1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sheldon Axler's "Algebra & Trigonometry" vs. "Precalculus: A Prelude."

  1. Jun 2, 2014 #1
    Hi all,

    I've been looking and searching around for a good book for some pre-calculus review, and decided on one of Sheldon Axler's books. Looking at his site and the contents of both books (links below), I'm not sure what the difference is between them, other than some re-ordering of things in the newer "Precaculus.." book. In fact, the "Algebra & Trigonometry" book seems if anything to have a bit more, which is a tad confusing. Maybe the newer "Precalculus.." books has corrections, better layout, etc.? Anyone use any or have any opinion on which to get? Check them out below. Besides the marketing reasons, why would anyone get the "Precalculus.." over "Algebra & Trigonometry"?




  2. jcsd
  3. Jun 2, 2014 #2


    User Avatar
    Homework Helper

    I expect they will both be proof-based but the algebra/trig one will be at a lower level, for young people.

    If this is for some kind of home schooling situation, definitely don't use one of these. Youngsters shouldn't be learning from proof books, period.

    PS. I've looked at the precalculus one before but not the alg/trig, it may be different in style.
  4. Jun 2, 2014 #3


    User Avatar
    Gold Member

    I have the A & T book now and used to have the 1st ed of the Pre C book (the grey one). The A and T book has 125 more pages-a lot of the difference is from Ch. 7 Systems of Equations, esp. section 7.4 Matrix Algebra, which was not in the Pre C book. To me, the books are about the same: they're both a bit too tough for me. I'm using Blitzer's 3rd ed. of Pre C, it's a lot easier for me. I might try Axler's book when I'm finished with Blitzer's. Hope this helps.
  5. Jun 2, 2014 #4


    User Avatar
    Homework Helper

    What do you mean by proof-based? Why is it bad? What do you mean by youngsters? Do you mean all youngsters? Some? Many? Most?

    People of all ages benefit from understanding what they are doing and why.
    Rote learning is not the best way.
  6. Jun 2, 2014 #5


    User Avatar
    Homework Helper

    I mean, preteens and young teenagers have short attention spans, they need short lessons with some kind of "cash value", something to hold the interest. They want to see a number line, not a successor axiom.

    And if you read the introduction to his Precalculus book, it reads very similar to the linear algebra one, that this is real math, if you're not spending an hour per page, you're going to fast, question and probe everything told to you, yadda yadda. I mean it's just not suitable for young first-time learners in general.
  7. Jun 2, 2014 #6
    I guess I should have posted a bit about myself. I am an adult student going back to finish my undergraduate degree that I put off as I worked in the IT field for many years (almost 20 years). I took calculus 1-3 before, and did very well, found it intuitive and not that hard to be honest, but I forgot most of it, and not only that, but the algebra and trig that are so important to understadning it. So this summer my plan is to review all the "pre" calculus mathematics on my own before I start school in the fall and take calculus 20+ years later. Things will come back, but I've got to work at it too. So I've been looking for a good, succinct, book that I can use to go and review all the things I've forgotten. And the Axler books I mentioned seem right on the money for me. I don't want a 1000+ page book with pretty pictures, 100 exercises, etc. I'm fine reading text like Axler's - in fact I prefer it. The math books I used 20+ years ago were less heavy and (I feel) better written, though I could have gotten lucky at the university I went to. Needless to say I didn't keep any! :(

    Anyway, I've looked again the the "Table of Contents" for both books I linked, and they seem to really be exactly the same. The order of topics is a bit different, as I was saying, and really minor stuff is shuffled around, but either will accomplish the same thing I feel. I'm probably just nitpicking. If you go to the links and look at the table of contents for both you'll see they are indeed the same. Same rigor, etc. I'm not sure why a "Precalculus" book is even needed when you have an "Algebra & Trigonometry", as that IS precalculus...I think "precalculus" is somewhat a confusing subject, and maybe because high schools in the US break down algebra I II, geometry, and trig too much. Anyway I digress...

