Precalculus text? opinions wanted

[mom1720]

I've been researching  precalc texts for DS and one thing I did was search what our local CC uses as well as the state flagship which happens to be our closest U.

Anyway, the CC uses Lial which I've read a lot about here; however the U uses Swokowski and Cole: Precalulus in the engineering school and Axeler: Precalculus: A Prelude to Calculus in the college of A&S. Anyone know anything about either? I don't. DS is thinking engineering, but isn't sure yet.

Thanks.

 

 

 

[kiana]

I think Axler is a good book but too theoretical for some. I've never seen Swokowski but I believe it's similar. Both of them will expect you to extrapolate a bit in the homework problems. Axler's a very good mathematician who wrote his own linear algebra textbook following a different paradigm than the normal. Swokowski (deceased) was better known as a calculus textbook author and the pre-calculus book was written based on aiming the student at calculus. Lial, on the other hand, was a mathematics educator through and through; her books started with arithmetic (bcm) and continued higher. They're very well done for self-instruction and expect less extrapolation. I found Lial *can* be a little bit cookie-cutter as far as "follow the examples" although it's certainly not a bad textbook. A student who worked industriously through the Lial series would be quite well-prepared for most university calculus classes, other than highly theoretical ones at some colleges. They'd definitely be prepared for engineering calculus. 

Other popular books: I used Cohen's precalculus when I learned it and again in graduate school when I taught it. It fits again in the slightly more theoretical explanation category, similar to Axler and Swokowski. Blitzer's books are also very popular. I loathe their explanations (they are very monkey-see-monkey-do in MY opinion) but their word problems are really great. Some might find them a bit too social-justice oriented but for me (and most of my students at the CC) this is a plus. I mention it only so that noone is surprised. One of the things I really DO like about Blitzer's is the cumulative reviews. I find that this is often lacking. 

Opinion: I think it'd be great to have more than one book (and these are all sufficiently well-aged that you can get an older edition cheaply). For example, the 5th edition Lial (the one that I have taught out of repeatedly) is available used on Amazon for $4.94 (and there is absolutely no reason to go with a newer edition ... I hate Pearson and their predatory edition changes ... sorry ... what the heck happened to the rant on/rant off emoji).

Ideally, I'd get one of the more theory-oriented ones, one of the slightly more hand-holdy "this is how you do it" ones, and something like "precalculus demystified/precalculus for dummies" when I just needed a ***RRRGGGHHH WHAT IS GOING ON*** explanation (I know the name is insulting, but I learned some great teaching techniques from calculus for dummies), and I'd buy them all used. The topics/order are fairly standardized so it's easy to check explanations in multiple textbooks (plus index). Ideally, I'd work the problems out of the one that requires more extrapolation in the homework problems, but if the student is not there developmentally, it should not be forced.

However, frankly, getting *any* standard pre-calculus textbook with 3.5 or higher stars on amazon, working through it, and understanding it, and if something is not understood, possibly moving to a different chapter (for example, if someone is just NOT GETTING logarithms, there is nothing wrong with going and doing a trig chapter and then coming back to continue work on logarithms -- they're a hard topic) and then returning to make sure things are *thoroughly* grokked, will result in above-average preparation. 

Sorry that I wrote a book instead of simply answering your question. Hope you find something useful there anyway ? 

[mom1720]

Oh my gosh, thank you so much! This is more than I ever could have hoped for!!

I'll have my DH read your response as well since he's the math teacher -- he's a physicist, so we leave it to him.  Neither of us had a class called precalculus back in the day -- my progression was Alg. 1, Alg. 2, Geo, Trig/Analyt., Calculus (AB equivalent). He doesn't remember what he did at all -- went to three different high schools -- other than he ended with Calc BC.

Again, thank you so much!

