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I'm looking for a rigorous pre-calculus book so I can start learning Calc and beyond. I have taken some precalc topic, but have a 40%ish comprehension rate. I've done a few bits on limits, continuity, functions, surds, trigonometry incl. identities but it is just a few bits here and there.

I'm looking for a rigoruous pre-calc book that will prepare me for calculus, and importantly, contains answers to all exercises (for example, not just every second one). This will be for self-study, but I don't think that should make a difference?

Thank you,

entm8
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  • Take a look at Knuth's Concrete Mathematics to see whether it's what you like? – Yai0Phah Mar 28 '15 at 08:56
  • @FrankScience That doesn't seem like a very "precalc-ish" sort of book IMO. However, a "rigorous" precalculus book, especially in today's mathematical climate, seems like a very odd characterization. – Daniel W. Farlow Mar 28 '15 at 09:03
  • @crash I didn't really understand what's pre-calculus, but I suggested Concrete Mathematics because most part of the book isn't relied on calculus and should prepare readers techniques of manipulating $\sum$, binomial coefficients, etc. Well, on the other hand, I started my first systematic study of calculus from Rudin's Principles of Mathematical Analysis. It's concise but terse and without solutions. – Yai0Phah Mar 28 '15 at 10:26

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First things first: you are very unlikely to find a math book with all of the solutions in it unless it is the instructor's edition, and even if it is the instructor's edition, the "solutions" are far more likely to appear as "answers," where explanations are largely done away with. I greatly sympathize with your situation though because I am an avid self-learner myself, and I try to get as many books with complete solution manuals as I can.

For your particular case, I would highly suggest not getting bogged down in the trenches of pre-calc, somewhere you have already been for a good bit it sounds like. Take your first taste of elementary calculus. I would suggest James Stewart's Calculus, but I would not get the most recent edition as it is ridiculously expensive. Fortunately, you can find quality material for cheap now that the value has depreciated so much thanks to greedy textbook publishers. I would purchase all of the following books (I have purchased them myself and am quite happy with them; if you purchased them all right now, your total should be about $25 USD):

The entire first chapter of Stewart's text is devoted to "review." Thus, I doubt you would feel too uncomfortable. Good luck and happy hunting!

Daniel W. Farlow
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