What Is the Best Textbook for Precalculus?

[Akratic]

To begin, I must say that this website has become quite a reference. It's full of capable minds that are willing to help anyone. It's structured, individual, and it possesses a high-IQ community, and I thank you for allowing me to surf freely over the forums. I suppose I'll make my contribution eventually. I just have yet to find my niche as I am only a senior in high school, slightly intimidated by the nearing presence of college.

Like I said, college is just around the corner, and I want to get a jump start. I won't be taking a precalculus/calculus class until my first semester in college. I am currently in trigonometry, passing by with a mid-grade B. This is depressing because I know my true potential, although that potential is by no means measured by an emboldened letter on a report card. I do, however, have the motivation to pick up a book, read through it, understand it, and teach myself on my own time.

So, what books and/or methods can you recommend to me that will allow me to get ahead before I actually go into college? I'm trying to get a firm grasp of precalculus and a sneak peak at calculus.

And another side note: I am, unfortunately, an average mathematician, pressured by my peers into believing that mathematics is the only pathway to success. I disagree. In all honesty, I've come to find math as an entirely separate world of logic and possibility rather than a straight shot to success and opportunity. It is with this mentality in mind that I'm pursuing my interests in math not only to satisfy my beliefs of me being an intellectual, but also to expand my horizons one step at a time.

~ Yours truly.

P.S. I'm aware my posts are lengthy and unnecessarily wordy. I like to interact with you guys. :)

 

[micromass]

Just skip precalculus and go straight to calculus. If you're scared about missing some knowledge, then I advice you to go through the excellent book "basic mathematics" by Lang. It contains everything you need before starting calculus. And I think you will find that you know most of it already.

A lot of precalculus questions actually involve memorizing stupid formulas. Once you know calculus, there is no more need to memorize the formulas since you can then derive them very easily. But in fact, having a textbook give you formulas without a proof is very contrary to the spirit of mathematics. This is another reason that precalculus is not a valuable class.

 

[Akratic]

I apologize for not getting back to you sooner, Mass. Thank you for the recommendation.
Will this book help my ability to think logically by reintroducing me to proofs?

On a side note, you said precalculus is an invaluable class. If it is not a prerequisite course, would you recommend skipping it entirely in college? Honest question.

 

[mathwonk]

The answer to this question depends on the meaning of the term "precalculus". Micromass' dismissive answer assumes the term means the content of the standard trivial current day course with that title. However if one means by it, things it would help to know before studying calculus, then the list is much longer, and includes ideally, Euclid's Elements, Euler's Elements of Algebra, and more ambitiously, Euler's Analysis of the Infinite.

Briefly, one should know properties of right triangles and their connection with the circular functions (sin and cos), be able to multiply and divide polynomials and know basically why x=a is a root of a polynomial f(x) if and only if (x-a) is a factor. One should also know how to graph linear functions and find equations for circles. Basic principles of logic are also useful, like "one should fix something only if it is broken" is equivalent to: "if it ain't broken, don't fix it".

 

[rezeew]

I appreciate your enthusiasm and dedication to learning math on your own time. It's great to see that you have a strong motivation to improve your skills and understanding in precalculus and calculus, even before starting college.

In terms of textbooks, there are many options available. It would be best to consult with your future college or university to see what textbook they use for their precalculus and calculus courses. This will give you a good idea of what to expect and what topics you should focus on.

In addition, I recommend looking for textbooks that have clear explanations, plenty of practice problems, and supplementary materials such as online resources or study guides. It's also helpful to find textbooks that are well-reviewed and recommended by other students or teachers.

Aside from textbooks, there are also many online resources and videos that can help supplement your learning. Khan Academy, for example, offers free online lessons and practice problems for precalculus and calculus.

Lastly, I want to commend your perspective on mathematics. It's important to remember that success and opportunity come in many forms, and math is just one pathway. Pursuing your interests and expanding your horizons is a great mindset to have, and I wish you all the best in your mathematical journey. Keep up the great work!