    Another book I looked at is this:


    Lang's book linked above seems to be a good little gem, but not sure if it's enough on its own. Ideally I would just use one book. Axler or Lang. Any opinions?
    Last edited by a moderator: May 6, 2017
  8. Jun 2, 2014 #7
    Lang covers everything you need in order to succesfully study calculus and higher math. It doesn't cover more or less. So it most definitely is enough on its own.
  9. Jun 2, 2014 #8
    I looked and the only thing I saw maybe lacking a tad was the trig section, but I could be wrong just going on the table of contents from Amazon's "Look Inside".

    I forgot to mention that another gem seems to be this:

    Last edited by a moderator: May 6, 2017
  10. Jun 3, 2014 #9


    User Avatar
    Homework Helper

    It sounds like you know what you want. Of the Axler books you mentioned, I'd choose the precalculus one; it's probably the one he wrote first and will have a nicely abstract approach.
  11. Jun 5, 2014 #10
    While it may be true that I may know what I want, that doesn't make it easier to navigate dozens of books to find a good one. This has proven to be more taxing than I expected. I'm actually surprised at how bad most books have become, content watered down, 1000 examples, etc. Axler's books seem refreshing, but perhaps there are even better ones. Like Lang's "Basic Mathematics". So I'm curious and looking for opinions. While 1-2 books are good, too many (for me at least) leads to confusion, strange overlap, etc.

    In the process I'm also looking for a decent Calculus book to review from. There again seem to be the 1000+ page ones with dozens of examples, not enough theory, etc. Then there are ones that are on the other end - theory and not meant for review. The best I've seen so far, and please chime in, in terms of striking a good balance in terms of theory and application is George Simmons' "Calculus with Analytic Geometry" 2nd ed.


    MIT uses it, but I haven't seen much talk about it. A lot of talk about Apostol (Caltech uses it) and Spivak on this forum, but they seem a bit on the theory end for review. Thoughts?
    Last edited by a moderator: May 6, 2017
  12. Jun 5, 2014 #11
    Simmons is an excellent writer. I like all his books. Unfortunately, I have never had the chance of reading his calculus book. But I have no doubt it's very good.

    If you're not much into theory, then Spivak and Apostol are not good choice. I think Simmons will be best for you.
  13. Jun 5, 2014 #12
    I very much like theory, but wonder if Apostol or Spivak are the best choices when going back to review Calculus. When I took it, I found it easy and got top grades, but that was a while ago. I need something to kick me back into things. One thing I do know from experience, is that starting with the wrong book can be OK for a little while. You may do well and get top grades in Calc I-III, Linear Algebra, Diff Eq, etc. But if you are coming from a more "computational approach - i.e. engineering math courses", you will have trouble when later taking more advanced math courses which are more theoretical in nature. So for me, even now, the best way to start is with more words, less pictures, more imagination, more proof-based, etc. But there has to be a balance, and I'm not sure how balanced Apotol or Spivak are.
  14. Jun 5, 2014 #13
    Apostol really has a good balance. It's more theoretical than other books, but it's also practical. If you're already familiar with some calculus (perhaps long long ago), and if you're not adverse to theory, then try Apostol.

    Spivak would probably have too much theory for now.
  15. Jun 6, 2014 #14
    OK, maybe I should start a new thread as this is diverging into Calculus books, as I got the original topic out of the way. But I'll try it here first and hope people chime in :)

    I've looked at the 2 schools I need to choose between for attending starting this fall, and what books they use for their calculus curriculum.

    School 1 uses Thomas' "Calculus Early Transcendentals (12th Edition)":


    School 2 uses "Stewart's Calculus: Concepts and Contexts (4th Edition)":


    These seem similar to me from browsing them on Amazon's site, but don't know enough details about either.

    So the question is, which additional calculus book would best supplement either the Thomas or Stewart books? I'd like to supplement to better be prepared for the later courses, which will be more theoretical and harder. I'm not sure a smooth transition from either the Thomas or Stewart book will be easy without another book to supplement.

