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.
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,..
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.
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!
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.
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 ❤
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 !
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.
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.
Thanks for clarifying that. I'm on Chapter R the review chapter of Algebra & Trigonometry. Right I'm watching videos on the Pythagorean Theorem because I'm on something about the theorem in Algebra & Trigonometry. I know about A squared + B squared = C. But watching the videos anwya
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.
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 :)
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 😅
Getting all this down at this early point saves you tons of "getting stuck for hours" moments later on. 6:30 agreed, if you can somehow get good at the identities you increase by a power level you can feel. 8:40 these kinds of books that list and explain EVERY step in the process are both rare and worth their weight in gold.
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.
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...
My personal best algebra and trig book are by Vance. His book Modern College Algebra and Modern Algebra and Trigonometry is the text that I use to self taught myself at age 12. Instead of just plug and chug math, the author wants the reader to think algebra as a logical subject, the book is proof based and some of the problems asked student to prove smth. Field axiom, Order axiom and other topics that shouldn’t be taught at college algebra level were introduced.
Good book. "Trigonometry: A Unit Circle Approach" also by Dr. Sullivan is also great especially if you want a book dedicated to trigonometry. I picked up a used copy of that and the book in this video for $ 8.00 a piece. That is a lot of knowledge for not a lot of money.
The layout of Sullivan's Precalculus book shown here closely mirrors his College Algebra textbook. The CA book has two extra chapters at the beginning: an "R" chapter for Review, and Chapter 1 is Equations and Inequalities. Other than that the other 12 chapter headings are exactly the same and have very similar lengths. These chapters may have been revised in some manner to be distinct, I am not sure. Just a heads up, if you have his CA book you may basically already have Sullivan's PreCalc book.
Very nice review. I purchased a copy for myself after watching this. However I purchased on the website Abe's books which had many more selections than Amazon. Thanks for pointing out this text.
I'm very wlling to buy that book. I'm working my way through Sullivan's Algebra & Trigonometry at the moment, and I just wonder if Sullivan's Algebra & Trigonometry and his precalculus contain material that is similar or same. I don't mean to be negative. Someone told me a few weeks ago told me all the math books I'm buying contain overlapping material. I don't mean ruin other's fun with these math books. Personally I like to have all the books I can get and I probably get this book I have ordered 2 precalculus books and a calculus book
In my country I could only buy the Precalc: Concepts through Functions version by this same autor. I hope the topics be enough to prepare for calculus and then real analysis.
A few questions, how does the seventh edition compare to the tenth edition? The book I purchased was the 10th. Also, would you recommend this book or Precalculus: Mathematics for Calculus for self-study? Or are they both solid options? I've been working up from the basics with the 2005 Glencoe series (I'm more familiar with Glencoe, as my high school back in the day taught from them) and have hit Precalculus.
I hate how every precalc book assumes that you learned basic coordinate geometry in middle school, whereas middle schools assume that you will learn coordinate geometry in precalc. I did finally manage to lay my hands on a good coord book: Riddle's Calc teaches coord using lots of diagrams and easy definitions. That, combined with Thomas, does the job. But it doesn't go super deep into stuff like auxiliary circle etc. For that, you need Osgood. Loney is too looney. He teaches conics using some sort of supersymmetry (everything is derived from eccenyricity) that is far from beginner-friendly. It only makes sense if you already know coord.
@TheMathSorcerer Great video as always. Between the precalculus of Sullivan, the Stewart, the Leithold and the Serge Lang. ¿Wich one is better? Or at least. ¿Better organized and cover more topics while developing more proofs? I have money to buy only one of them. Greetings
Hi. I'm a former college student who was doing high school level pre calc. I made it up to grade 11 physics and grade 11 math at the -1 level. I don't go back to school until January and am looking to find a book to keep my mind sharp and not to difficult to practice at the level I'm at before I go back to school. Do you have any suggestions for me?
Hey Math Sorcerer, I will be taking precal at my community college this fall semester. I want to begin self studying over the summer to give myself a leg up; I purchased the same book shown in the video, I was wondering if you can give me some advice on what topics I should review.
Hey sir i am confused in India we have these 5 textbooks for JEE(an exam) : algebra, coordinate geometry, trignometry, vectors and calculus so which books falls into pre calculus and which fall into calculus and where to put vectors?
