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I need a no-fluff book with great exposition on precalculus. It should cover up intermediate algebra, trigonometry and anything else needed to get a strong preparation for Spivak's Calculus. It shouldn't contain annoying images or anything agitating, just serious math. But above all things, it should be very comprehensive and rigorous. It should help me to understand the concepts, and not just memorize them like we're supposed to do with most American textbooks...

Jesus Christ
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  • Not exactly what you are looking for but I would heavily recommend both 'A mathematician's delight' and 'Prelude to Mathematics' by W.W. Sawyer. Others you may be interested in are 'You Are a Mathematician' by D. Wells and 'Thinking Mathematically' by J. Mason. – Gridley Quayle Jun 12 '15 at 20:00
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    What makes an image "annoying"? – anak Jun 12 '15 at 20:02
  • You might want to look at Mary P. Dolciani's Modern Introductory Analysis. See the comments here and here. This was the standard U.S. high school "precalculus" text from the mid 1960s through the 1970s, but there are probably very few places it could be used now because such a course (in high school) is no longer confined to the upper 10% or so of the population. – Dave L. Renfro Jun 15 '15 at 16:51
  • Possible duplicate of Recommendation for a precalculus textbook –  May 28 '18 at 04:11

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What you want are Gelfand's books: Algebra, Trigonometry, Functions and Graphs, and The Method of Coordinates. It is a shame these books are not better known and used.

Axler has a book on precalculus, but it is far more boring and typical than Gelfand's.

Simmons also has a lovely little book, Precalculus Mathematics in a Nutshell.

symplectomorphic
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  • You are an excellent mathematician and me? I'm just another idiot but I have a question, do these 4 books (Algebra, Trigonometry, Functions and Graphs, The Method of Coordinates) cover up Algebra 1 to 4? and will only reading these books prepare me for a calculus course? Most importantly, in what order should I read these books? – Jesus Christ Jun 13 '15 at 19:38
  • @JesusChrist: I don't know why you're calling yourself an idiot. I also don't know what you mean by "Algebra 1 to 4." Those books would form a good basis for a rigorous calculus course such as Spivak's. But they certainly aren't standard. I was answering the question you asked in your OP: they are rigorous and emphasize conceptual understanding. I'd recommend reading Algebra, then Functions and Graphs, then Trigonometry, then The Method of Coordinates. But the last isn't essential. – symplectomorphic Jun 13 '15 at 19:50
  • Algebra 1 is considered to be elementary, while Algebra 4 is intermediate. I was just wondering if only reading these books by Gelfand would prepare me for a rigorous calculus course like Spivak. – Jesus Christ Jun 13 '15 at 19:53
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If you want to study trigonometry and algebra rigorously then go for S.L Loney trigonometry and Hall & Knight.For calculus Thomas Calculus is the best. Everything is included, including some precalculus needed for calculus, in it so you don't have to search anywhere else. I would personally suggest that for precalculus go for Khan academy because explanations there are sometimes better than books.

Who am I
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When I was studying precalculus, I found a free book, completely typeset in $\LaTeX$ that I think suits what you want. There are a total of zero annoying images and silly graphics and absolutely all topics are discussed very carefully and thoroughly. The book is Precalculus by Carl Stitz and Jeff Zeager, and you can find them here: http://www.stitz-zeager.com/

The book has hundreds of exercises, most of them are trivial and mechanical in nature, designed to be solved in something like 3-5 minutes each. Their purpose is to get you used to calculating things, and calculating fast. Then, there are the more advanced problems which will require some thinking.

Another book that I imagine must be very good is Serge Lang's Basic Mathematics. Lang is a great and famous author and you might just want to use his Calculus textbook to study Calculus after studying Basic Mathematics.

Sigma
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  • I will look at that Stitz's book. It sounds interesting and had never heard of it before. I gather you went through it as well? Can you tell a little bit about your experience? – Alex Ruiz Jun 17 '22 at 20:34
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    @AlexRuiz yes, I studied a lot of precalculus using that book. I found it to be good and rich in details, and it suits the mathematical maturity of someone studying precalculus exactly because things are explained carefully. I recommend it. – Sigma Jun 21 '22 at 13:45