Foundations Precalculus: Sixth Edition by Warren W. Esty, is it Rigorous?

[Chandller]

Hi PF,
I happened up a textbook called Precalculus (Sixth Edition) by Montana State University Professor Emeritus, Dr. Warren W. Esty and I understand that it is supposed to be a great textbook book for Precalculus self-study. I was just wondering if anyone had heard of, or used it in the past, and considered it to be a rigorous Precalculus textbook, that would also be good for self-study.
Thank you in advance!

Chandller

 

[Chandller]

Nothing, huh?

 

[archaic]

Nothing, huh?

I don't think you would get a "No, I haven't heard of it" answer here. However, if it is an inquiry for yourself, then you can directly ask for a textbook that has certain traits and, hopefully, you'd get an answer.

 

[Mark44]

I was just wondering if anyone had heard of, or used it in the past, and considered it to be a rigorous Precalculus textbook, that would also be good for self-study.

I don't think people rate precalculus textbooks in terms of rigor. Really, textbooks in this area cover algebra and maybe trigonometry, neither of which has changed in hundreds of years.

 

[Chandller]

I actually already have the book. So, I was mainly looking for opinions. Seeing how PF is full of threads asking as to the rigor and/or the quality (or rating, as you mentioned,) of various books, even Precalculus books containing two hundred year old information, I don't see how one more would hurt.

 

[Mondayman]

Most precalculus books aren't rigorous. They present the information as clearly as possibly and provide tons of exercises to hammer the method in. I see there are six editions of this text. I'm sure its no different from the many precalculus out there. They tend to focus on computation, and have little proof based exercises, if any.

 

[Chandller]

I can see this is a dead end road...

 

[Mondayman]

With the number of different Precalculus texts out there, it's unlikely anyone has used this particular one.

 

[TurboDiesel]

Hi Chandller,

It looked interesting so I just ordered a copy.

PF is an incredible resource for textbook recommendations (see the search box). One free pdf book recommended by some here sounds like what you want: David Santos's "Precalculus: An Honours Course"

Another in that direction, endorsed by mathwonk, among others, is Allendoerfer and Oakley's "Principles of Mathematics." I like this book but it's hard to get a decent copy at a low cost.

A standard book in this direction is that of Barnett, Ziegler, Byleen, and Sobecki: "Precalculus."
From B&N: "Mathematical reform is the driving force behind the organization and development of this new precalculus text . . . The development of each topic proceeds from the concrete to the abstract . . ."

For standard texts, I really like David Cohen's "Precalculus: With Unit Circle Trigonometry" as well as his "College Algebra" (aka algebra II in high school). Check out the problems. :-)

The gods of abstraction might want to smite me, but I give a strong endorsement to the Art of Problem Solving curriculum--including its Precalculus text. These books teach mathematical thinking in a broader context than pure abstraction. And they are super fun too.

The AoPS books are highly challenging, so if you are not well prepared already, you should consider starting no higher in the AoPS curriculum than with what you have most recently covered--Algebra II, in many US schools--rather than going from, say, normal Algebra II to AoPS Precalculus. If you are a top 5% math student, go ahead and see if you can move directly to AoPS Precalculus. [BTW, the AoPS books have solution manuals offering complete, educational solutions for the entire problem sets.]

I happened up a textbook called Precalculus (Sixth Edition) by Montana State University Professor Emeritus, Dr. Warren W. Esty and I understand that it is supposed to be a great textbook book for Precalculus self-study. I was just wondering if anyone had heard of, or used it in the past, and considered it to be a rigorous Precalculus textbook, that would also be good for self-study.
Thank you in advance!

Chandller

 

[Chandller]

Hi TurboDiesel,
I really appreciate the great info and response. Let me/us know when you get it. Did you get the Solution booklet, as well? If not, let me know. I am a fan of AoPS, as well. I found another pretty rigorous Precalculus book from Dr. David H. Collingwood at the University of Washington, which I understand has a nasty Mathematics Program (They are a Microsoft feeder school, so you know it has to be good.) They have actually written there own Precalculus book (Precalculus by David H. Collingwood) for their Precalculus or Math 120 course. The course has a pretty cool website with old tests and quizzes too. Just a little background, but I am a non-traditional Applied Mathematics major that is at College Trig level, but I have had to take a break for a while, do to finance's, so until I can get back in, I would like to find the Precalculus book or books that will solidify my Mathematical foundation so well that I can CLEP Precal/Trig and be so foundationally sound through the rest of my undergraduate coursework that I can, hopefully, get an academic scholarship and, hopefully again, do my post-grad at a top level school. I am seriously considering moving through this book list https://www.physicsforums.com/threa...igh-school-pre-university-book-thread.307797/

Thank you for the help and any other ideas or advice are surely welcomed!

 

[Mark44]

Seeing how PF is full of threads asking as to the rigor and/or the quality (or rating, as you mentioned,) of various books, even Precalculus books containing two hundred year old information, I don't see how one more would hurt

Typically, when people ask questions about the rigor of textbooks, they're asking about textbooks at the calculus level or above. One criterion here would be whether the author derives results versus just providing "cookbook" formulas.

 

[Chandller]

Mark44,
What about these...
https://www.physicsforums.com/threads/rigorous-precalculus-and-rigorous-arithmetic-algebra-books.962961/
https://www.physicsforums.com/threads/rigorous-precalculus-text-needed.411259/

 

[Mark44]

Mark44,
What about these...
https://www.physicsforums.com/threads/rigorous-precalculus-and-rigorous-arithmetic-algebra-books.962961/

As advertised, lots of proofs and theorems, a lot more than most of the books that are usually used in precalc courses at the college level. The book by Santos has more of the flavor of how math books used to be. Current books have more color and figures, which are more costly to print and probably a big factor in how expensive they are.

https://www.physicsforums.com/threads/rigorous-precalculus-text-needed.411259/

I couldn't really tell about most of the books listed. One of the books, by Gelfand, seems more like an analysis type of book, something post-calculus.

