Course Practice

Classwork Questions

Homeworks

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Course Notes

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Proof by Induction and Summations

1) Introduction to Induction

2) Proof by Induction Examples

3) Sigma Notation

4) Summation Formulae

5) Method of Differences

6) Strong Induction

7) Further Induction Examples

8) Additional Notes on the Binomial Theorem

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Introductory Number Theory

NIM

1) Division with Remainder

2) The Fundamental Theorem of Arithmetic

3) Modular Arithmetic

4) Fermat's Little Theorem

5) The Euclidean Algorithm

6) Public Key Cryptography

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Graph Theory

1) Graphs; definitions and Isomorphisms

2) Eulerian Graphs

3) Planar Graphs and Euler's Formula

4) Platonic Duals

5) Platonic Solids

6) Kuratowski's Theorem

7) Graph Colourings

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Group Theory

1) Symmetries and Permutations

2) A closer look at Permutations

3) Introducing Groups

4) Groups and Cayley Tables

5) Groups of Order 4

6) Group Isomorphisms