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Intro Math Self-study book list

  1. Dec 10, 2015 #1
    Hi, I'm embarking on a mission to self-study math, and would like some recommendations on any missing books or ones that should be replaced in my repertoire.

    The goal is to build a strong mathematical foundation. My naive idea of what that means is something like an undergraduate math major, so I have googled a bit to get an idea of the relevant areas, and searched amazon for the best books on those topics, this is what I have so far:

    Savov - No Bull**** Guide to Math and Physics
    Velleman - How to Prove it
    Spivak - Calculus
    Axler - Linear Algebra Done Right
    Mendelson - Introduction to Topology
    Kleene - Mathematical Logic
    Graham - Concrete Mathematics
    Ghorpade - Course in Multivariable Calculus and Analysis
    Rudin - Principles of Mathematical Analysis
    Pinter - Abstract Algebra
    Farlow - PDE for Scientists and Engineers

    My long-LONG term goal is a PhD in CS, specifically AI. So please advice me! Keep in mind that I'm really starting from basics here, as I'm currently only 7/10 through Khan Academy and nothing more.
    Last edited: Dec 10, 2015
  2. jcsd
  3. Dec 10, 2015 #2
    Most students arrive at college with weak algebra and trig skills.

    Don't waste your time with those books before you have completed the ALEKS pre-calculus course (online) to make sure you are ready.
  4. Dec 10, 2015 #3
    My idea was to master the World of Math mission on Khan Academy [0] before starting books. That program includes pre/calculus, so if I can complete it, that would indicate that I'm ready to start some of those books, don't you agree?

    [0] https://www.khanacademy.org/math
  5. Dec 10, 2015 #4
    I'm not entirely sure it would, to be honest. Khan academy doesn't have enough practice questions, and the ones it does have aren't very challenging.

    Plus, I don't believe video lectures replace learning straight out of a textbook at all. You're not always going to have Khan to hold your hand throughout difficult concepts. Especially if Michael Spivak is going to be your first exposure to calculus.
  6. Dec 10, 2015 #5
    I also think you need a lot of practice and validated assessments of learning. ALEKS has that.

    A lot of math departments have validated and confirmed that ALEKS pre-calc ensures readiness for calculus.
  7. Dec 10, 2015 #6
    What do you mean by not enough practice questions? As in variety, or difficulty? Because KA keeps generating new questions forever until the student gets it right enough times.

    And in my plan Spivak would not be the first exposure, I was thinking KA -> Savov No BS Guide -> Velleman Proofs -> Spivak.

    But please tell me bluntly if this is a bad idea, because I'm here to find advice for the best learning path!
  8. Dec 11, 2015 #7
    Hello, I'm currently working myself through Spivak, and that was after I've worked through most of "Book of Proof"; even then Spivak proved to be exceedingly tough. It is really a whole other ball game compared to anything you may have learnt in school. I'm not sure about the "No BS Guide" since I've never heard of it, but I strongly suggest you follow Dr Courtney's advice, you need to be very good at Algebra and Trig, I learnt that the hard way by trying to overcome rigorous Math without said skills. If you would like a book instead of using ALEKS you could try Mathematics: The Core Course for A-level
  9. Dec 11, 2015 #8
    Thanks, I will take your advice under consideration, and add the book to my list of potential study material.

    I think the "No BS Guide" seems good since it supposedly takes the reader from high school math to calculus, and everyone on amazon is singing high praise in the reviews, so if they are honest reviews then it seems like a good book to start with.
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