    So given all this, maybe it's easier now to recommend either the Apostol, Simmons, or Spivak books? Which combo would work best?

    Thomas/Stewart + Apostol
    Thomas/Stewart + Simmons
    Thomas/Stewart + Spivak
    Last edited by a moderator: May 6, 2017
  16. Jun 6, 2014 #15


    User Avatar
    Homework Helper

    So what book did you choose for algebra/precalculus? And how long do you think it'll take to work through it? Because I assume you want to get through that before starting calculus. Also that could influence your decision on which calculus book to buy.
  17. Jun 6, 2014 #16
    I chose Axler's "Precalculus 2nd Edition". It will take me 2 months at most to get through it now that I have it and have looked through it.
  18. Jun 6, 2014 #17
    Thomas/Stewart + Apostol and Thomas/Stewart + Simmons would be overkill, I'd go with Thomas/Stewart + Spivak

    By the way, I love these beautiful books, you should check it out :

    Analysis by Its History by Ernst Hairer and Gerhard Wanner
    Geometry by Its History by Alexander Ostermann and Gerhard Wanner
  19. Jun 6, 2014 #18


    User Avatar
    Homework Helper

    Ok, that is what I was waiting to see. [strike]This should set you in good stead for Apostol. If you like Axler, that is my recommendation. Otherwise, come back wiser later and you'll be better equipped to choose a book to follow it with.[/strike]

    Wow, $90 for Apostol volume 1, $240 new, who are they trying to kid? I'll follow this with a new post with some recommendations.
    Last edited: Jun 6, 2014
  20. Jun 6, 2014 #19


    User Avatar
    Homework Helper

    Last edited by a moderator: May 6, 2017
  21. Jun 7, 2014 #20

    I haven't looked at Lang's Calc stuff yet, but it seems the recommendation was because Apostol's price was too high? How do you think they compare in content and presentation, price aside. It seems Apostol was your first choice, but curious about more of an insight in addition to the recommendation.

    To your previous post, yes I do like the Axler book, and find it easy to work with, and things coming back quickly. It might have been 20 years ago I took these things, but I guess my brain cells are still there for the most part :) So I think calculus will come back quickly as well.

    I don't intend to use Apostol, Lang, Simmons, or Spivak for review over the summer (I may if I have time), but to simply complement the Stewart or Thompson texts, as I feel they are too computational and will not prepare me best for later courses as I was saying. I have a personal example of this if I may deviate for a minute here. When I was a physics student back in the day (at Cornell), I took mostly the math department variants of Calc I-III, Linear Algebra, etc. But one semester I needed to double up and had to take 2 of the math courses in the engineering department. Similar things, but more applied instead of theoretical. I did very well, As, etc. But the following semester, when taking a Mathematical Physics course which used 2 texts and special notes (one text was this one - https://www.amazon.com/Mathematical-Physics-Eugene-Butkov/dp/0201007274), for the first time in my life with math, I had a bit of a struggle at first. It wasn't that the material was harder, but that I wasn't able to just read the books anymore. And I think some of that had to do with having taken the engineering maths courses instead of the pure math courses the semester prior. I felt I came in inadequately prepared, had to work more at it, and it was very challenging. I ended up doing well, but yeah, I still think (and this is why I'm asking here) that a more theoretical approach initially, even in beginner courses, will prepare one better for later, more advanced texts. Thoughts?

    I'm also curious, how DO people here feel about Stewart/Thompson? Same as me? I wanted to get some discussion going more in depth, besides the welcome recommendations too.
    Last edited by a moderator: May 6, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Sheldon Axler's Algebra Date
Algebra Sheldon Axler's Algebra and Trig/Precalculus for proofs? Feb 22, 2016
Linear Algebra Serge Lang's Linear Algebra Mar 6, 2015
Linear Algebra Axler vs Shilov? Nov 9, 2014
Linear Algebra Linear Algebra Done Right by Axler Jan 24, 2013
Algebra and Trigonometry by Sheldon Axler Apr 27, 2012