Looking for a good non-Pearson book on beginning algebra

[UsableThought]

A little background first: As my https://www.physicsforums.com/members/usablethought.611113/ explains, I'm a retired writer/editor, never good at math as a kid but always fascinated by physics, who has decided to take a long, slow, pleasurable road toward learning the necessary math to get to at least high school-level physics. My approach is self-study supplemented whatever good MOOCs I can find (I just completed a great one in entry-level logic & proofs, from Stanford's Kevin Devlin); ALEKS, which I just learned about yesterday; and (maybe) auditing courses at my local state university once I turn 60, which happens in April.

My current target is re-learning precalc & high school algebra. My impression (from taking the logic/proofs course mentioned above) is that although this level of algebra isn't "advanced," it is nonetheless essential to many, many further branches of math (not to mention physics). I've got Gelfand and Shen's enjoyable little volume Algebra, and have gotten about a quarter way through it; but I have read a review that says that as good as this book is, it's intended as a supplement to a standard algebra textbook. Plus, I've heard that although the pie in ALEKS is great for telling you what you need to focus on, the topic presentations are rather brief & perhaps best supplemented with a good book. So that's what I'm looking for - a basic "beginning/intro" algebra book to go w/ Gelfand and ALEKS.

Now . . . my dilemma: I dislike Pearson-style books intensely; but that is practically all I can find on Amazon; that, plus a few Dover books that don't seem quite right. Nor do I like the "Art of Problem Solving" books. Blizter almost seems good despite having the usual Pearson faults; however I find complaints on Amazon with his series about even simple aspects of production, e.g. student solutions not matching the problems, etc.

The one book I have found that looks like it will be quite good is a Wiley book, https://www.amazon.com/dp/047064804X/?tag=pfamazon01-20 Sheldon Axler, 2nd edition. However Axler warns in the introduction that his book assumes as a prerequisite "the usual course in intermediate algebra." Oops! So possibly I'm not quite ready for Axler, and might need something more basic to start with?

Of course such a book (well written, not overpriced, not overstuffed, not full of unnecessary color graphics and stupid "real world" pseudo-examples) may not exist. And it may not strictly be necessary; when ALEKS points me to a particular topic, I can probably just search on the web for appropriate articles & math sites for more background. But I'm curious if anyone knows a favorite intro algebra book that is non-Pearson that they could recommend. I may just end up going with the https://www.amazon.com/dp/B00W1VZSFS/?tag=pfamazon01-20, since it isn't expensive & he starts off nice and easy.

 

[NathanaelNolk]

If you want a taste of more advanced mathematics, Serge Lang's Basic Mathematics is a great book by a great author. As for precalculus, I highly suggest Simmons' Precalculus in a Nutshell (it covers algebra too). You can find it for less than 20 bucks on Amazon. Cohen's Precalculus is another reputed book but I haven't seen it personally.

 

[UsableThought]

Well, I think I've found what I need to help me with my beginning/intermediate algebra review: https://www.amazon.com/dp/B00DC91GBS/?tag=pfamazon01-20, 4th Ed., by Miller, O'Neill, and Hyde. It's a Pearson book after all (shudder) but I found recommendations for it on other sites, in particular a suggestion that it can serve as a good introduction to Axler. I've actually already started on the review chapter in Axler and so far I find him pithy & engaging.

I also did get a copy of Euler's Elements of Algebra after reading reviews that praised it; but I think that will be mostly for comparing & contrasting and also for enjoyment - his style, even in translation, has been praised for its lucidity.

 

[alan2]

My recommendation is to stay away from Miller. I don't teach algebra at that level but I know many people who do and all I've ever heard are complaints. Pretty pictures though.

The classic textbooks on algebra are by Paul Foerster:

https://www.amazon.com/dp/0131657089/?tag=pfamazon01-20
https://www.amazon.com/dp/0131657100/?tag=pfamazon01-20

Or by Brown and Dolciani:

https://www.amazon.com/dp/0395977223/?tag=pfamazon01-20
https://www.amazon.com/dp/0395977258/?tag=pfamazon01-20

 

[UsableThought]

My recommendation is to stay away from Miller. I don't teach algebra at that level but I know many people who do and all I've ever heard are complaints.

Thanks for the reply. Pretty pictures seem endemic to Pearson, Do you remember what the complaints were? My preferences are particular to myself, and what might bother a teacher might not bother me at all. Bear in mind I only need the textbook for a short time before I transition to Axler, whose style and presentation I already find suitable. So I will probably stick with Miller unless I immediately find big problems. The preview pages and TOC looked fine.

The Foerster books are probably quite nice given the number of good reviews. I do wish they had previews on Amazon, as I no longer buy books blind unless I already know the author or have some other compelling reason.

 

[alan2]

The general complaints are the same as usual. It doesn't explain things well, it's full of errors, it's incomplete, it's mechanical and algorithmic, students aren't encouraged to think, students don't understand the material enough to be successful in their next class, etc. But about a month ago this email came from someone in the department who does use the book.I sent the following message on Tuesday, "Is anyone finding mistakes in the fourth edition? I have been. They are similar to the mistakes in the second edition which were already corrected. For example sec 5.7 prob # 57 was already corrected before, but now it's back to how it was in the 2nd ed. Power does NOT vary jointly as the current and the square of the resistance" as stated." The corrections were already submitted to them and made, why do they show up again? I think the issue is a lot bigger than this. Since the mistakes happen to be the same ones that were in the second edition, I would hate to discover that all they did was revert to the second edition and justify charging the students $250 for a hard copy.

 

[UsableThought]

The general complaints are the same as usual. It doesn't explain things well, it's full of errors, it's incomplete, it's mechanical and algorithmic, students aren't encouraged to think, students don't understand the material enough to be successful in their next class, etc. But about a month ago this email came from someone in the department who does use the book.

Thanks, that's enough to convince me. I've canceled that order.

Meanwhile, I did a bit more searching, and was able to find a used copy of Brown's "Algebra: Structure and Method" for $20, too good to pass up. Plus, in addition to the large number of positive comments on Amazon, I found a very positive, cogent review of the book on someone's tutoring blog:

This book doesn’t have a ton of frills—there are barely any pictures or “extras.” But what makes this book exceptional is its GREAT sequencing. It does an excellent job of breaking the math down without dumbing it down. The problems get harder very incrementally . . .

The students I’ve used this book with acquire very, very strong algebra skills without getting bored or frustrated. And I think it’s because the sequencing forces students to learn how to “chunk,” a concept I learned from Daniel T. Willingham’s book, https://www.amazon.com/dp/0470279303/?tag=pfamazon01-20

 

[alan2]

I hope that works out for you. I always think books should be straightforward and coherent, something lacking in many modern textbooks.