A radical approach to real analysis
by David M. Bressoud · first published 1994
60% recommend40% neutral
"In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on infinite summations, differentiability and continuity, and convergence of infinite series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the
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…of the way math is often taught. For example, real analysis is often taught as meaningless proof-finding (e.g. proving things that seem either pointless or obvious). But there's a fantastic book, _A Radical Approach to Real Analysis_ by David Bressoud, that teaches the exact same subject matter as the fruit of deep, pressing, and non-obvious questions that stirred debate among mathematicians for around 100 years.
on “Ask HN: Where did you top out in math classes?” ↗One of my favorite not-much-talked about analysis books is "A Radical Approach to Real Analysis" by Bressoud. Must read if you enjoy reading about the history of mathematics and famous mathematicians. A lot of people here recommend Rudin or Royden, but I have seen many people become turned off to…
on “Ask HN: Learning advanced math” ↗…examples, but mentions topics which may be too specific and not covered in your course. Elinho is much more terse, and great if you need a quick summary. I would also consider reading David Bressod's "A Radical Approach to Real Analysis". It's an awesome book, which mentions historical motivations for everything, and has a really different approach to teaching analysis (it will certainly help you learn analysis, but might not help too…
on “Ask HN: Resources to learn real analysis?” ↗…it seemed to work.[0] I picture this in my head as Fourier setting some shit on fire, hand calculating Fourier coefficients, then just pointing and yelling "SEE! SEE!" at Poisson and Lagrange. [0]: A Radical Approach to Real Analysis - David Bressoud
on “The Utility of Mathematics” ↗…modern limit-based field Weierstraß and others built. It's really confusing [1]. Statistics is even worse. A mix of old tricks developed to avoid computations when these were expensive. See [2]. [1] A Radical Approach to Real Analysis https://www.davidbressoud.org/aratra/ [2] The Introductory Statistics Course: A Ptolemaic Curriculum? https://escholarship.org/uc/item/6hb3k0nz
on “The dirty secret of mathematics: We make it up as we go along (2018)” ↗