Real Analysis A Longform Mathematics Textbook Jay Cummings by Jay Cummings 9781077254541, 1077254547 instant download after payment.

** This is a scanned copy of the book.

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. 

The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own.

Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible and contains over 100 illustrations. The writing is relaxed and includes periodic historical notes, poor attempts at humour, and occasional diversions into other interesting areas of mathematics.

The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. 

The first appendix contains a construction of the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavours to help change this.

Jay Cummings believes that learning math has become far too expensive, and is striving to write textbooks that are enjoyable to read, highlight the beauty in mathematics, and are significantly more affordable than the others on the market. After receiving his PhD from UC San Diego under Ron Graham, he joined the faculty at California State University, Sacramento. His combinatorics research continues and he particularly enjoys involving students in his work. He is passionate about his teaching and enjoys designing new courses.