Recommended books on set theory and lambda calculus?

Discussion in 'Mac Programming' started by Cromulent, Jan 27, 2010.

  1. Cromulent macrumors 603

    Cromulent

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    #1
    Can anyone recommend a book on each of these subjects please? I'm looking for introductory undergrad books with a computer science leaning if possible.

    I was thinking about the following book but the reviews scared me a little I have to be honest. Maths is not my strong point.

    An Introduction to Lambda Calculi for Computer Scientists
     
  2. chown33 macrumors 604

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    Aug 9, 2009
    #2
    What's your experience level on each of the subjects?

    "Introductory undergrad" isn't specific enough, because every undergrad has different levels of math and CS experience on entering a CS program.

    If you've never seen, used, or heard of lambda calculus before, then pretty much any book is going to be too difficult, even if it says "Introduction to" in its title. Same with set theory.

    Personally, I wouldn't even be trying to find a book until after I had read every Wikipedia article I could find on the subject, and was conversant with the basics of the subject, as well as the fundamentals behind those basics. Then I'd probably read the linked refs from Wikipedia, and google for more material by the referenced authors.

    http://en.wikipedia.org/wiki/Special:Search?search=lambda+calculus&fulltext=Search

    I have to say I'm puzzled by the fact that you're trying to find books on your own. Usually the textbook for a class is the preferred book, or you ask the instructor about other books, including prerequisites. Otherwise you have the student trying to do a comparative review of books on a subject they're wholely ignorant of.
     
  3. Cromulent thread starter macrumors 603

    Cromulent

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    #3
    Less than it should be. Having said that I do tend to learn better by jumping into things. I did it with programming so I don´t see why this should be any different.

    This isn´t for a course (I don´t even start my comp sci degree for another week or two and even then the maths side of things don´t come in for at least 6 months), I just want to improve my knowledge of these areas as a book I am trying to use makes heavy use of them.
     
  4. Denarius macrumors 6502a

    Denarius

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    #4
    I just checked Amazon and apparently Lambda Calculus for Dummies doesn't exist. :eek:

    To be frank I know nothing whatsoever about the subject, just wanted to wish you the best of luck with the course.
     
  5. autorelease macrumors regular

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    #5
    Learning lambda calculus isn't going to make you a better programmer. Unfortunately, since functional languages have yet to see widespread use, lambda calculus and type theory have little practicality/relevance in the software industry. Most systems/app developers, including myself, either a) only have a basic understanding of it, b) are completely confused by it, or c) have never heard of it.

    That being said, it's part of the foundation of "abstract" computer science. If you "get it," you'll find type theory, programming language theory, the Curry-Howard isomorphism, etc. very enlightening. (And you'll probably go to grad school!) If you don't, don't worry, no one will ask you about lambda calculus in a job interview.

    I'd post a link to the lecture notes from the type theory class I took, but they've disappeared from the professor's website.
     
  6. GorillaPaws macrumors 6502a

    GorillaPaws

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    #6
    Quote of the week for me!
     
  7. telecomm macrumors 65816

    telecomm

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    #7
    Do you have any experience in formal logic?

    This is essential if you're going to be able to understand first-order set theory or type theory.

    Two popular options are Symbolic Logic (which is in it's fifth edition, and now contains a chapter on set theory), or The Logic Book.

    I'd suggest trying to find one of these at a library and go from there.
     
  8. Cromulent thread starter macrumors 603

    Cromulent

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    #8
    My Dad has leant me the first edition ofthis book, which I will be working through. It seems pretty comprehensive dealing with propositional and predicate calculus as well as relations and grammars.

    I'm well aware that this is a big task but I have 3 years while I am doing my course so time is not exactly pressing.

    Thank you, I appreciate it.
     
  9. telecomm macrumors 65816

    telecomm

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    #9
    Once you're through with that book you'll be able to get started in set theory (which I'd suggest you have a look at before lambda calculus).

    Formal set theory is usually presented in a first-order (i.e., predicate) calculus with identity, and a single binary relation symbol (∈), so you can see why a background in formal logic will be useful. It's sort of like learning French before trying to understand French poetry.
     
  10. Martin Frické macrumors newbie

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    Feb 27, 2010
    #10
    Lambda and Predicate Calculus

    [Well, one's always hesitant to blow one's own trumpet.]

    But you might try looking at my website http://SoftOption.Us where there is any amount on predicate calculus and lambda calculus, recommendations of books etc.

    There are also a number of applets you can run (they are a little slow to load and Apple helps not at all with this). I am rewriting most of them in javascript so all that should improve shortly.

    Enjoy!

    Martin Frické
     
  11. benano macrumors newbie

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    Feb 27, 2010
    #11
    Structure and Interpretation of Computer Programs
     
  12. Cromulent thread starter macrumors 603

    Cromulent

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    #12
    Nice site, I'll certainly take a look at it.

    Thanks.
     
  13. Cromulent thread starter macrumors 603

    Cromulent

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    #13
    I had to put this on hold for a little bit but has anyone heard of the book "Elementary Set Theory with a Universal Set"? Any good?
     
  14. telecomm macrumors 65816

    telecomm

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    #14
    I'm not familiar with it, but it's probably worth mentioning that set theory with a universal set is non-standard. (You run into something called Russell's paradox if you were to introduce a universal set in standard, Zermelo-Fraenkel set theory.)
     

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