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The following list is mostly intended for undergraduates. The recommendations here generally emphasize clarity of exposition over technical detail.

Algebra and Number Theory

Geometry and Topology

Other

### 22 Responses

1. […] Blogs (for example, Qiaochu Yuan’s blog has a reading list) […]

2. Is the Euler’s Gem link an easter egg?

3. How many of these did you read cover to cover?

4. I read Galoia’s dream, when I was a junior high school student.

5. Nice list. By the way how do you display math formulas in your blog? I found no button for mathjax plugin on my control panel (and it seems wordpress.com has banned the users freely using plugins)

6. It would be great if you can refine the list!

7. Regarding graph theory: I’ve really enjoyed Pearls in Graph Theory (see link if need be: http://www.amazon.com/Pearls-Graph-Theory-Comprehensive-Introduction/dp/0486432327 ). Sadly, both authors passed away.

8. Sir this is an excellent list. I have about 9 of these and they are all at about my level of comfort. Ash and Gross’s Elliptic Tales is a great companion to Fearless Symmetry with a focus on BSD.

9. How about some unorthodox means of instruction like the short video series ‘The Catsters’ by Cheng & co; I couldn’t get a handle on Category Theory until I saw them.

10. How about Sets for Mathematicians or Conceptual Mathematics?

• I haven’t read Sets for Mathematicians but I’m happy to add Conceptual Mathematics to the list. Thanks for the suggestions!

11. I notice you recommend a lot of “soft” books, yet reference “harder” books in your blog posts. What has worked better for you?

• I mostly don’t learn from books either way, but part of the motivation behind this list is to counter a tendency towards a “harder = better” mindset when it comes to mathematical resources.

• It takes a lot of courage to go against that mindset. I find that the softer books discuss the “why” that I yearn for in the harder books, at difficult spots.

• on September 17, 2013 at 8:08 pm | Reply Muhammad Faizan

Out of curiosity, what’s your main source of learning/knowledge if not books? I’m guessing that right now you’re probably at the point where most of your knowledge comes from attending lectures and conferences, talking to other mathematicians, and reading papers. But I’m more interested in how you got to this point, especially during your undergrad years, since your pace of learning would be impossible to maintain solely on undergrad math courses. If not primarily books, what sources did you use (and would recommend) to quickly build up a solid foundation of mathematical knowledge pre-grad school?

Thanks!

• Some combination of papers, Wikipedia, the nLab, math blogs, occasionally books, MathOverflow, and blogging.

12. good recommendations, thanks c:

13. Am I blind or is there no Serre?!

14. Have you paid for, and read all these booiks?