MATH 714 Real Analysis
This course is at a higher level compared to MATH 324 and covers more advanced topics as well 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 on how to employ the Riemann-Stieltjes integral, and how to use the Weierstrass M-test for 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 provides the students with the ability 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.
Offered
Fall