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Should I take Number Theory or Abstract Algebra

  1. May 30, 2014 #1
    Which course do you think is more important or interesting to take for someone interested in theoretical computer science or theoretical mathematics, number theory or abstract algebra?

    I am mainly interested acquiring skills and knowledge that will enable me to prove something significant in the area of complexity theory, computability theory, or abstract math.
  2. jcsd
  3. May 30, 2014 #2
    Abstract Algebra
  4. May 31, 2014 #3
    Number theory is interesting, but abstract algebra is fundamental.
  5. May 31, 2014 #4
    Abstract Algebra (for me at least) allowed me to peer inside a mathematical universe that I didn't know existed. Additionally, the language of abstract algebra is used to build other branches of modern mathematics that you might want to study in the future. I would recommend it over number theory (admittedly I have no experience with number theory so my opinion is biased).
    Last edited: May 31, 2014
  6. May 31, 2014 #5


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    Abstract algebra is sometimes even a prerequisite for number theory. So as someone who has become interested taking classes on these topics myself, I agree that you should at least take abstract algebra first.
  7. May 31, 2014 #6
    Abstract algebra is fundamental. Number theory is more of an aside. Of course, for someone wanting to do theoretical computer science, why not take both? It will certainly be to your benefit. Maybe even throw in some set theory and graph theory while you're at it.
  8. May 31, 2014 #7

    Vanadium 50

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    There are, however, elements of number theory that are often used in computing. Much of modern cryptography, for example.
  9. May 31, 2014 #8

    D H

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    I recently read an interesting article on the huge differences between the theory of numerical computing and theory of computation. You'll never see mention of Turing machines in the former, IEEE floating point (or for that matter, anything on the reals) in the latter. I've looked, but I can't find it.

    Regarding the topic at hand, number theory is a rather esoteric field with limited applications. Abstract algebra is ubiquitous in its applications (including number theory).

    However, some people are strongly attracted to the esoteric. If that's what grabs you, tAllan, then maybe you'll do better there. (But it's hard to argue that abstract algebra itself isn't esoteric.)
  10. Jun 1, 2014 #9


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    To the OP:

    I would definitely recommend taking abstract algebra first (and number theory later if you can fit it in your schedule), given its relevance of much of modern mathematical research, as well as its applicability in various cognate fields such as theoretical physics, statistics, and theoretical computer science (particularly in complexity theory and the theory of computation).
  11. Jun 1, 2014 #10
    I think I will learn both, probably mostly through self study. I may have to choose between number theory and abstract math this next quarter because I have some CS courses I really need to take. Thank you all for your advice.

    If any of you have any advice for me in finding a topic, in either abstract math or theoretical computer science, with promising research potential, that would appreciated.
  12. Jun 3, 2014 #11
    Hi tAllan :) I don't know much about them but I want to learn abstract algebra and number theory too. I had algebra in my college for a semestre. And I study number theory with my own , sometimes.(and I quit :) ). Anyway, if you start to study one of those to write an article, just notice me. That may be efficient for both of us, see you.
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