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Plane Geometry and Logic

  1. Nov 13, 2011 #1

    After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane geometry. The subjects aren't related, I just wanted to combine them into one post :P

  2. jcsd
  3. Nov 14, 2011 #2
    Logic paired with analysis. What does that mean? Logic has very little to do with analysis. So I fear there won't be much books that combine the two topics.
    What kind of logic do you want anyway?? Do you want things like truth tables and stuff (basically what Velleman does)? Or do you want real mathematical logic?? If you want mathematical logic, then I highly recommend Ebbinghaus.

    What do you mean with "plane geometry"?? Do you want a high school text?? A university level text?? Here are some books you could try:

    - Euclid' Elements: The classic book on plane geometry. I'd still recommend it to people if they want to learn classic geometry. It won't get into analytical geometry like equations of lines.

    - Geometry by Serge Lang: this is high school geometry done on college level. It focuses on equations of lines and so on. Serge Lang is an excellent writer, so the book is highly recommended.

    - Introduction to geometry by Coxeter: if you know high school geometry well, then this is the book for you. It is basically a survey of all of mathematical geometry. It even introduces things like differential geometry and algebraic geometry.
  4. Nov 14, 2011 #3
    you're right, I was rather vague.

    I'm looking to steer away from the pure logic and move into mathematical logic. So Ebbinghaus?

    Perfect, thank you very much.
  5. Nov 15, 2011 #4
    "mathematical logic" is quite different from what you might expect ( it will be nothing like "how to prove it" ). For example, in mathematical logic, you will learn about the consequences of having a "theory" ( imagine I develop a theory describing physical phenomena, will I be able to derive contradictions? can I *really* describe everything that can possibly happen? ).
    Another thing that may be a consequence of having a theory, is that you may be able to generate all the theorems ( imagine with a computer ) possible ( plane geometry can do this ). Or, if you are given a statement, can you in general decide whether or not this statement follows from your theory? ( or, provide a method that will help you check ).

    Anyway, good mathematical logic texts I think ( for the general logic level) are: Ebbinghaus, Monk, Shoenfield and J.L. Bell.

    A good book that is less dry and is a lighter read is "A friendly introduction to mathematical logic" by Chris Leary.
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