Real Analysis: A Long-Form Mathematics Textbook - Brossura

Cummings, Jay

Brossura

ISBN 10: 1724510126 ISBN 13: 9781724510129

Casa editrice: CreateSpace Independent Publishing Platform, 2018

Riassunto

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 humor, 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 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 endeavors to help change this.

Dettagli dell?edizione

• Editore: CreateSpace Independent Publishing Platform
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 1724510126
• ISBN 13: 9781724510129
• Rilegatura: Copertina flessibile
• Numero di pagine: 375
• Contatto del produttore: non disponibile