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In this course, you will :
- How should we conduct inductive proofs and when should we employ them?
- Prove (by induction) the validity of several formulas for natural numbers.
- Prove (by induction) some statements concerning natural number divisibility.
- Prove (by induction) explicit formulas for recursively specified sequences.
- Prove some simple inequalities for natural numbers (by induction).
- Also, learn about more complex examples of inductive proofs.
- Be given a brief explanation of how to utilise the symbols Sigma and Pi to calculate sums and products.
Syllabus :
1. What is mathematical induction and how it works
- What kinds of statements can be proven by induction
- Induction: this is how it works
- Both cases are necessary
2. Examples of proofs by induction
- Proving formulas, Problem 1
- Sequences: guess and prove, Problem 2
- Sequences: guess and prove, Problem 3 with two base cases
- Proving divisibility, Problem 4
- Not necessarily for all natural numbers: an inequality, Problem 5
- A difficult proof, Problem 6
- Another difficult proof, Problem 7
- Proofs by induction, Wrap-up
