MA138 (Warwick) University of Warwick

Sets and Numbers

Sets, functions, number systems, proof techniques and an introduction to groups.

1. Sets, subsets and power sets

   MA138 Sets, subsets and power sets, sheet A: questions (PDF) worked answers and mark scheme (PDF)

2. Functions: injective, surjective, bijective, composition

   MA138 Functions: injective, surjective, bijective, composition, sheet A: questions (PDF) worked answers and mark scheme (PDF)

3. Cardinality, Cantor and Cantor–Schröder–Bernstein

   MA138 Cardinality, Cantor and Cantor–Schröder–Bernstein, sheet A: questions (PDF) worked answers and mark scheme (PDF)

4. Ordered pairs, cartesian products, lists and strings

   MA138 Ordered pairs, cartesian products, lists and strings, sheet A: questions (PDF) worked answers and mark scheme (PDF)

5. Union, intersection, difference and the boolean algebra of sets

   MA138 Union, intersection, difference and the boolean algebra of sets, sheet A: questions (PDF) worked answers and mark scheme (PDF)

6. Equivalence relations and orders

   MA138 Equivalence relations and orders, sheet A: questions (PDF) worked answers and mark scheme (PDF)

7. Partitions, equivalence classes and the integers

   MA138 Partitions, equivalence classes and the integers, sheet A: questions (PDF) worked answers and mark scheme (PDF)

8. Modular arithmetic and linear congruences

   MA138 Modular arithmetic and linear congruences, sheet A: questions (PDF) worked answers and mark scheme (PDF)

9. Logic: booleans, truth tables and quantifiers

   MA138 Logic: booleans, truth tables and quantifiers, sheet A: questions (PDF) worked answers and mark scheme (PDF)

10. Proof techniques

    MA138 Proof techniques, sheet A: questions (PDF) worked answers and mark scheme (PDF)

11. Induction, recursion and the pigeonhole principle

    MA138 Induction, recursion and the pigeonhole principle, sheet A: questions (PDF) worked answers and mark scheme (PDF)

12. GCDs, the euclidean algorithm and Bézout's lemma

    MA138 GCDs, the euclidean algorithm and Bézout's lemma, sheet A: questions (PDF) worked answers and mark scheme (PDF)

13. Groups: definitions, dihedral groups, subgroups and generators

    MA138 Groups: definitions, dihedral groups, subgroups and generators, sheet A: questions (PDF) worked answers and mark scheme (PDF)

14. Permutations: Sym(n), cycle notation and parity

    MA138 Permutations: Sym(n), cycle notation and parity, sheet A: questions (PDF) worked answers and mark scheme (PDF)

15. Homomorphisms, isomorphisms, cosets and quotients

    MA138 Homomorphisms, isomorphisms, cosets and quotients, sheet A: questions (PDF) worked answers and mark scheme (PDF)

16. Group actions, fields and linear congruences

    MA138 Group actions, fields and linear congruences, sheet A: questions (PDF) worked answers and mark scheme (PDF)