Mathematical Proof

This module of Maths Extension 2 continues to explore and develop the concept of mathematical proof. In this module you will learn how to formally communicate statements related to proofs, fundamental logical concepts and more complicated proofs based on techniques including mathmatical induction and contradiction.

The Nature of Proof

In this section you will learn the formal language of proofs. You will also learn how you can apply these concepts in your proofs to utilise a technique called proof by contradiction, and prove results that involve inequalities

Propositions in a Formal Mathematical Proof
Implications in a Formal Mathematical Proof
Equivalence in a Formal Mathematical Proof
Qualifiers in a Formal Mathematical Proof
Formal Language in Mathematical Proof
Proving Mathematical Propositions Directly
Proving Mathematical Propositions By Contradiction
The Fundamental Theorem of Arithmetic
Proofs Involving Inequalities
The Arithemtic Mean - Geometric Mean Inequality

Further Proof by Mathematical Induction

In this section we explore some more complicated applications of mathematical induction and how this can be applied to prove results in other branches of mathematics.

Sigma notation for series
Sigma notation in inductive proofs
Applications of mathematical induction
Non-standard mathematical induction problems
Advanced induction proofs

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