An introductory course designed to teach the fundamental concepts and techniques of mathematical proofs.
Mathematicians use a variety of techniques to create proofs, each suited for different situations.
Break the problem into a finite number of cases and prove each one separately.
Actually build or demonstrate an example to show something exists.
Show that a statement is false by finding just one example where it fails.
Prove statements about all natural numbers by showing it's true for the first case, then that if it's true for one number, it's true for the next.
Picking the right technique can turn a tricky proof into a simple one!
These techniques are like different tools in your math toolbox. Practice helps you know which to use, and when.
Using casework to prove that any integer is either even or odd.
Using induction to prove that the sum of the first \( n \) odd numbers is \( n^2 \).
Different proof techniques are used for different types of problems.