000			01971nam a22002417a 4500
005			20250805153607.0
008			250805b |||||||| |||| 00| 0 eng d
020			_a9781077254541
028			_aDonated by Prof. Sanjeev Agrawal
082			_a515 CUM
100			_aCummings, Jay.
245			_aReal Analysis _b: A Long-Form Mathematics Textbook . _c/ Jay Cummings.
260			_a, UK _b: Milton Keynes _c, 2019.
300			_aviii, 434p. _c: 32cm.
365			_b00
490			_a The Long-Form Math Textbook Series
520			_aThis 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 LongFormM.
650			_aReal Analysis
650			_aAnalysis
650			_aMathematics
700			_aJay Cummings
942			_cBOOK
999			_c65967 _d65967