[JoJosMom]

3 hours ago, kiana said:

I think Axler is a good book but too theoretical for some. I've never seen Swokowski but I believe it's similar. Both of them will expect you to extrapolate a bit in the homework problems. Axler's a very good mathematician who wrote his own linear algebra textbook following a different paradigm than the normal. Swokowski (deceased) was better known as a calculus textbook author and the pre-calculus book was written based on aiming the student at calculus. Lial, on the other hand, was a mathematics educator through and through; her books started with arithmetic (bcm) and continued higher. They're very well done for self-instruction and expect less extrapolation. I found Lial *can* be a little bit cookie-cutter as far as "follow the examples" although it's certainly not a bad textbook. A student who worked industriously through the Lial series would be quite well-prepared for most university calculus classes, other than highly theoretical ones at some colleges. They'd definitely be prepared for engineering calculus. 

Other popular books: I used Cohen's precalculus when I learned it and again in graduate school when I taught it. It fits again in the slightly more theoretical explanation category, similar to Axler and Swokowski. Blitzer's books are also very popular. I loathe their explanations (they are very monkey-see-monkey-do in MY opinion) but their word problems are really great. Some might find them a bit too social-justice oriented but for me (and most of my students at the CC) this is a plus. I mention it only so that noone is surprised. One of the things I really DO like about Blitzer's is the cumulative reviews. I find that this is often lacking. 

Opinion: I think it'd be great to have more than one book (and these are all sufficiently well-aged that you can get an older edition cheaply). For example, the 5th edition Lial (the one that I have taught out of repeatedly) is available used on Amazon for $4.94 (and there is absolutely no reason to go with a newer edition ... I hate Pearson and their predatory edition changes ... sorry ... what the heck happened to the rant on/rant off emoji).

Ideally, I'd get one of the more theory-oriented ones, one of the slightly more hand-holdy "this is how you do it" ones, and something like "precalculus demystified/precalculus for dummies" when I just needed a ***RRRGGGHHH WHAT IS GOING ON*** explanation (I know the name is insulting, but I learned some great teaching techniques from calculus for dummies), and I'd buy them all used. The topics/order are fairly standardized so it's easy to check explanations in multiple textbooks (plus index). Ideally, I'd work the problems out of the one that requires more extrapolation in the homework problems, but if the student is not there developmentally, it should not be forced.

However, frankly, getting *any* standard pre-calculus textbook with 3.5 or higher stars on amazon, working through it, and understanding it, and if something is not understood, possibly moving to a different chapter (for example, if someone is just NOT GETTING logarithms, there is nothing wrong with going and doing a trig chapter and then coming back to continue work on logarithms -- they're a hard topic) and then returning to make sure things are *thoroughly* grokked, will result in above-average preparation. 

Sorry that I wrote a book instead of simply answering your question. Hope you find something useful there anyway ? 

 

This is fabulous post, kiana.

A bit of a tangent: Would you have a recommendation for a companion text to AoPS precalc? My DD is taking the online class, and I would love to find something to help her through when something's not clicking.

[kiana]

26 minutes ago, JoJosMom said:

This is fabulous post, kiana.

A bit of a tangent: Would you have a recommendation for a companion text to AoPS precalc? My DD is taking the online class, and I would love to find something to help her through when something's not clicking.

Aww thanks.

Unfortunately I really don't have a single text. I haven't gotten this yet (my professional development fund is limited) and it's sufficiently advanced that there are bits and pieces not covered in standard precalculus textbooks.

Most of the trigonometry stuff and some of the linear algebra and complex numbers stuff will be covered in a standard precalculus textbook, but for a fair amount of the linear algebra material (chapters 9-13) you'd really need a proper linear algebra book, and much of the complex number stuff (7.3 onwards) will be covered ab initio in a complex variables textbook -- and the complex variables textbooks usually assume you've had at the very least calculus 3. 

There are other people who've actually worked through it and I'll defer to one of them to answer. 

(I *want* the book, but then I want a million books -- if I had a million bucks I'd spend them on a million books)

[Kathy in Richmond]

4 hours ago, JoJosMom said:

 

A bit of a tangent: Would you have a recommendation for a companion text to AoPS precalc? My DD is taking the online class, and I would love to find something to help her through when something's not clicking.

Quick thoughts:

For the trig, I'd suggest Gelfand's Trigonometry, which has much the same flavor as AoPS. 

