- To provide students with sufficient mathematical knowledge to enable them to understand the foundations of their subject for both study purposes and later career development.
- To bridge the gap in style and content between A-level and university mathematics and to introduce students to the language and methods of professional mathematics.
By the end of the module the students should be able to:
- Understand and use basic mathematical terminology.
- Understand the role of formal definitions and proofs and be able to apply them in problem solving.
- Understand the basics of propositional and predicate logic.
- Understand the basics of elementary set theory.
- Understand the basics of mathematical relations and functions.
- Understand the basics of graph theory.
- Understand the basics of probability.
- The axiomatic method: Basic concepts, axioms, definitions, theorems, finite and infinte sets, natural numbers, induction.
- Logic: Statements, truth values, Boolean operators, laws of propositional logic, predicates, quantifiers, laws of predicate logic.
- Sets: Connection between sets and predicates, operations on sets, laws of set operations.
- Relations: Relation composition and inverse, properties of relations, equivalence relations, equivalence classes, quotient sets, partial orders.
- Functions: Properties of functions, equinumerous sets, countable and uncountable sets.
- Graphs: Graph isomorphism, graph connectivity, Eulerian and Hamiltonian graphs.
- Probability: Definitions, conditional probability, Bayes' theorem, expectation, variance, standard deviation.