Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Jul 23, 2015 #1

    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)

    Ancient Greek's not only know the world was a Sphere... they worked at a very accurate estimate of it's circumference

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: When do you begin to prove? which maths lead to proofs?
  1. How do you prove this (Replies: 6)

  2. How do you prove this? (Replies: 10)