Module overview
This module provides students with some fundamental mathematical concepts relevant to applications in AI and CE. The focus will be on applying mathematical proofs to solve computer science problems as well as introducing basic concepts and techniques in linear algebra and calculus. In addition to theoretical treatments, there will be laboratory applications using Python and Jupyter to visualize, manipulate and explore mathematics.
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Apply general rules of derivatives and integrals to solve differentiation and integration problems
- Apply operations on vectors and matrices and solve systems of linear equations
- Recognise, understand and construct rigorous mathematical proofs
- Use the language of logic and set theory in order to make precise formal statements
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Use matrices of numeric data to solve problems derived from example data
- Use symbolic methods to solve systems of equations derived from real problems
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Principles of mathematical proof and sound logical reasoning
- The interplay of syntax and semantics in mathematics, logic and computer science
- Functions and relations as fundamental structures in computer science
- The language of set theory and common operations on sets, including infinite sets
- Elementary concepts of linear algebra, pre-calculus and introductory calculus
Syllabus
Logic
- Propositional logic
- Predicate logic
- Natural deduction
- Mathematical proof
- Induction and recursion
Sets, functions and relations
- Basic set notation and operations
- Tuples, Cartesian Products, Power set
- Relations, equivalence relations and partial orders
- Functions: injections, surjections, bijections
- Cardinality, infinite sets
Single-variable calculus
- Elementary functions: linear, quadratic, polynomials
- Limit
- Differentiation
- Integration
Algebra
- Vector algebra
- Matrix algebra
- Systems of linear equations
- Eigenvectors and eigenvalues
Learning and Teaching
Teaching and learning methods
The module consists of:
- Lectures
- Tutorials
- Guided self-study
- Labs as part of the AICE Lab Programme which will cover practical aspects
Type | Hours |
---|---|
Lecture | 32 |
Independent Study | 108 |
Specialist Laboratory | 10 |
Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Lab work | 5% |
Exam | 60% |
Coursework | 35% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Lab Marks carried forward | 5% |
Exam | 95% |
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 |
---|---|
Exam | 95% |
Lab Marks carried forward | 5% |
Repeat Information
Repeat type: Internal & External