Module overview
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- The language of set theory and common operations on sets, including infinite sets
- The interplay of syntax and semantics in mathematics, logic and computer science
- Elementary ideas of probability theory and statistics
- Logical systems and the concept of formal proof
- Principles of mathematical proof and sound logical reasoning
- Functions and relations as fundamental structures in computer science
- Elementary concepts of linear algebra
- Basic counting techniques and their applications to common data structures
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Use the language of logic and set theory in order to make precise formal statements
- Critically analyse and solve counting problems on finite, discrete structures
- Use statistical analysis, including sampling, hypothesis testing and regression
- Recognise, understand and construct rigorous mathematical proofs
- Apply operations on vectors and matrices and solve systems of linear equations
- Calculate probabilities of events and recognise probability distributions
Syllabus
Mathematical proof
- 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.
Logic
- Propositional logic. Logical connectives.
- Syntax and semantics.
- Natural deduction, soundness and completeness.
- Quantifiers and predicate logic.
Combinatorics
- 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.
Algebra
- 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
Type | Hours |
---|---|
Preparation for scheduled sessions | 18 |
Follow-up work | 18 |
Lecture | 36 |
Tutorial | 24 |
Wider reading or practice | 43 |
Revision | 10 |
Completion of assessment task | 13 |
Total study time | 162 |
Resources & Reading list
Textbooks
compiled by Pawel Sobocinski. Foundations of Computer Science. Custom Pearson Textbook.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Final Assessment | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Examination | 100% |
Repeat
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.
Method | Percentage contribution |
---|---|
Examination | 100% |
Repeat Information
Repeat type: Internal & External