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Comment by WinterMount223 | Hacker News Reader

Good books but still quite standard. Spivak’s is standard on initial calculus courses at universities.

If you really wanted non-standard but relevant authors I would add Feyerabend, Kuhn, Kahneman, Dostoyevsky, Borges, Taleb, Montaigne, Popper, Hofstadter, Don Norman, Alexandrescu. Add something about systems of representation by Kierkegaard or Nietzche or some interpretations by later authors.

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Hoftstadter is fairly near standard isn't it? Assuming you mean actually reading GEB and not The Mind's I or I Am A Strange Loop. Not generally a course text but very common reading among CS/AI students. Some of whom even read all the way to the end instead of just pretending to!

The book I would most recommend software developers read is Mindstorms: Children, Computers and Powerful Ideas by Seymour Papert.

It's a lot shorter. And probably more valuable.

And one random side recommendation: The Daughter Of Time by Josephine Tey. It's a narrative exploration of how to challenge consensus belief, explore gut instincts and follow research leads, expressed as a perception-challenging historical review of Richard III by a fictional detective.

The BBC audio book is worth a go. My copy of this book (which was my mum's copy) is one of the few things I'd rescue from the hypothetical fire. It stays with you.

Remember reading Papert's Mindstorms book and being reminded of the fun you can have with computers, these powerful modelling machines - as Douglas Adams put it too

I found Hofstadter's _Le Ton beau de Marot_ fascinating, and also almost nobody has even heard of it!

I had not heard of it either. Very interesting. Thanks!

Hofstadter's amazing, mind-boggling satirical essay/alternate history A Person Paper on Purity in Language from Metamagical Themas. Much more fun than the title suggests!

https://www.cs.virginia.edu/~evans/cs655/readings/purity.htm...

I think Spivak is way less common as an initial calc text than Stewart. Spivak's approach is much more rigorous than most calc textbooks, and is in many ways almost an introduction to real analysis. Note, for example, that Spivak prefers to view the definite integral as the proper form of an integral rather than the typical approach taken by many introductory texts where the integral is viewed as the anti-derivative and then for ∫_a^b f(x)d(x) they just take F(b)-F(a) and call it a day. I would imagine that most introductory calculus students do close to zero proofs with most of the time spent on memorizing the various rubrics for finding derivatives and anti-derivatives. Spivak covers those, but the exercises are at least 50% proofs rather than being 90–100% calculation.

The Calculus pick is completely fungible. There are at least two other popular Calc books that different people would say the exact same things about.

Euclid as the ideal place to learn logic seems debatable, although I can't think of a better resource off the top of my head.

The Xinu OS and LISP recommendations I've never seen before, so those were potentially valuable for me at least.

What calc books are those? Reading a calculus book is a massive investment because I will be rereading pages. So I’d like to find the best one first

_Calculus Made Easy_ by Thompson (now in a new edition revised by Martin Gardner) was a former classic used by all sorts of people, and Feynman learned calculus from _Calculus for the Practical Man_, which was hardly sophisticated by modern standards. As long as you stick to a book some sizeable number of people think is okay, I don't think it matters that much what you learn from; the important thing is that you work through theorems carefully enough that you really understand them. Whether it's Spivak or Velleman or Thompson or OpenStax or Stewart (only for those who are assigned it, since otherwise there's no reason to spend >=$100 on it—it's not worth the premium) or Ross (his _Elementary Analysis_ book), worry about learning the concepts more than worrying about which book you chose. You can always refer to alternative books or youtube videos if a concept isn't clear in the primary book you chose.

Others have already mentioned the classics, but if you're looking for something more off the beaten path, you can check out my book: No Bullshit Guide to Math & Physics which covers calculus in approx. 150 pages (Chapter 5).

You can see an extended preview of it here: https://minireference.com/static/excerpts/noBSmathphys_v5_pr...

And a standalone concept map here: https://minireference.com/static/conceptmaps/math_and_physic... (bottom of the page)

Check out the reviews on amazon if you're interested. It hasn't been adopted as the main textbook at any university yet, but many teachers recommend it as supplemental reading for their courses.

I, for one, couldn't find a better one at the time I've read it. There are a lot of crappy ones, on the other hand. You are right in affirming that this is a massive investment.

Depends enormously on your level and willingness and dedication. At that level the best ones are Spivak, Apostol, Fichtenholtz, Kudryavtsev.

Just be careful in mixing the "best one at teaching" with the "best one at the level of detail and correctness". One is good for aha moments, the other for going into research. Depends on your needs. Similar to the question of "what is the best language to learn?". Depends on your needs.

If I remember right, Apostol uses a non-standard sequence (integration first, then differentiation). That probably only matters if you might be using a different book for another part of the sequence, though.

I self-taught from an early edition of Stewart and loved it.

What book would you recommend for learning practical calculus from? I haven't touched the subject since high school.

https://tutorial.math.lamar.edu/ is a good place to find answers to things.

I learnt calculus from a copy of a book called "Calculus, A complete course" which I quite liked but have literally never seen anywhere else. The fact I got the book was basically by accident, completely changed my future.

Thank you!

https://news.ycombinator.com/item?id=30660126

What about How To Prove It by Velleman as a substitute?

For a truly non-standard, very good Calculus book, I recommend Elementary Calculus: An Infinitesimal Approach, by Jerome Keisler. It's available for free at https://people.math.wisc.edu/~keisler/calc.html

It's horribly inaccessible but while we're throwing out truly nonstandard recommendations, and apropos to the connection made elsewhere in this thread between the theory of forms and object-oriented programming, Whitehead's Process and Reality is good for the same reasons OOP sucks.

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