Best books for relearning precalculus maths the right way [duplicate]

I am looking for advice on the best texts to remind myself how to do math. I am 35 and an attorney (patent) but was once very good at math (best in my high school, 800 SAT) but then stopped completely after taking Calculus in college as that was all I needed for the MCAT. How I ended up an attorney is a long story...

Anyway, as I get older, I am drawn more and more to understanding simply for understanding's sake. I always enjoyed math because it required a lot of mental effort that led to a real, correct answer. I've gone back to math now and then for fun, took a class at a local college years ago but now I've decided I want to go back again and pick up where I left off but focus more on a rigorous understanding and not just the computational Calculus I took in high school and again in college. I searched online, including reading lots of threads on this site, and ultimately went with Apostol's Calculus Vol 1 and planned to look at the notes in MITs 18.014 class (Calculus w/ Theory).

Long story long, I received the book, got to the first proof in the introduction and realized I have forgotten just about everything. My arithmetic skills are still excellent as even as an attorney those get used day to day, but he might as well have been speaking Greek when he proved the area under the curve/method of exhaustion.

So, hence why I am here. :) I want to find the best book/books to re-ground myself in the mathematics needed to make a go at a rigorous study of calculus. There is no career goal in mind here, I just want to do it for the sake of it.

I came up with several ideas from reading threads here or reading Amazon reviews, including:

Gelfand (Algebra and Trigonometry) Lang (Basic Mathematics) Simmons (Precalculus in a Nutshell) Velleman (How to Prove It)

and I have Euclid already on the shelf, hah.

I am a perfectionist, fortunately or unfortunately, so if I am going to go through the effort, I want to do it well and with full understanding, not just blow through some Kahn Academy videos and on to Calculus. But, I also need to be efficient.

Does the list above make sense? Are they redundant or is anything missing? Any other recommendations?

Thanks very much.

Solution 1:

If you want a slightly rigorous pre-calculus re-education, you could try Hall and Knight's Higher Algebra. Alternatively, you could take a look at the pre-calculus section in Thomas' Calculus or Stewarts' Calculus. Both are intro to high-level calculus books and the first chapter is about the real-number system,etc. And I'd recommend using Thomas' Calc. instead of Apostol's (although Apostol's is also fantastic) because Thomas' has exhaustive explanation for each chapter. And if you really want to start right at the basics for pre-calculus, you could always check out KhanAcademy's videos; you need not use it as the only source, as you say you don't want to blow through them, but they do provide an intuitive understanding.

Note: Higher Algebra has more than a basic precalculus education, especially the later chapters!

Solution 2:

As far as I've seen, pre-calculus is comprised in majority of past algebra. You could always begin practicing that (as it is essential). My past pre-calculus class had a chapter on matrix algebra and 2nd degree polynomials. I'm sorry to say I can't remember what the book was, as it was over a year ago.

The book ended with an intro for calculus I, involving easy limits and derivatives using the derivative quotient.

Solution 3:

Since Pre-calculus is an assembly of several basic mathematical concepts, you could always start studying from any of those books you recommended, there wont be too much of a difference. A book that I used was Precalculus by Ron Larson, which isn't a very good book for someone who is learning functions and their graphs for the first time, but since you are relearning it, it would be efficient because of the way it is structured and has many exercises.

However if you want something that explains the concepts well and goes through it quickly there is a free site that is very well recommended by many, the link of which is:

http://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

Any how, good luck! I felt the same way you did and got back into math and has been a really positive and rewarding effort.