The seventh workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with a variety of questions: questions involving decimal expansions; modular arithmetic: squares and fourth powers modulo 5; finding an example of a function with specified properties.

These videos are also available for download on iTunes U at: itunes.apple.com/us/itunes-u/foundations-pure-mathematics/id950755120
Dr Feinstein's blog may be viewed at: explainingmaths.wordpress.com.
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

1. Introduction to Pure Mathematics
2. Sets and Numbers
3. Workshop 1: About this module
4. Definitions and Direct Proofs
5. Rational and Irrational Numbers
6. Workshop 2
7. More on Rational and Irrational Numbers
8. Bezout's Lemma and Prime Factorization
9. Workshop 3
10. Sets and Subsets
11. Cartesian Products and Relations
12. Workshop 4
13. Equivalence Relations and Equivalence Classes
14. Unions and Partitions
15. Workshop 5
16. Equivalence Classes and Modular Arithmetic
17. Decimal expansions and rational numbers
18. Workshop 6
19. Functions and their graphs
20. Functions and sets
21. Workshop 7
22. Properties of functions
23. Finite sets and cardinality
24. Workshop 8
25. Permutations of finite sets
26. Permutations continued
27. Workshop 9
28. Cardinality for infinite sets
29. Conclusion of Cardinality for infinite sets