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When do you begin to prove? which maths lead to proofs?

  1. Jul 23, 2015 #1
    Hi,

    Could someone please tell me at which point in learning maths do you begin to write and solve proofs? I have taken high school maths so far except for discrete math.

    If there is a list of different maths that lead up to proof writing, please let me know of them and in which order I should take them.

    Thank you~!
     
  2. jcsd
  3. Jul 23, 2015 #2
    The first proof based courses you will encounter are abstract algebra, linear algebra, analysis. Some colleges offer a primer course on mathematical proof and logic.
     
  4. Jul 23, 2015 #3
    Okay, so maybe a book on logic to start?
     
  5. Jul 23, 2015 #4
  6. Jul 23, 2015 #5
    Ok I have a much better idea now, thank you
     
  7. Jul 23, 2015 #6
    Hi @ilii

    Don't fall into the trap of thinking that proofs have to be some formal maths that you have to spend years working up to. Here's a couple of proofs that the greeks knew back in the day - and a fabulous video proof of the area of a circle that doesn't even need words!

    Proof that square root of 2 is irrational (can't be represented by a fraction - i.e. a ratio of whole numbers)
    http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php

    Ancient Greek's not only know the world was a Sphere... they worked at a very accurate estimate of it's circumference
    https://en.wikipedia.org/wiki/Eratosthenes

    Proof that the area of a circle is Pi x r2


    And one more... how to prove there's an infinite number of something (in this case, prime numbers)
     
  8. Jul 23, 2015 #7
    Actually, proof usually starts in the beginning of high school with a simplified Euclidean geometry course. For instance, in the US, it's typical to write two-column proofs for theorems about 2-dimensional objects such as parallelograms or circles. Often, proofs are included in textbooks for algebra and trigonometry. Proofs of trigonometric identities are a common exercise sophomore or junior year; ultimately, however, more sophisticated proofs occur in a pre-calculus and calculus courses, for instance, proof by induction for finite or infinite series. I just found a simple but effective algebraic proof of the Pythagorean theorem that could have been taught to my students in a second-year algebra course. It's these proof techniques that lay the basis of understanding for more sophisticated undergraduate work.
     
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