Does anyone know if I can review/learn all of high school algebra/trig with only this precalc book? I learned it a loong time ago but still remember some algebra until log functions. I was planning to learn those topics a long time ago but didn't know if I should go all the way from pre-algera, algebra1/2, algebra-trig to precalc or just precalc is enought. (I already have the book on the video)
I tried it for while, it is nice to hear the voice of a human being and follow along, it also gives you a sense of community, and sometimes it feels more interesting than plodding through a textbook. But personally I feel a textbook is better organized, you can go back and fourth, using the table of contents, the headings and subheadings, a lot easier to navigate, go back and review important concepts and formulas, etc.. and I feel a textbook leaves fewer "missing links", it's just not the same amount of content, these precalculus books are 1000 pages long, with thousands of exercises, whereas what you find on Khan academy is basically a sample of a textbook, that's my experience and opinion anyway.. hope it helps, maybe a combination of both would be ideal for some people...
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.
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,..
Yes, Stewart should be mandatory book for any math related degree, instead of any other.
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.
are you doing all the excercises ??
How about Stewart's?
Which version did you get?
Just when I was thinking of whether or not to do Precalculus next
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!
I see that Precalculus: Mathematics for Calculus starts with math fundamentals, including fractions, so maybe should have gotten that book instead. ;)
I love this comment. Best of luck on your math journey and I admire your dedication.
This is where I'm starting....I have the 3rd edition.... I'm 65 and having a blast here. Thanks for the review!
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.
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 ❤
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 !
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.
I LOVE LOGS NOW. They're so simple and easy to do in my head.
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.
Thanks for clarifying that. I'm on Chapter R the review chapter of Algebra & Trigonometry. Right I'm watching videos on the Pythagorean Theorem because I'm on something about the theorem in Algebra & Trigonometry. I know about A squared + B squared = C. But watching the videos anwya
Just left the same comment above, I guess I hould scroll the comments first to avoid repeating what's already been said.
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.
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 :)
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 😅
6:37 I love trig identities. Very fun ❤
Thank you, your passion for the book is contagious! 😁
Getting all this down at this early point saves you tons of "getting stuck for hours" moments later on. 6:30 agreed, if you can somehow get good at the identities you increase by a power level you can feel. 8:40 these kinds of books that list and explain EVERY step in the process are both rare and worth their weight in gold.
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.
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!!
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...
Btw, the book I got was "Precalculus 6th ed."
My personal best algebra and trig book are by Vance. His book Modern College Algebra and Modern Algebra and Trigonometry is the text that I use to self taught myself at age 12. Instead of just plug and chug math, the author wants the reader to think algebra as a logical subject, the book is proof based and some of the problems asked student to prove smth. Field axiom, Order axiom and other topics that shouldn’t be taught at college algebra level were introduced.
Good book. "Trigonometry: A Unit Circle Approach" also by Dr. Sullivan is also great especially if you want a book dedicated to trigonometry. I picked up a used copy of that and the book in this video for $ 8.00 a piece. That is a lot of knowledge for not a lot of money.
The layout of Sullivan's Precalculus book shown here closely mirrors his College Algebra textbook. The CA book has two extra chapters at the beginning: an "R" chapter for Review, and Chapter 1 is Equations and Inequalities. Other than that the other 12 chapter headings are exactly the same and have very similar lengths. These chapters may have been revised in some manner to be distinct, I am not sure. Just a heads up, if you have his CA book you may basically already have Sullivan's PreCalc book.
Holy Smokes, I have that exact book and the matching Student Solutions manual. Bought them both used for $2!! Awesome:)
Why repeat algebra 2 stuff? It should start with trig and cover more infinite sequences, vectors, etc.
Very nice review. I purchased a copy for myself after watching this. However I purchased on the website Abe's books which had many more selections than Amazon. Thanks for pointing out this text.
Hi I don't know why some times the upper edition changethe nine editon is Addison wesley but i suppose that the whole is almost the same Thanks
Timing couldn’t have been more perfect
Some collages has modified version of it, i saw one started from chapter 3
I'm very wlling to buy that book. I'm working my way through Sullivan's Algebra & Trigonometry at the moment, and I just wonder if Sullivan's Algebra & Trigonometry and his precalculus contain material that is similar or same. I don't mean to be negative. Someone told me a few weeks ago told me all the math books I'm buying contain overlapping material. I don't mean ruin other's fun with these math books. Personally I like to have all the books I can get and I probably get this book I have ordered 2 precalculus books and a calculus book
Please see my comment regarding the differences. I own both books.
