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Best way to acquire Proof/Logic skills

  1. Mar 10, 2015 #1
    Dear P.F. friends,

    What is the best way to learn and sharpen the proof methodologies and logic in mathematics, reading the proof books or attempting the proof problems in analysis texts without the proof basics?
     
  2. jcsd
  3. Mar 10, 2015 #2
    I would do both, look over the steps and tips for proofs and then do problems. Focus on the problems a lot more; they are much more important to refining your sense of logic. Work through problems, check them, find what went wrong, identify what in your process of thinking went wrong, and try to fix it in the next problem. Rinse and repeat until you're confident in your abilities, then do 3-5 more. If you get them correct, then you're all good for that particular methodology or area or whatever.
     
  4. Mar 10, 2015 #3
    Learn common proof techniques. I believe you'll find similar proofs crop up a lot in analysis.
     
  5. Mar 10, 2015 #4
    Start with a text or course on discrete math. Counting, proof by induction, predicate calculus, proof by contradiction, set theory, etc. It sharpens your proof muscles a lot.
     
  6. Mar 11, 2015 #5
    I second the recommendation to look at discrete math, but I'd also add that it would be very helpful to think logically and rigorously in general.

    My own introduction to logic came from learning Latin in high school. Studying rhetoric or argument in general would be just as good a place to start as learning math. I would say that it might even be better since solving math problems is more about thinking and seeing problems logically than about a specific set of techniques.
     
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