How to think like a mathematician

What Hacker News says

1. mindcrimeJan 2023
   Maybe not "made me better at math" per-se, but definitely "made me more enthusiastic about math":

   The Universe Speaks in Numbers[1] by Graham Farmelo

   I found this very motivating and insightful, in terms of developing even more of an appreciation for how much math underpins other branches of science. Not that that is a novel insight by any means... but the details of the incidents where breakthroughs in mathematics allowed further advances in physics, etc. and looking at the "back and forth" between the domains, that was wildly interesting to me. Reading this book definitely helped motivate me to get serious about committing more time / focus to studying mathematics.

   I also enjoyed the "counterpoint" book by Sabine Hosenfelder, Lost in Math[2]. I think these two books complement each other nicely.

   Then the handful of additional (no pun intended) books that jump to mind would be:

   - How Mathematicians Think by William Byers[3]

   - How to Think Like a Mathematician by Kevin Houston[4]

   - Discrete Mathematics with Applications[5] by Susanna Epp

   - How Not To Be Wrong[6] by Jordan Ellenberg

   - Introduction to Mathematical Thinking[7] by Keith Devlin

   - How to Measure Anything[8] by Douglas Hubbard

   [1]: https://www.amazon.com/Universe-Speaks-Numbers-Reveals-Natur...

   [2]: https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/15...

   [3]: https://www.amazon.com/How-Mathematicians-Think-Contradictio...

   [4]: https://www.amazon.com/How-Think-Like-Mathematician-Undergra...

   [5]: https://www.amazon.com/Susanna-S-Epp-Mathematics-Application...

   [6]: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143...

   [7]: https://www.amazon.com/Introduction-Mathematical-Thinking-Ke...

   [8]: https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...

   Show morethread
2. ColinWrightJul 2020
   A list:

   https://www.topicsinmaths.co.uk/cgi-bin/sews.py?SuggestedRea...

   For a single suggestion, "How to Think Like a Mathematician" by Kevin Houston.

   A second suggestion: "A Companion to Analysis" by Tom Körner.

   But it depends a lot on whether you want books about math, or books of math. It sounds like you want the latter ... at some point I'll get around to putting annotations on the choices in the list that would help distinguish.

   Show morethread
3. yesenadamJan 2020
   Amazing books that are a joy to read:

   Polya's How To Solve It is great for 'how to think like a mathematician'.

   I love Knuth et al's Concrete Mathematics. Discrete maths plus jokes in the margins.

   Stillwell's Mathematics and its History - meet the main strands of mathematics, their origins, and the great mathematicians.

   Needham's Visual Complex Analysis - complex functions, differentiation & integration, Möbius transformations, hyperbolic geometry, vector fields etc - explained with a lot of pictures.

   Show morethread
4. ppsFeb 2019
   What field of mathematics interests you? Or you want some digestable intro to all of them? In that case I would recommend Kevin Houston "How to Think Like a Mathematician".
   thread
5. RossBencinaMar 2018
   To the above I would add:

   How to Think Like a Mathematician - Kevin Houston (an excellent book to read before starting)

   How to Read and Do Proofs - Solow

   The Keys to Advanced Mathematics: Recurrent Themes in Abstract Reasoning - Solow

   Calculus - Spivak (Actually a Real Analysis book, not a Calculus book, see e.g. https://math.stackexchange.com/questions/1811325/spivaks-cal... )

   Linear Algebra Done Right - Axler (Intended for a second course in Linear Algebra, but I found it helpful during my first course.)

   And for something from left-field:

   Visual Group Theory - Carter http://web.bentley.edu/empl/c/ncarter/vgt/

   There are many many many books on every mathematics topic under the sun. Finding books that speak to you is important. I have had mixed success buying books upon other people's recommendation. You would be best to get access to a library.

   Show morethread
6. gtaniFeb 2018
   Some books on proof, theorems/axioms, set theory, epsilon/delta/continuity/limits/differentiability, natural/rationals/reals/countability etc before heading into your first proof based LA or analysis sequence:

   - Kevin Houston "How to Think Like a Mathematician"

   - Keith Devlin "Intro Mathematical Thinking"

   - "How to Study as a Mathematics Major" Lara Alcock (for some reason, she/Oxford Press has 2 books with seemingly identical content under Math Major and Math Degree titles)

   Show morethread