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Hacker News Comments on
The How and Why of One Variable Calculus

Amol Sasane · 1 HN comments

HN Books has aggregated all Hacker News stories and comments that mention "The How and Why of One Variable Calculus" by Amol Sasane.

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Amazon Summary

First course calculus texts have traditionally been either “engineering/science-oriented” with too little rigor, or have thrown students in the deep end with a rigorous analysis text. The How and Why of One Variable Calculus closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus and analysis. Logically organized and also very clear and user-friendly, it covers 6 main topics; real numbers, sequences, continuity, differentiation, integration, and series. It is primarily concerned with developing an understanding of the tools of calculus. The author presents numerous examples and exercises that illustrate how the techniques of calculus have universal application.The How and Why of One Variable Calculus presents an excellent text for a first course in calculus for students in the mathematical sciences, statistics and analytics, as well as a text for a bridge course between single and multi-variable calculus as well as between single variable calculus and upper level theory courses for math majors.

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May 24, 2022 · mikevm on Ask HN: Serious mathematics books that can replace a good teacher?

I couldn't disagree more. I studied Analysis in the Uni, and even in that environment Rudin is pretty bad. For a total newcomer that book will leave you completely helpless. Also, solutions are a must have, without them you are almsot totally lost. In their absence, it is OK to ask on StackExchange or #math on EFnet.
First let's start with a few books to prep you for college-level maths:
* https://www.amazon.com/How-Study-as-Mathematics-Major-ebook/...
* https://www.amazon.com/How-Read-Proofs-Introduction-Mathemat... ; or
* https://www.amazon.com/Numbers-Proofs-Modular-Mathematics-Al... ; or
* https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-... (I believe you can find solutions to the 2nd edition online)
For Single-Variable Analysis
* https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...
* https://www.amazon.com/How-Why-One-Variable-Calculus/dp/1119...
* https://www.amazon.com/Mathematical-Analysis-Straightforward... (contains solutions to exercises)
* https://www.amazon.com/Understanding-Analysis-Undergraduate-... (there are solutions online for the 2nd edition)
* https://www.amazon.com/Numbers-Functions-Steps-into-Analysis... (this book is a brilliant exercise-guided approach that helps you build up your knowledge step by step + solutions are provided).

⬐ Koshkin
Agree, Rudin is excellent as a second course on real analysis, but as a first one it is absolutely terrible.

⬐ bell-cot
+1, but nitpicking: There are situations where baby Rudin ("Principles of Mathematical Analysis") can be very good for a first course...but those are corner cases, that you'd want a really good, experienced instructor to sign off on.

Hacker News Comments on The How and Why of One Variable Calculus

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Hacker News Comments on
The How and Why of One Variable Calculus