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Reasonable approach to learning mathematics? (Starting with logic.)

  1. Jun 8, 2006 #1
    Good evening,

    I'd like some advice on my approach to learning mathematics (e.g. is this reasonable).

    Right now I'm interested in computing. I understand basic algorithms such as how quick, heap, merge, insertion and bubble sort work. But that is the extent--I'd love to learn more about algorithms, computability and complexity topics.

    My immediate interests are centered around learning Mathematical Logic for the Prolog programming language (which, from what I understand, is based on first-order predicate calculus). I'd like to work on some *very* minimal AI systems and other things that build directly on top of Mathematical Logic.

    In 2-3 years time, I plan to pursue my interests in science. At that time I will focus on other areas such as calculus, algebra, differential equations, differential geometry, topology... (this is according to the curriculum for the programme I wish to enter).

    Recalling that some great mathematicians attempted to axiomize the logic and suggest that everything comes from the foundations--mathematical logic and set theory--I wondered if it would be wise to start off with logic? Would it benefit me for my later studies (re: science). More importantly, would it make me much stronger with the math?

    About me:
    I have a background in programming. Not computer science. I have minimal exposure to algorithms and my bachelors program did not contain any math offerings. My math abilities end at the high school level.

    So I would like to know whether or not it is a good idea to dabble with logic, algorithms, (and time permitting) computability and complexity theory and then to later (~2-3 years) try my hand at the other topics listed.

    Is this a "sound" approach, or should I be doing it another way? I really have no concept of how difficult these topics are, so please enlighten me :biggrin:

    Best regards and thanks for your thoughts.

    P.S. How deep does the rabbit hole go with regard to the topic of Mathematical Logic?

    (Can anyone recommend David Hilbert's Principles of Mathematical Logic ? I've managed to read the first 6 pages (of ~170) on Amazon and they are quite accessible--would it get very difficult after that? The TOC reads: I. The Sentential Calculus, II. The Calculus of Classes (Monadic Predicate Calculus), III. The Restricted Predicate Calculus, IV. The Extended Predicate Calculus.)
  2. jcsd
  3. Jun 23, 2006 #2


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    mathematical logic is probably of no help in learning math at all, although basic understanding of principles of reasoning is essential.

    for math about all the logic you need is when syllogisms are true, when false, what it means to combine statements by "and", "or", "implies", and what applying "not" does.

    e.g. it is not true that A implies B, if and only if A is true and B is false.

    It is not true that "A and B", if and only if one or both of A,B is false. That kind of trivial thing. Math is mostly about imagination, analogy, generalization, specialization, ability to visualize, and computing power, not formal logic at all.

    But some people are very good at math and very interested in logic too. in fact people who liked logic tend to be among the smarter people i have known, and they were all very good at math.
  4. Jun 23, 2006 #3
    Thanks, Mathwonk.

    Even though it may be of no direct benefit to my later studies, I think I should enjoy this for my programming pursuits (re: prolog).

    I'm just not confident on whether or not I am 'capable' of learning logic from Hilbert's book. The first six pages are quite accessible but whether or not it builds on other mathematical knowledge and expects the reader to be experienced... I do not know! :frown:
  5. Jun 26, 2006 #4


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    from my limited experience, whenever you try hard to read a master like hilbert, you always get something from it. even if you only make it through a few pages, you find out later that you understand more than other people who have studied writings of lesser mortals.

    i remmber one day in grad school i went to the librarry to read zariski's paper on non singular points. it took me three hours or so to get through a page or two. i felt discouraged. but when i returned to class, i knew the answer to every question the lecturer posed, until he told me to stop answering as it was "obvious i knew the subject well".
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