Undergraduate Mathematics/The Meaning and Methods of Proof
|Undergraduate Mathematics/The Group Theory of the Symmetries of Simple Shapes|
In this first module, we look into the core of everything that follows: proof. Mathematics is an attempt to discover truth considered from the perspective of logic and without proof we will get nowhere.
The distinction between proof and verification by experiment is that proven ideas are precisely as reliable as the assumptions you make and the logical vadility of the proof.
We will look at a few different methods of verifying the truth of an idea that will become very familiar to anyone that uses mathematics in the sense of a mathematician. Engineers, physicists and other scientists may use our theorems and corollaries without needing to understand the proofs but that is precisely because we do.