@@ussdfiant okay. thanks. I'll probably just order the book😁😁next time the funds become available. I'll check your comments out too
In my country I could only buy the Precalc: Concepts through Functions version by this same autor. I hope the topics be enough to prepare for calculus and then real analysis.
Hello sir! Sir recommend the best book for Analytic geometry.
A few questions, how does the seventh edition compare to the tenth edition? The book I purchased was the 10th. Also, would you recommend this book or Precalculus: Mathematics for Calculus for self-study? Or are they both solid options? I've been working up from the basics with the 2005 Glencoe series (I'm more familiar with Glencoe, as my high school back in the day taught from them) and have hit Precalculus.
8:04 I prefer to solve the equation then check my solution
I hate how every precalc book assumes that you learned basic coordinate geometry in middle school, whereas middle schools assume that you will learn coordinate geometry in precalc.
I did finally manage to lay my hands on a good coord book: Riddle's Calc teaches coord using lots of diagrams and easy definitions. That, combined with Thomas, does the job.
But it doesn't go super deep into stuff like auxiliary circle etc. For that, you need Osgood. Loney is too looney. He teaches conics using some sort of supersymmetry (everything is derived from eccenyricity) that is far from beginner-friendly. It only makes sense if you already know coord.
@TheMathSorcerer Great video as always. Between the precalculus of Sullivan, the Stewart, the Leithold and the Serge Lang. ¿Wich one is better? Or at least. ¿Better organized and cover more topics while developing more proofs? I have money to buy only one of them.
Greetings
Hi. I'm a former college student who was doing high school level pre calc. I made it up to grade 11 physics and grade 11 math at the -1 level. I don't go back to school until January and am looking to find a book to keep my mind sharp and not to difficult to practice at the level I'm at before I go back to school. Do you have any suggestions for me?
I loved precalculus. So many “aha” moments.
This book was edited in Spanish too, you should make a video about it on your other channel.
Could you find the lightest precalculus book? You had one for calculus.
We also need videos on calculators of all types
Looks like a great precalculus book, just the right amount of color.
God bless you. Thank you!
Hey Math Sorcerer, I will be taking precal at my community college this fall semester. I want to begin self studying over the summer to give myself a leg up; I purchased the same book shown in the video, I was wondering if you can give me some advice on what topics I should review.
Are there any precalculus texts that include material on linear algebra or beginning complex analysis?
I purchased this PreCalc by Sullivan 3rd edition at Goodwill for $6.95.
Hey sir i am confused in India we have these 5 textbooks for JEE(an exam) : algebra, coordinate geometry, trignometry, vectors and calculus so which books falls into pre calculus and which fall into calculus and where to put vectors?
How does this compare with Stewart's precalculus?
Does anyone know if I can review/learn all of high school algebra/trig with only this precalc book? I learned it a loong time ago but still remember some algebra until log functions. I was planning to learn those topics a long time ago but didn't know if I should go all the way from pre-algera, algebra1/2, algebra-trig to precalc or just precalc is enought.
(I already have the book on the video)
Do you have the "Art of Problem Solving" collection?
They are used by people who are into math contests.
Would be very nice reviews of those books.
sadly this book is SO much expensive here in brazil, even for kindle, i'll look for other similar options but seems like a great one
Usa a versão jacksparrow
send me a message, I have a PDF version of the 11th edition I can send you
WHat do you think of khan academy for learning maths at least precalc?
I tried it for while, it is nice to hear the voice of a human being and follow along, it also gives you a sense of community, and sometimes it feels more interesting than plodding through a textbook. But personally I feel a textbook is better organized, you can go back and fourth, using the table of contents, the headings and subheadings, a lot easier to navigate, go back and review important concepts and formulas, etc.. and I feel a textbook leaves fewer "missing links", it's just not the same amount of content, these precalculus books are 1000 pages long, with thousands of exercises, whereas what you find on Khan academy is basically a sample of a textbook, that's my experience and opinion anyway.. hope it helps, maybe a combination of both would be ideal for some people...
Ongggggggg you inspire me .
I don't understand why Counting and Probability are important for Calculus. I never use these tools to teach Calculus.
Snagged this exact edition, hardcover, for $12.80 on eBay.
Publishers of math books had some amusing names back in the day: Harcourt Brace Jovanovitch... JOVANOVITCH! my friends and I would joke
hehehehe
nice!!
Keren
Im not undrstand the barabla and huparbolla fancation in the life