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Pure Mathematics study - question

  1. Apr 28, 2015 #1
    I am planning to study the following pure mathematics areas (on my own) and wanted to know if this is the best sequence:

    1- Formal Logic
    2 -Philosophical Logic
    3- Sentential Logic
    4- Predicate Logic
    5- Symbolic Logic

    6 -Set Theory

    7 -Pure Mathematics (Intro, Pure Math I and II and Hardy) - not sure if this belongs here? Should I begin here?

    8 -Abstract Algebra


    I do not want to study applied / discrete mathematics. My background is computer science.
     
  2. jcsd
  3. Apr 29, 2015 #2

    Svein

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    You could do it that way - if you want to end up hopelessly confused. If you want to study mathematical logic, Predicate logic is easiest and closest to computer science. The next level is first-order logic, but I do not recommend that until after a season or two of Pure Mathematics Intro. I would also defer set theory and abstract algebra until after that intro.
     
  4. Apr 29, 2015 #3

    micromass

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    I would suggest:

    1) Introduction to proofs, for example using the book of proof: http://www.people.vcu.edu/~rhammack/BookOfProof/

    2) Abstract Algebra, for example using Pinter: https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178

    3) Introduction to foundational mathematics, for example using Stillwell: https://www.amazon.com/Real-Numbers-Introduction-Undergraduate-Mathematics/dp/3319015761

    Then you can go on to study mathematical logic and axiomatic set theory.

    Please do no hesitate to contact me with further questions or guidance!
     
  5. Apr 29, 2015 #4
    For a soft but good introduction to set theory, I would suggest Halmos' "Naive Set Theory". Google it, and you have the choice between a free but poor pdf copy or a respectable paid copy; but a lot of libraries have it.
     
  6. Apr 29, 2015 #5

    mathman

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    When I was getting my math education, I was never exposed to your steps 1-5. Mine started (after calculus, etc.) with 6 (set theory).
     
  7. May 2, 2015 #6
    Thanks to all...

    Why is Set Theory a topic to wait on after studying Pure Math? I am an IT Data Architect where relational theory is based on set theory. The theory of relational databases is built upon the mathematical theory of sets.
     
  8. May 3, 2015 #7

    micromass

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    OK, you didn't specify that you wanted to obtain a background in set theory in order to understand relational databases. From your post, I gathered that you were interested in mathematical logic and axiomatic set theory.
    First of all, I want to say that when I studied relational databases, I never found my knowledge of set theory very useful, but maybe I didn't go very deep into it. I think it would be good for you to go through a basic proof book such as Velleman: https://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995 That should be enough background for everything to do with relational databases.
     
    Last edited by a moderator: May 7, 2017
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