Mathematics 1

Module aims

By the end of the course, students will be confident with mathematical notation and concepts concerning linear algebra and calculus. Students will understand important concepts of linear systems,  linear independence, real convergence, power series representation and transform representation.

Learning outcomes

Learning Outcomes - Knowledge and Understanding

To know the specific material covered in the Syllabus, including the ability to do the following:

- Check for convergence of sequences and series

- Convergence proofs 

- Limit values

- Solving linear equation systems

- Diagonalization of matrices

- Basic understanding of linear mappings (homomorphisms, isomorphisms etc.)

- Basis change

- Affine mappings

- Projections and rotations

Module syllabus

Sequences, Series and Power Series (8) for numerical algorithms, scientific programming, Functional Programming

+ convergence of sequences and series (arithmetic, geometric, harmonic)
+ comparison test/absolute convergence
+ power series/radii of convergence
+ Taylor's theorem
+ finite precision arithmetic and effect on computations

Linear algebra (12) for Computer Graphics, Optimization, Simulation and Modelling, Coding theory, Machine Learning, Robotics

Motivated by: Computer Graphics (3D transformations) and
PageRank algorithm (eigenvector/eigenvalue)

+ Groups
+ Linear equation systems
+ Gaussian elimination
+ Linear independence
+ Linear mappings
+ Affine Mappings
+ Vector spaces
+ Determinants
+ Eigenvalues, diagonalization
+ Intersections of (affine) subspaces (planes, lines, ....)
+ Scalar products, orthogonality
+ Projections
+ Rotations

Pre-requisites

School maths

Teaching methods

 Lectures and tutorials.

Reading list

Module leaders

Professor Abbas Edalat
Professor Michael Huth