MATH 622 Real Analysis
This course is at a higher level compared to MATH 324 and covers more advanced topics as well as the standard topics more deeply. In this course, students will be introduced to the difference between pointwise and uniform convergence. The integration and differentiation of a sequence of functions will be treated in depth. The course provides a foundation for employing the Riemann-Stieltjes integral and using the Weierstrass M-test for a series of functions. Determining whether a series of functions converges uniformly will be discussed as well as the facility with power series of functions and their use in solving differential equations. This course also allows the students to demonstrate familiarity with common pathological counterexamples regarding sequences and series of functions. It introduces the students to Riemann integration and its use in analysis, various convergence theorems and their applications, equicontinuity and the Arzela-Ascoli theorem, the Arzela-Ascoli theorem to ODEs, and how to use the Stone-Weierstrass theorem in practical situations.
Prerequisite
Undergraduate courses in fundamental of mathematical reasoning, calculus II, and real analysis