Which book made you understand what real mathematics was all about? Not rote calculations we do in school. Or in other words, which book got you curious to learn more of mathematics and make a career out of it??
Things to Make and Do in the Fourth Dimension by Matt Parker is a fun, accessible, and fascinating explanation of how math can be a big game.<p>The Annotated Turing by Charles Petzold really is great. It comes up a lot on this website but it was a great follow up, a good bridge from the fun almost hack-y math to a more "serious" approach. This led me to:<p>Computability and Logic by George S Boolos. A standard textbook in universities across North America (and maybe further?).<p>In the end I didn't become a mathematician. I hardly use advanced math compared to many other engineers and scientists but the ideas have stuck with me for years, and I think my life is richer for knowing them
In the US, high-school linear algebra, geometry and calculus were de rigeur. Three courses of calculus were, at the time I went to university, required for engineers, along with differential equations and matrix algebra.<p>However, the pure-mathematics coursework ended up being the most useful: two or more mathematical analysis courses, non-Euclidean geometry, statistics, algorithmic analysis, and mathematical topology.<p>The two take-these-if-you-want-a-future courses I’d recommend are discrete mathematics (which I use every day) and abstract algebra (which I also use every day).<p>There are a lot of good college textbooks for both; mine is long gone, though you may find one that you absolutely love.