Earlier quoted context omitted.
What is the prerequisite for reading this book. Can I read this book effectively with basic knowledge of high school algebra and some calculus?
Yes. I did. It will be very challenging. I, quite a few times, spent more than four hours with a pencil and paper making my way through 2-4 pages of material, as since my background was lacking, there were parts where I had to figure out how they got from A to B. IIRC, I spent multiple days on a few paragraphs at one point. That said, it is written how I think math books should be written, is considered part of the s…
Ask HN: Good Reading/Immersion in Mathematics
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Re: Ask HN: Good Reading/Immersion in Mathematics
#32Assuming that you want to learn some 'university-level mathematics', then you'll really need to be prepared to study and work through problems rather than just read. Mathematics is an area where it's hard to get breadth of knowledge without also having at least some depth because things build very much on each other.
If you really do just want an overview of areas of different areas of mathematics to whet your appetite, there are books by people like Ian Stewart, Marcus du Sautoy and Keith Devlin, all worth reading. Just be aware that reading these is a bit like reading about different programming languages without ever having written a computer program.
If instead you just want to keep your brain engaged mathematically without learning more serious mathematics, there are also plenty of recreational mathematics books out there - Martin Gardner being the name that instantly springs to mind. On a similar vein, you may also enjoy the books of Raymond Smullyan which are more focused on logic.
The only really nice non-textbook taster of university-level mathematics that I have found in Alice in Numberland by Baylis and Haggarty. However it's out of print so you might have problems getting hold of a copy. It is a lovely book though if you can get your hands on it.
Otherwise you are looking at textbooks. I'd recommend maybe 'Introductory Mathematics: Algebra and Analysis' by Geoff Smith as a gentle but rigorous intro to the basics that I'd expect every maths student to learn at the start of their degree course. There are lots of alternatives out there too though. I taught myself lots from Herstein before going to university but that's pretty heavy going and there are better books out there these days. If you look at other books, I'd probably suggest getting one on abstract algebra maybe, covering things like sets/functions and group theory rather than say analysis or linear algebra to start off with, as it's easier to get into the right mathematical mindset if you're not distracted by content which you already have intuitions about.