Unit 5: Important Topics to Cover
1. Natural Numbers & Induction
Introduction to Natural Numbers
Peano’s Axioms (Basic Properties of Natural Numbers)
Mathematical Induction (Basic Principle & Steps)
Strong Induction (Definition & Application)
Induction with Nonzero Base Cases (Handling Different Starting Points)
2. Recurrence Relations & Generating Functions
Introduction to Recurrence Relations
Generating Functions (Definition & Properties)
Simple Recurrence Relations with Constant Coefficients
Linear Recurrence Relations Without Constant Coefficients
Methods of Solving Recurrence Relations (Substitution, Characteristic Equation, Iteration)
3. Combinatorics
Introduction to Combinatorics
Basic Counting Techniques (Permutation, Combination)
Pigeonhole Principle (Definition & Examples)
Polya’s Counting Theorem (Introduction & Application in Counting Problems)
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