts of mathematical analysis including properties of the real numbers, countable and uncountable sets, the topology of metric spaces including compactness, connectedness, sequence/series convergence, continuity, and complete metric spaces. Rigorous proofs of the Heine-BoreI theorem, the extreme value theorem, and the intermediate value theorem are given. Other topics studied include differentiation, Riemann-Stieltjes integration, normed linear spaces, uniform convergence and the Stone-Weierstrass theorem, and Fourier analysis. Requisite Courses: MATH-2405(3) and MATH-2106(3), and MATH-2203(3) or MATH-2221(3) [prerequisite(s)].