Calculus
by Michael Spivak · first published 1967
67% recommend30% neutral3% critical
Why HN recommends it
Rigorous, proof-based introduction to analysis built from first principles, with well-written text and excellent problems; suits self-learners wanting real pure mathematics beyond standard calculus.
Summarised by Claude from recommending comments
Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach t
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What are you looking for that isn't simply a math textbook? Honestly, that's how mathematicians learn "actual" mathematical subjects, too. If you're comfortable with calculus as a subject, for example, and want a "pure mathematics" approach, I recommend Michael Spivak's Calculus. If you've never worked through a pure math textbook from start to finish, that's a good start.…
on “Great books about mathematics” ↗The book 'Calculus' by Michael Spivak. In the same way that SICP transforms you from a high-schooler into a wise adult when it comes to programming, so too does Calculus when it comes to maths. If you find the book to…
on “Learning Math” ↗Anybody have insight into how to actualize these nuggets into some semblance of a self-learning course? Buy Calculus by Micheal Spivak. Solve at least one problem every day. Make it ritual and a daily requirement. Watch MIT lectures for corresponding chapter you are on. To learn this, don't trouble over the path and…
on “Calculus distilled into hours” ↗You may want to try working through Spivak's _Calculus_ [1] textbook. It is a bit more involved than most calculus textbooks used in universities today, so it will likely not feel like you are simply repeating something that you have already done. I would…
on “Ask HN: Ramping up math skills?” ↗I agree. As far as calculus goes, I am more enamored with books like Spivak's (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098...) that take a proof-centric approach to teach calculus from first principles. Incidentally,…
on “Too Much Calculus – Gilbert Strang (2001) [pdf]” ↗i learned from this back in college: https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/091409... one of my favorite text books ever. (tho it was paired w/ one of my favorite teachers ever, which i'm sure helped a lot.)
on “Topology Illustrated (2015)” ↗…would be to get a book on any topic which interests you, read through it, and do a significant number of the exercises. You might try Epp's Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive…
on “Ask HN: Is there a website specialized in mathematics courses?” ↗I am not sure if they can replace a teacher, but some good mathematics books are "Euclid's Elements", "Introduction to Algebra" by Richard Rusczyk, and "Calculus" by Michael Spivak.
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…point. :) In that, they're basically re-proving the binomial theorem (or more accurately, using the same method) rather than just using its results with the new dual number arithmetic. Michael Spivak's Calculus has some great chapters on Taylor polynomials, Taylor's remainder theorem, and Taylor series. I've been looking into this stuff lately, to try and justify mathematically why automatic differentiation…
on “Differentiable programming from scratch” ↗Calculus by Michael Spivak
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098896 I am learning calculus from this book on my own. It's great if you already know a lot of logic.
on “Calculus in 20 Minutes” ↗…subject they are describing. If you want to actually be able to solve problems using math (the fun part, for most amateur mathematicians), a textbook would be a better bet. If you stopped math at business calculus and want a great introduction to the calculus that mathematicians use, I wholeheartedly recommend Michael Spivak's Calculus as a next step.
on “The nicest math book I own” ↗…time to work on AMC and Olympiad style problem solving, http://www.artofproblemsolving.com/Books/AoPS_B_CP_AMC.php http://www.artofproblemsolving.com/Books/AoPS_B_CP_Olympiad.... and also the best calculus textbooks, such as those by Spivak or Apostol. http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098918/ http://www.amazon.com/Calculus-Vol-One-Variable-Introduction... http://www.amazon.com/Calculus-Vol-Multi-Variable-Algebra-Ap...…
on “A Textbook Example of What’s Wrong with Education” ↗Spivak's Calculus, http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098... is a good bet. But it's very theory-involved.
on “Ask HN: How can I discover math?” ↗…http://matrixeditions.com/UnifiedApproach4th.html and work through it if you want a rigorous treatment of MV calc and intro analysis. Or this book: http://www.amazon.com/gp/product/0914098918/ref=pd_lpo_k2_dp... for regular calculus. Read them, work through the problems, get an answer key, email your solutions to professors asking them to look at them. You will get a good introduction to analysis (and exposure to many other parts…
on “Ask HN: How Do I Get Math?” ↗