Precalculus Book for Self-Study

This is a great book you can use to learn precalculus. It is called Precalculus and it was written by Sullivan.

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[starter]

a lot of time students who struggle in higher level mathematics really bogs down to their lack of foundation in PreCalc. It was one of my weakness as well only because some instructors do NOT cover all of the material. Moreover, most instructors do not treat PreCalc with precision even at the university level (grad students) because they understand that many students who are taking PreCalc are at the terminal course for mathematics. I think this severely cripples potential mathematicians that decided to become mathematicians during undergraduate Uni or community college.

I was so confused at my PhD qualifying exam that required me to know information like P(0) = c for a polynomial function P and c a constant as a part of a proof without any guidance or hints in a rush exam. Yes of course I know that property holds for polynomial functions if I set x = 0, however I never once had that property formally discussed in any mathematics. To me it was a slap to my face for missing that question but there was no way I would've found that trick because instructors in early mathematics rush formulas and procedural skills rather than attentive precision and rigor implications on definitions. I couldnt even imagine how to even start on formally proving that every real-valued ( dont know if I can extend this to complex) periodic function f will have some t in R such that f(t) = f(t+c/2) for c the period amount. As sad as it sounds, I did not even imagine using cosine or sine as a concrete example for guidance of the proof because I never took a "Precalculus Trigonometic" course.

As a full-time instructor in college now, I constantly realize how important these introductory courses are for building strong mathematicians. It's strange how higher level mathematics course are more careful in building structure and having strong mastery when really our introductory courses should be where it starts so we have a strong foundation.

Unfortunately, finding a balance between instructing an introductory math course so that mathematicians AND nonmathematician strive is rough. You can't really have a perfect balance in catering towards both.

[edgarperez]

I started teaching myself Precalculus with the free OpenStax Precalculus book, but 500 pages in I felt kind of lost, I realized that the book is just too wordy, I started to look for an alternative and decided to go for an old copy of Stewart's Precalculus, so far I'm super pleased with it, it's not wordy at all, it has tons and tons of examples, graphs, tables, and figures. And there is something about having the physical book that motivates you more than reading through a PDF. Sullivan's book must be a great option too! I just went with Stewart based on popularity... Also, older editions are way less expensive, and they virtually have exactly the same content, anyway, enjoying my journey through precaculus, ..

[jjr]

This is where I'm starting....I have the 3rd edition.... I'm 65 and having a blast here. Thanks for the review!

[joey]

I used Sullivan for precalculus and I love it. It's just so organized. Each section is divided into titled subsections. Each lesson also shows the concepts you'll be using for that particular lesson and will have the page numbers so you can review them in the appendix.
Also the ebook version is very cheap. Less than $20, I believe.

[anuragmalik]

Just when I was thinking of whether or not to do Precalculus next

[kjmav]

I just got it from eBay today. All the mathematics in this book is ‘way over my head, because I’m still working through 5th grade. I have barely mastered fractions and order of operations. I like reading this, though, even though I don’t understand a word of it. It motivates me to keep going. Someday, I am going to get into this book, and struggle through it until I understand!

[tarmiziadam]

Great book ! I have this book right here on my office desk. I used to study from Sullivan's book back in my college years. Now, I take examples and questions from this book to teach my students back !

[geekwhoeatsrice]

The way I like to distinguish Algebra from Precalculus is that Precalculus often uses more of a function approach and there's much more emphasis and discussion on domains and transformations compared to an algebra class which would focus more on the equations of it all.

[seasn]

SIR, Thank you for helping me on my journey of learning to love math. I had undiagnosed learning disabilities growing up, so after graduating high school, I didn't go into higher education because I was scared that I would end up exactly where I was in high school 5 years later. Thanks to you and a handful of other classes, IM ACING MY MATH COURSES.

[danielmrosser]

There are many great pre-calculus textbooks. One very fine example is Precalculus Mathematics in a Nutshell by Simmons. That said, every good calculus textbook worth reading begins with chapter on pre-calculus.

[albertow.]

Thank you, your passion for the book is contagious! 😁

[Soyosan]

That's the seventh edition of Sullivam's "Algebra and Trigonometry" that you showed some time ago. From what I see, added one more chapter to the older edition. It's an extensive book, and you can learn a lot from it :)

[AhirZamanSairi]

I know this just seemed like a random book review but I felt compelled to comment. IHO, this is the best pre-calc. book there is out there, in terms of didacticizm (good-teaching), and how I know, is that I researched for such a pre-calc. book, because I wanted a good reference for trig. and stuff. Because even though I'm an EE major, and I've been through it all (differential equations, calculus etc.) I realized that owing to the education system's flaw, it is possible to know how to, say, do integration by parts, or other higher computational things, which are considered higher math, but all the while not actually being completely well versed in what is considered lower math (pre-calc.). The system makes us gloss over so much superficially, in the name of only teaching the practical stuff, that you end up learning things without knowing where they came from. You have to do that to a degree, to actually learn things, because the topics just don't end in math and science, so this isn't entirely a very bad approach, but I believe it is just over-done, in the current education system. Maybe it's so inevitable, that it's not even the system's fault, who knows... So through my research, I found this book to be the best in terms of range of topics, and more importantly, in terms of clear explanations. Also it had sufficient practice problems. So I purchased an old edition which was within my reach, and I'm happy that I did. I would be open to have my mind changed with another book being proposed, to best this one in the specific attributes I specified, but mainly, I wanted to impart this experience of mine, in case it benefits anyone, thanks...

[ussdfiant]

Hello friend. I own both this book and for some reason the Algebra and Trigonometry book by Sullivan. That one doesn’t have the intro to calculus chapter, but the first chapter is a review chapter and the second chapter is Equations and Inequalities. Otherwise the books are identical.

[jbbentley]

PreCal and College Algebra/ Trignometry the big difference is the unit circle ⭕️. I bought Blitzer CA/T and PreCal and it’s the same book just a chapters. Unit circle, Calculus limit chap, and something else..
I hope I can save someone some money 😅

[Algebrainiac]

7:57 many students I tutor have a lot of trouble understanding logarithms. I always tell them that it takes time. I wasn’t good at logs when I was in high school algebra 2. They were really hard. But I practiced them so much and I ended up loving them. It takes time though. But once you know those properties they’re super fun ❤

[Wandering_Horse]

Holy Smokes, I have that exact book and the matching Student Solutions manual. Bought them both used for $2!! Awesome:)

[tethyn]

Always amazed when I have the same book. This one I got by chance since it wasn’t something I used in a class but retained as a resource; however, my son should be taking calculus for his senior year I have been referencing this to him to help make sure he is ready. It is a good text to use.

[Algebrainiac]

6:37 I love trig identities. Very fun ❤

[NichtWunderkind]

I was about to try to learn pre-calculus on my own because i'm on vacations
This video came at the right time
Thank you math sorcerer!!