For the linear algebra, look at Gilbert Strang's class on MIT OCW.

Another thought is Pre-Calculus Mathematics by Shanks, Brumfiel, et al. .It's an older text from the 1960s, so you should be able to get it for a few bucks. It covers most of the AoPS precalc material at a more challenging level than modern texts.

[HollyDay]

Oldest dd used Lial's Pre-Calculus.  Youngest is currently using Pre-Calculus Concepts Through Functions by Sullivan and Sullivan

[Emerald Stoker]

On 10/31/2018 at 12:50 PM, Kathy in Richmond said:

 

Another thought is Pre-Calculus Mathematics by Shanks, Brumfiel, et al. .It's an older text from the 1960s, so you should be able to get it for a few bucks. It covers most of the AoPS precalc material at a more challenging level than modern texts.

My eldest used that one--it's a really good book, I think.

[MamaSprout]

Any thoughts on Sullivan or Larson? ETA- Axler has an Algebra 2 book, too. Looks interesting.

Edited November 4, 2018 by MamaSprout

[RootAnn]

Doesn't Larson have a few PreCalc books? Or maybe I'm thinking different editions? My dd#1 used Larson's Precalculus with Limits last year as part of an online class. I'm not a fan (ETA: especially for the price!).

 

Edited November 5, 2018 by RootAnn
added

[MamaSprout]

3 minutes ago, RootAnn said:

Doesn't Larson have a few PreCalc books? Or maybe I'm thinking different editions? My dd#1 used Larson's Precalculus with Limits last year as part of an online class. I'm not a fan (ETA: especially for the price!).

 

True- I have this one one my shelf: https://www.amazon.com/gp/product/0618660909/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

I figured out from the website which set of videos go with it... but I like it better as our second explanation book. So I'm following this thread with great interest.

[MamaSprout]

On 10/31/2018 at 7:39 AM, kiana said:

I think Axler is a good book but too theoretical for some. I've never seen Swokowski but I believe it's similar. Both of them will expect you to extrapolate a bit in the homework problems. Axler's a very good mathematician who wrote his own linear algebra textbook following a different paradigm than the normal. ?

 

Is Axler... enough? I really like the approach looking through the samples, but it is certainly a much smaller book than most.

[kiana]

I cannot really say whether it is ... enough ... because enough is so variable by student. I think it might well be necessary to supplement with drill-type problems for many students. For example, going off http://precalculus.axler.net/ChapterThree.pdf, the average student would need a lot more drill on problems like 43-44. Something like Lial would be a great source for additional problems. 

I can say that I do not feel there are any necessary topics that have been omitted. 

[MamaSprout]

On 10/31/2018 at 10:36 PM, HollyDay said:

Oldest dd used Lial's Pre-Calculus.  Youngest is currently using Pre-Calculus Concepts Through Functions by Sullivan and Sullivan

 

How do you like Sullivan?

[HollyDay]

1 hour ago, MamaSprout said:

 

How do you like Sullivan?

Good.  The charts are confusing says dd.  She is using it local CC.  Have you looked at MIT online? MUS Calculus might be an interesting option too. 

[JoJosMom]

On 10/31/2018 at 12:50 PM, Kathy in Richmond said:

Quick thoughts:

For the trig, I'd suggest Gelfand's Trigonometry, which has much the same flavor as AoPS. 

For the linear algebra, look at Gilbert Strang's class on MIT OCW.

Another thought is Pre-Calculus Mathematics by Shanks, Brumfiel, et al. .It's an older text from the 1960s, so you should be able to get it for a few bucks. It covers most of the AoPS precalc material at a more challenging level than modern texts.

 

Thank you, Kathy, and I apologize for being so late with the reply. I will see what I can get from Amazon. Unfortunately, my daughter has to have major surgery next month (scoliosis), and she has had a hard time with focus. AoPS is letting her transfer from her current class into a later-starting class at the time of her surgery, so she won't have to re-start from the beginning (her preference). We'll see how it goes, though, because she is more than a little stressed, and things have slowed down considerably.

