- #1

john Snow

- 1

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below is what is going to be covered

**Set Theory/Logic.**

Sets, relations, equivalence relations and partitions, partial ordering, inverse relations, composition of relations, applications of relations to databases, predicate logic as a language, methods of proof, mathematical induction. Boolean algebra, equivalent boolean expressions..

**Probability.**

Basic probability to iclude axioms, independent events, conditional probability and some probabilty distributions..

**Functions.**

Functions as a special case of relations, Injective, surjective and bijective functions, one-sided inverses, inverse functions, polynomials and the remainder theorem. Domain and range of functions. Inequalities..

**Limits & Continuity.**

Simple finite and infinite limits. Simple tests to establish if piecewise-defined functions are continuous..

**Calculus.**

Techniques of differentiation (first principles, product, quotient and chain rules) and integration (substitution and integration-by-parts). Curve sketching, optimisation and area under the curve applications..