 

[TurboDiesel]

Hi Chandller,

Thanks, I appreciate that. Nice to see your enthusiasm and the Collingwood mention. I saw those too. There are many ways to approach mathematics. What is important is finding an approach that inspires you to further study and allows you to find success in progression.

Given this background information and your goals, here's my suggestion.

First, finish precalculus in pretty much any text you like (do all the hard problems and understand why you were wrong or right). I like Cohen's book. Second, buy these four books:

• Jenny Olive's "Maths: A Student's Survival Guide"
• Stroud and Booth's "Engineering Mathematics" and "Advanced Engineering Mathematics"
• Apostol's "Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra"

Work through Stroud and Booth (S&B) for "a first look" and follow with Apostol for a rigorous foundation. Use Jenny Olive whenever and wherever you need a second viewpoint to catch you up with the material in S&B. S&B covers all the mathematics you need to get straight A's in early STEM and gives you the basic understanding needed to excel when you approach texts like Apostol. Using S&B would save you a ton of time searching around and a ton of cash buying separate books. They are highly pedagogical.

The Apostol text is sooo clear in its rigor (look on amazon / ebay for a global/international edition). Munkres has some notes to accompany Apostol. An alternative to Apostol would be Spivak. A video course alternative to Apostol for single variable calculus would be MIT's edX sequence (free if you don't need a certificate): https://www.edx.org/xseries/mitx-18.01x-single-variable-calculus

The S&B texts are in prerelease for a new edition this month and next (I have them on order):
https://www.amazon.com/gp/product/1352010275/?tag=pfamazon01-20
https://www.amazon.com/gp/product/1352010259/?tag=pfamazon01-20

If you want to start from the basics, my suggestion is to work through the AoPS curriculum starting with Prealgebra, buying the solutions manual for each text. Feel free to do this alongside more advanced books such as my four suggested texts. If you instead opt to finish AoPS through Precalculus first, then you could reasonably move directly to Apostol or Spivak. Howers' list is really nice, and you have my alternative suggestions here.

Hi TurboDiesel,
I really appreciate the great info and response. Let me/us know when you get it. Did you get the Solution booklet, as well? If not, let me know. I am a fan of AoPS, as well. I found another pretty rigorous Precalculus book from Dr. David H. Collingwood at the University of Washington, which I understand has a nasty Mathematics Program (They are a Microsoft feeder school, so you know it has to be good.) They have actually written there own Precalculus book (Precalculus by David H. Collingwood) for their Precalculus or Math 120 course. The course has a pretty cool website with old tests and quizzes too. Just a little background, but I am a non-traditional Applied Mathematics major that is at College Trig level, but I have had to take a break for a while, do to finance's, so until I can get back in, I would like to find the Precalculus book or books that will solidify my Mathematical foundation so well that I can CLEP Precal/Trig and be so foundationally sound through the rest of my undergraduate coursework that I can, hopefully, get an academic scholarship and, hopefully again, do my post-grad at a top level school. I am seriously considering moving through this book list https://www.physicsforums.com/threa...igh-school-pre-university-book-thread.307797/

Thank you for the help and any other ideas or advice are surely welcomed!

 

[Chandller]

Hi TurboDiesel,
This is Spectacular. Thank you.

Hi Chandller,

Thanks, I appreciate that. Nice to see your enthusiasm and the Collingwood mention. I saw those too. There are many ways to approach mathematics. What is important is finding an approach that inspires you to further study and allows you to find success in progression.

Given this background information and your goals, here's my suggestion.

First, finish precalculus in pretty much any text you like (do all the hard problems and understand why you were wrong or right). I like Cohen's book. Second, buy these four books:

• Jenny Olive's "Maths: A Student's Survival Guide"
• Stroud and Booth's "Engineering Mathematics" and "Advanced Engineering Mathematics"
• Apostol's "Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra"

Work through Stroud and Booth (S&B) for "a first look" and follow with Apostol for a rigorous foundation. Use Jenny Olive whenever and wherever you need a second viewpoint to catch you up with the material in S&B. S&B covers all the mathematics you need to get straight A's in early STEM and gives you the basic understanding needed to excel when you approach texts like Apostol. Using S&B would save you a ton of time searching around and a ton of cash buying separate books. They are highly pedagogical.

The Apostol text is sooo clear in its rigor (look on amazon / ebay for a global/international edition). Munkres has some notes to accompany Apostol. An alternative to Apostol would be Spivak. A video course alternative to Apostol for single variable calculus would be MIT's edX sequence (free if you don't need a certificate): https://www.edx.org/xseries/mitx-18.01x-single-variable-calculus

The S&B texts are in prerelease for a new edition this month and next (I have them on order):
https://www.amazon.com/gp/product/1352010275/?tag=pfamazon01-20
https://www.amazon.com/gp/product/1352010259/?tag=pfamazon01-20

If you want to start from the basics, my suggestion is to work through the AoPS curriculum starting with Prealgebra, buying the solutions manual for each text. Feel free to do this alongside more advanced books such as my four suggested texts. If you instead opt to finish AoPS through Precalculus first, then you could reasonably move directly to Apostol or Spivak. Howers' list is really nice, and you have my alternative suggestions here.