ABSTRACT
This chapter shows that all students who are seriously interested in mathematics at the master’s and doctoral level should have a passion for analysis even if it is not the primary focus of their own research interests. It shows that although differentiation is intellectually quite a different type of limit process, it is intimately connected with the Riemann integral. The other students typically either don’t like analysis at all and are only there because they have to be or they like analysis but it is part of their studies in number theory, partial differential equations for computation area. Measure Theory: This course generalizes the notion of integration to a very abstract setting. The set of notes readers are reading is a textbook for this material. For example, not everyone may have seen the equivalent of part of undergraduate analysis where Riemann integration is carefully discussed. The chapter also presents an overview of the key concepts discussed in this book.
