Mathematical Proof and Reasoning

What is mathematical proof?

Statements and truth values

Conditional statements

Converse, inverse, contrapositive

Biconditional statements

Logical connectives: and, or, not

Truth tables

Valid arguments

Invalid arguments and fallacies

Direct proof structure

Writing direct proofs

Proof by contrapositive

Proof by contradiction

Proof by cases

Mathematical induction: concept

Mathematical induction: examples

Counterexamples

Existence and uniqueness proofs

Proof in geometry

Proof in algebra

Proof in number theory

Set theory basics

Set operations and proofs

Functions: injective, surjective, bijective

Proof writing: style and clarity

Reading and evaluating proofs

Famous proofs and theorems

Unsolved problems in mathematics

The nature of mathematical truth

Unit assessment