Module Description

The aim of this module is to cover fundamental mathematics for Computer Scientists. It does not assume A-level mathematics, and the emphasis and delivery will be on understanding the key concepts as they apply to Computer Science.

Additional support is provided by the Talent Development Centre. Participants not having AS or A level mathematics should take a diagnostic test to see whether they would benefit from this extra support.

Learning Outcomes

After completing this module, students will be expected to be able to:

1. Apply propositional logic to simple problems
2. Use counting methods including permutations and combinations
3. Apply the basic notions of sets, and illustrate answers through Venn diagrams
4. Use methods of probability on simple problems
5. Solve problems in linear algebra using vectors and matrices

Outline Syllabus

Propositional Logic:
Propositions and logical operators. Truth tables. De Morgan's laws. Algebraic rules and inference. Logical identities, Tautologies and Contraditions

Fundamental Principle of Counting. Ordered and unordered selections. Selections with and without replacement. Permutations and combinations. Counting methods.

Set notation and basic concepts. Definition of sets through propositions. Set intersection, union and complementation. Venn diagrams. Cardinality. Cartesian products. Sample spaces and events.

Experiments and outcomes. Sample space, events, relative frequency and probability. Mutual exclusivity and independence. Counting methods. Conditional probability. Mean and variance. The binomial distribution.

Vectors and Matrices:
Basic definitions. Addition and multiplication of matrices, multiplication by scalars. Inversion of 2x2 matrices. Applications. Transformations of the plane. Solving simultaneous equations in two unknowns.