What are some recommended readings for precalculus and lower level calculus?

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A graduating senior is seeking recommendations for self-study materials in mathematics, specifically precalculus topics like algebra and trigonometry, as well as introductory calculus. They express a desire for resources that provide a solid understanding of real mathematics, feeling that previous courses have fallen short. Gelfand's books on Trigonometry and Algebra are mentioned positively, along with a Dover series that has been useful for learning Differential Calculus and other advanced topics. Another recommended text is by Axler, which has received mixed reviews regarding its style but is noted for its quality. Additionally, Leithold's "Calculus" is highlighted as a standard resource that effectively explains concepts and maintains rigor in proofs. The discussion emphasizes the importance of finding materials that resonate personally with the learner's style and comprehension needs.
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Hi all, I'm a graduating senior and I'm interested in covering and recovering mathematics to the calculus level. I've been feeling that all of my math courses to this point, high school and before, haven't really taught me much of anything in the way of real mathematics. I was looking for some recommended reading that would cover precalculus topics, such as algebra and trig, and some lower level calculus.

I've heard good things about Gelfand's Trigonometry and perhaps Algebra as well, but not much outside of that. Any help?
 
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There's a good series (Dover, I think) that produces a "teach yourself ..."

I used it for Differential Calculus (exclusively, never took a "real" course) and it's held up through the full Calculus sequence, Diff Eq, Linear Algebra, and all my physics courses.

I'd recommend it, definitely.
 
There's a precalculus book that came out recently, by Axler. I don't like his style, but I was impressed with the book.
 
Poisonous said:
Unknot:

Is this the text? https://www.amazon.com/dp/0471614432/?tag=pfamazon01-20

What didn't you like about the style?

It's something very personal, how he bashes determinants and how he explains the concepts. But he's a good writer. You shouldn't be concerned about my taste, it's unlikely that you will feel the same thing.
 
Good, i'll look into it. Any others?
 
leithold... the calculus 7.
pretty much the standard calculus book. explains things so well without losing the proofs and such.
 
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