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Algebra Looking for a good College algebra book

  1. Aug 17, 2016 #1
    Ok so a bit of background about myself

    I finished
    1. Algebra 1 and 2
    2. Trigonometry (Basics)
    3. Basics of complex numbers
    4. The very basics of matrices (addition, subtraction, multiplication, identites, inverses only)
    5. Basic differential Calculus

    I wanna learn mathematics in this order
    1. College Algebra
    2. Everything in Brilliant.org under the name of algebra (not abstract or linear algebra tho)
    3. Introductory Abstract Algebra
    4. Introductory Linear Algebra
    5. Integral Calculus

    So right now i'm on the college algebra stage.
    I wanna learn all of these using FREE resources (textbooks, pdfs, videos, sites, flashes etc.. albiet I prefer books)

    I've searched the internet for good resources and here's what I have found:

    1. MA 109 College Algebra (2002)
    2. MA 109 College Algebra (2004)
    3. Udacity College Algebra Course
    4. Paul's[/PLAIN] [Broken] Online College Algebra Notes

    So um, those are only 4 resources, I've taken a fast look at each of them (first resource I actually solved some exercises and went on it) but that had gotten me very confused, why is the syllabus very very different from each course to course? and why there are some concepts repeated again?

    Those are couple of questions I have thought of.

    But the more important thing is, how should I study college algebra? I'm not asking as how do I study maths? I'm asking what resources should I study in what order to finish college algebra? Myself, I wanna learn as much as possible, if there are 1000 things under the name of college algebra in a book but only 800 things are really taught in college algebra (the other 200 are taught in more advanced classes) then I would like to learn the 1000 things, I wanna have a very very very thorough book, something like Thomas calculus 11th for calculus, If it's clear too, that's a bonus, but if it isn't thorough and clear, then no thanks.

    So those are all my thoughts, I know there are many questions there, but I'll summarize all of them here:

    1. How good are the 4 resources mentioned above? How thorough are they? How much percent do they cover of college algebra? Do they cover things in more advanced classes? How clear are they?
    Werll I could answer those questions myself, but given that I don't know a whole lot about college algebra, it will take me months to get familiar with college algebra then answer those questions, and after I get familiar with college algebra I won't need those books anyway so yeah.

    2. Which book (Could be mentioned in the resources above or not, but please If you suggest a book please do mention it's strengths and weaknesses) should I start with to learn college algebra, then after I finish it, which book should I read, then which book? until I finish college algebra
    Last edited by a moderator: May 8, 2017
  2. jcsd
  3. Aug 19, 2016 #2
    I always assumed college algebra to be a mixture of algebra 1/2 and trigonometry?

    Anyways, try Precalculus by Lial/Hornsby/Schneider. It is a 1200 page tome that covers everything that a student would need before calculus/linear algebra and then some. It's sections on trigonometry are particularly useful. It also has hundreds of exercises for each section. Shop around for a cheap copy on amazon maybe.
  4. Aug 19, 2016 #3
    For college algebra, I recommend following books:

    Serge Lang: Basic Mathematics
    Allendoerfer/Oakley: Fundamentals of Freshman Mathematics

    Both covers the pre-calculus, with A/O covers essential topics of calculus and some interesting topics like Boolean Algebra and probability theory. If you are interested in the basics of proof techniques, A/O will also teach you that.

    For abstract algebra, I recommend the combination of following:

    Pinter's Algebra + Hungerford's Abstract Algebra or MacLane/Birkhoff's Algebra.

    Pinter's book is an excellent introduction to the basics of abstract algebra and proof techniques. Although both Hungerford and M/B are graduate-level books, they are suitable for motivating undergraduates.
  5. Aug 19, 2016 #4


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    Have you seen any local source for CHEAP used books? A couple of good books, although maybe not complete for every possible College Algebra topic, are the College Algebra textbooks by Aufmann, Nation, & Barker; and the one by Larson & Edwards (or was it Larson & Hostetler?).

    College Algebra as a community college or university course is taught in one semester, but this is not always enough time to get good at it (for some students). Your feeling or guess that many months may be necessary if a valuable one. Go ahead and spend more than 4 months studying this on your own, more than twice, if you find it difficult and want to get better at it.

    College Algebra regardless of the course itself or combined with Trigonometry as the PreCalculus course, is definitely more advanced than "Algebra 2". For example, College Algebra reaches much deeper into polynomials and functions, and into rational functions than does Algebra 2. College Algebra may go more deeply in examining some details like end & limiting behavior of sequences and series.
  6. Aug 19, 2016 #5
    Thank you all for replying and for reading my long post, I want to clarify a couple of things

    1. First of all I don't need any precalculus stuff, I have mastered algebra 1, 2 and Trigonometry, really don't need precalculus
    2. Second, College Algebra isn't precalculus, it looks to me like a mix of number theory, abstract algebra and linear algebra, look at MA109 2002, that's what I think college algebra is, correct me if i'm wrong, but if that college algebra is precalculus, then prove to me that.

    3. Third, I can't, and I mean can't and I mean it's impossible, for me to get any paid stuff, even if it costs 0.1$


    First of all I don't live in USA, I live in Egypt, that is a third world country, I won't find any of the paid books you ask me to get that aren't available online in Egypt's libraries.

    Second I don't have a credit card.

    So I can only get stuff that is free and on the internet.

    Thanks again for replying
  7. Aug 19, 2016 #6


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    Excuse me/us.
    The meaning of named courses might be different according to region or culture. A way to know what is the content of a course is to read the course description and the course syllabus.
    According to how many of us have been taught and have learned, Precalculus or College Algebra is absolutely not abstract algebra and would usually NOT contain any abstract algebra. The course College Algebra certainly has been a mixture of topics but would always include polynomial functions, rational functions, functions of the domain of whole numbers (sequences and series), transcendental functions, inverses of functions, graphs of functions, AND AN INTRODUCTION TO LIMITS.

    post-add: College Algebra must also give a strong even if brief introduction to Binomial Theorem.
  8. Aug 19, 2016 #7
    Oh so THIS is college algebra, and MA109 2002 is just an advanced course.
    Well I'm conviced, thanks.

    I think this question is answered.
  9. Aug 19, 2016 #8


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    Most of the content of that book looks good but I see a few things lacking:
    Only one section on Sequences & Series
    Only one section on Exponential & Logarithmic functions
    No chapter on Rational Functions
  10. Aug 19, 2016 #9


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    Paul's Online Notes shows a mostly good listing of content also, but topics missing are Rational Functions and Sequences & Series.
  11. Aug 30, 2016 #10
    For College Algebra + Trig, has anyone read and worked through "College Algebra and Trigonometry with Applications" by Jose Barros-Neto? I'm liking it so far myself.
  12. Oct 9, 2016 #11
    A recent clear and solid book containing all the fundamentals of basic algebra is the text College Algebra by F.C. Paliogiannis
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