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I will make this question as objective based as possible. My curriculum teaches maths in a way that does not work well with me. Further, I also do not like the textbooks used (It was voted the worst in the state). The only way to succeed in this course was to get a tutor, objectively speaking. The highest non-tutor mark was about 60%~, majority severely failed the exam. I dropped the course as a whole.

In lieu of this, I still have a passion for mathematics. Currently, I just begin Calculus, but I am missing a solid development in all pre-calculus topics.

By solid development, I mean I have no intuitive way of grasping things - just stuff and methods rote learned from formulas provided.

I need a good textbook, and that is my question here, that provides a solid, rigorous, theory intensive approach to mathematics from all pre-calculus topics to beyond.

I don't mind if its multiple book recommendations in order, I am willing to study them hard.

Much thanks. I'm sure someone on this site has exactly what I'm looking for and am hoping they can share it with me.

CucumberComplex
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    What topics have you already mastered solidly? Are you comfortable manipulating various algebraic expressions? For example, are you okay with simplifying expressions like $x^{2/3}y^{1/5}/x^{-3/7}y^{3}z^{-1/2}$? – MPW Oct 05 '14 at 11:15
  • @MPW I think I am able to do that. I can certainly do it if the exponent wasn't fractional though I'd assume the process is the same. I don't mind relearning everything if the book is good later on. – CucumberComplex Oct 05 '14 at 11:17

3 Answers3

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Calculus and Analytic Geometry by George B. Thomas and Ross L. Finney. This is a great book for self learning, it balances clear explanations with enough rigor and will help you gain some intuition from the basics all the way to the multivariate integral theorems.

LaurentP
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Precalculus by Richard Rusczyk is a bit hard but if you get a small proportion of the stuff in there you will know much more than most high school text books teach.

http://www.artofproblemsolving.com/Store/viewitem.php?item=precalc

John Marty
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I started an overview of my math with Calculus a complete course by Robert A. Adams. I find it a wonderful book.

Mathink
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