The way of analysis
by Robert S. Strichartz · first published 1995
50% recommend50% neutral
Why HN recommends it
Intuition-first introduction to real analysis that builds ideas gradually, starting from flawed first attempts and revising toward rigorous definitions and proofs; suited to readers who find standard texts too dense.
Summarised by Claude from recommending comments
Mathematics is a way of thought. Attaining a deep understanding of mathematics is more than mastering a collection of theorems, definitions, problems, and techniques; it is understanding how theorems and definitions fit together with the overall strategy of arguments presented. This introduction to real analysis contains thorough and complete proofs with lively and generous explanation to guide the reader through the foundations and the way of analysis. Real analysis, in one and several variables, is developed from the construction of the real number system to an introduction to the Lebesgue
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…For that matter, the following books helped me a lot: - The visual series. Visual Complex Analysis and Visual Group Theory, for instance - Pinter's A book of Abstract Algebra - Strichartz's The Way of Analysis - Linear Algebra Through Geometry by Wermer. The book offers a comprehensive geometric interpretation to linear algebra concepts. It's especially helpful for me to understand quadratic forms. To understand…
on “Ask HN: Math books that made you significantly better at math?” ↗…skepticism, but here's my list: * Calculus * Real Analysis * Statistical Mechanics * Probability I'm not sure I have any good recommendations for Calculus, but for real analysis, I would recommend "The Way of Analysis" by Strichartz [0]. I don't have good recommendations for books on statistical mechanics, as I haven't found a book that isn't entrenched in coming from a physics perspective and teaches the underlying…
on “An Introduction to Stochastic Calculus (2022)” ↗Speaking of books about calculus, I like Robert Strichartz's The Way of Analysis. Robert develops intuition and motivation of key concepts in an amazingly detailed way. He often starts with an intuitive but flawed idea, and then gradually revises the idea to a mature definition or…
on “Calculus Made Easy (1910)” ↗…It's 125 pages of clarity and intuition building. More rigorous alternatives would be: 1. Elias M. Stein's 'Real Analysis: Measure Theory, Integration, and Hilbert Spaces'. 2. Robert S. Strichartz 'The Way of Analysis' Personally I would use the Baylis book and the other two as reference. Additional resources include the top voted mathoverflow.com and math.stackexchange.com answers. Beyond useful. Lastly, I have…
on “Ask HN: Resources to learn real analysis?” ↗…order, here are a list of books I've found exceptional (very much catered to my personal taste): [0] Computers and Intractability: A Guide to the Theory of NP-Completeness by Garey and Johnsen [1] The Way of Analysis by Strichartz [2] Introduction to Algorithms by Cormen, Leiserson, Rivest and Stein [3] Fundamental Problems of Algorithmic Algebra by Yap [4] Fundamental Algorithms for Permutation Groups by Butler…
on “Ask HN: Best resources to gain math intuition?” ↗…guess this is a matter of taste. I went to look at this and it really bothers me that, true to the name they give, the "completeness axiom" is presented as an axiom. My analysis class used Strichartz' The Way of Analysis, which is certainly not "short and sweet" -- the professor described it to us as "chatty" -- but it goes ahead and actually proves the "completeness axiom". Compare the completeness axiom > Every nonempty…
on “Real Not Complex: Free Math Resources” ↗Yes, in fact some recommendations at LW are odd: "On analysis in Rn, orthonormal recommends Strichartz's The Way of Analysis over Rudin's Principles of Mathematical Analysis and Kolmogorov & Fomin's Introduction to Real Analysis." Rudin or Kolmogorov & Fomin are waaaay more advanced than Strichartz. If they wanted a more conceptual…
on “The Best Textbooks on Every Subject” ↗…Normally I stay away from pop-math books with the words "The mind of..." or "Genius" in the title but this is a delightful book. Some "actual" math books: 1. Nonlinear Dynamics & Chaos (Strogatz) 2. the Way of Analysis (Strichartz) -- note, this one is controversial as to its quality as a math book but I really like the presentation style 3. The Nature of Computation (Moore & Mertens)
on “Ask HN: Books that made you fascinated to learn more mathematics?” ↗