Aims and Objectives
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Basic counting techniques and their applications to common data structures
- Logical systems and the concept of formal proof
- The language of set theory and common operations on sets, including infinite sets
- Elementary concepts of linear algebra
- The interplay of syntax and semantics in mathematics, logic and computer science
- Functions and relations as fundamental structures in computer science
- Elementary ideas of probability theory and statistics
- Principles of mathematical proof and sound logical reasoning
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Recognise, understand and construct rigorous mathematical proofs
- Use statistical analysis, including sampling, hypothesis testing and regression
- Critically analyse and solve counting problems on finite, discrete structures
- Calculate probabilities of events and recognise probability distributions
- Apply operations on vectors and matrices and solve systems of linear equations
- Use the language of logic and set theory in order to make precise formal statements
- Proof by case analysis, proof by contradiction.
- Induction and recursion.
- Universal properties.
Sets, functions and relations
- Basic notation, representations and examples. Membership and subsets.
- Operations on sets: union, sum, intersection and complement.
- Pairs, tuples, cartesian products, powersets.
- Relations, equivalence relations and partial orders.
- Functions: injections, surjections, bijections.
- Cardinality, infinite sets.
- Propositional logic. Logical connectives.
- Syntax and semantics.
- Natural deduction, soundness and completeness.
- Quantifiers and predicate logic.
- Basic principles of counting: product and sum rules, inclusion-exclusion principle, pigeonhole principle.
- Combinations, permutations and arrangements, binomial theorem.
Introduction to trees and graphs: directed, undirected and weighted.
- Probability and statistics
- Introduction to probability: elementary probability formulae, discrete and continuous probability distributions.
- Introduction to statistics: sampling, confidence intervals, hypothesis testing, regression.
- Linear and quadratic equations, systems of equations.
- Polynomials: basic properties and operations.
- Vectors: basic properties, scalar product, vector product.
- Matrix algebra: basic properties, inverse, determinant, Eigenvalues, Eigenvectors,
- Solving systems of linear equations.
Learning and Teaching
Teaching and learning methods
|Preparation for scheduled sessions||18|
|Wider reading or practice||43|
|Completion of assessment task||13|
|Total study time||162|
Resources & Reading list
compiled by Pawel Sobocinski. Foundations of Computer Science. Custom Pearson Textbook.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Repeat type: Internal & External