[Kathy in Richmond]

2 hours ago, JoJosMom said:

 

Thank you, Kathy, and I apologize for being so late with the reply. I will see what I can get from Amazon. Unfortunately, my daughter has to have major surgery next month (scoliosis), and she has had a hard time with focus. AoPS is letting her transfer from her current class into a later-starting class at the time of her surgery, so she won't have to re-start from the beginning (her preference). We'll see how it goes, though, because she is more than a little stressed, and things have slowed down considerably.

Aw, I'm so sorry that your girl has to face scoliosis. Sending prayers her way that surgery goes well and solves her problems!

Glad she can transfer into another AoPS section post-surgery, though.

[MamaSprout]

On 10/31/2018 at 3:50 PM, Kathy in Richmond said:

Quick thoughts:

For the trig, I'd suggest Gelfand's Trigonometry, which has much the same flavor as AoPS. 

For the linear algebra, look at Gilbert Strang's class on MIT OCW.

Another thought is Pre-Calculus Mathematics by Shanks, Brumfiel, et al. .It's an older text from the 1960s, so you should be able to get it for a few bucks. It covers most of the AoPS precalc material at a more challenging level than modern texts.

I was just wondering the other day if the Strang linear algebra could be done before a calculus class.

[Kathy in Richmond]

11 hours ago, MamaSprout said:

I was just wondering the other day if the Strang linear algebra could be done before a calculus class.

Sure, you could try it then, since linear algebra doesn't require any calculus background. It's usually taught later in the curriculum because it does require more mathematical maturity; i.e, comfort with more abstract thought and familiarity with proofs.

[kiana]

In addition to what Kathy said -- I'm not familiar with Strang specifically, but many common linear algebra texts (Anton for sure) have a few problems that incorporate calculus (less than 10%); these can be easily omitted without hampering student learning. They are just there to give more examples of places you can apply this. 

[JoJosMom]

In case anyone is still reading this thread, does anyone have any ideas for helping with roots of unity? Links to online explanations, maybe? I am of no use whatsoever, sadly, and she's really struggling with it. (Chapters 7 and * in the AoPS Precal book.)

[Roadrunner]

On 11/16/2018 at 2:35 PM, JoJosMom said:

 

Thank you, Kathy, and I apologize for being so late with the reply. I will see what I can get from Amazon. Unfortunately, my daughter has to have major surgery next month (scoliosis), and she has had a hard time with focus. AoPS is letting her transfer from her current class into a later-starting class at the time of her surgery, so she won't have to re-start from the beginning (her preference). We'll see how it goes, though, because she is more than a little stressed, and things have slowed down considerably.

 

Wishing her the speedy recovery. I am sorry she is dealing with the surgery. Hugs. 

If she ends up in a class that started on Nov 7th, she will have a study partner. 🙂 

[JoJosMom]

2 hours ago, Roadrunner said:

 

Wishing her the speedy recovery. I am sorry she is dealing with the surgery. Hugs. 

If she ends up in a class that started on Nov 7th, she will have a study partner. 🙂 

 

Thanks, Roadrunner.

[daijobu]

11 hours ago, JoJosMom said:

In case anyone is still reading this thread, does anyone have any ideas for helping with roots of unity? Links to online explanations, maybe? I am of no use whatsoever, sadly, and she's really struggling with it. (Chapters 7 and * in the AoPS Precal book.)

 

I'm sorry to hear about your dd.  I hope she has a quick recovery and a successful outcome.  

I thought chapter 7 did a nice job of stepping you through roots of unity, starting with specific examples (n=3, n=4) and then generalizing.  

I wonder if she can carefully work through the examples on paper as they are described in the book, if that would help.  (If she isn't already doing this.)  

Basically the n roots form the vertices of a regular n-gon in the complex plane.  

Did you already try searching youtube?  

[daijobu]

You might want to tell your dd, if she doesn't already have a corrected copy, that there is a typo on p.235.  In the solution to problem 7.20, second paragraph it reads: "Since r=1, the equation f(t)=1..."

It should read f(t)=0.