That's not to say I didn't learn from books at all before then, there are a handful of texts such as the original Art of Problem Solving books which were very influential. It was really only once I got to college that I began learning meaningfully from math books, with more of my learning before then coming from interactions with teachers, poking around online, and getting lost in my own head. There are undoubtedly many great books for those in high school and below, but I feel less well-positioned to give recommendations in that direction. The recommendations above are targeted at those in college or beyond. If it is out of the blue, it's okay to move forward anyway, just keep note of the fact that there is a lurking question mark.Īlso, although it’s not quite a book, you may also enjoy the expository papers written by Keith Conrad, especially if you’re looking to learn group theory or number theory. Be willing to meditate on what the right way to think about a given object is, and ask what would happen if definitions were tweaked.Īsk yourself if each new construct feels motivated, or if it's out of the blue. Try to predict what proofs will look like before reading them. Read with a pencil and paper in hand to jot down notes and work on exercises (yes, you should actually do the exercises!). If there's a field of research you've heard of, say something like analytic number theory, and you're curious to get a feel for what it's all about, the corresponding essay in that section is likely to do a fantastic job.įor any textbooks that you read, try to avoid being passive.
Where it shines is in section IV, which includes many expository introductions to various fields of modern math. By Timothy Gowers (and many, many others)īooks can never replace the intuition available if there's a professor down the hall whose door you can knock on to start asking questions.
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