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

[ilii]

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~!

 

[cpsinkule]

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.

 

[ilii]

Okay, so maybe a book on logic to start?

 

[cpsinkule]

if you want a primer on mathematical methods of proof i recommend
https://www.amazon.com/dp/0321797094/?tag=pfamazon01-20

or

https://www.amazon.com/dp/0321390539/?tag=pfamazon01-20

 

[ilii]

Ok I have a much better idea now, thank you

 

[mgkii]

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)

 

[aikismos]

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.