Real Analysis: A Long-Form Mathematics Textbook

Cummings, Jay

ISBN 10: 1077254547 / ISBN 13: 9781077254541

Editore: Independently published, 2019

May show signs of wear, highlighting, writing, and previous use. This item may be a former library book with typical markings. No guarantee on products that contain supplements Your satisfaction is 100% guaranteed. Twenty-five year bookseller with shipments to over fifty million happy customers. Codice articolo 37811120-5

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 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic 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.Hints and solutions to select exercises can be found at LongFormMath.com.

This is the 2 + epsilon edition of this book. The second edition was published in July 2019. In January 2024, an epsilon of changes were made and the manuscript was updated, without officially creating a new edition.

Dati bibliografici

Titolo: Real Analysis: A Long-Form Mathematics ...
Casa editrice: Independently published
Data di pubblicazione: 2019
Legatura: Brossura
Condizione: good
Edizione: seconda edizione