Real Analysis
Jay Cummings believes that learning math has become far too expensive, and he is working to create textbooks that are entertaining to read, highlight the beauty of mathematics, and are significantly less expensive than the competition. He joined the faculty at California State University, Sacramento after getting his PhD from UC San Diego under Ron Graham. His combinatorics study is still ongoing, and he especially appreciates incorporating students in his work. He is enthusiastic about teaching and enjoys creating new courses.
Real Analysis is intended for students. This text offers far more commentary, motivation, and explanation than the conventional definition-theorem-proof-repeat format. The proofs are not brief and are intended to promote economic comprehension. Moreover, dozens of proofs are preceded by "scratch work" or a proof sketch to provide students with a big-picture perspective and an explanation of how they would come up with it on their own. Examples frequently drive the story and challenge the reader's intuition. The book also includes over 200 images to help make the ideas more visible.
The writing is casual, with fascinating historical notes, efforts at humor, and occasional detours into other interesting fields of mathematics. The real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions are all covered in the text.
Each chapter concludes with exercises, and almost all of them include some open questions. The first appendix is a reals construction, and the second is a collection of extra strange and pathological examples from analysis. The author believes that most textbooks are significantly overpriced and is working to remedy this.
Author: Jay Cummings
Link to buy: https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547/
Ratings: 4.7 out of 5 stars (from 345 reviews)
Best Sellers Rank: #56,531 in Books
#11 in Mathematical Analysis (Books)
#20 in Calculus (Books)
