Mathematical Methods

Lecturer : Jeremy Bradley (homepage)
For course notes click on the lecturers homepages.

Learning Outcomes

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


Methods Syllabus

[Vector algebra (3)] for Computer Graphics, Computational Techniques

Motivated by: Computer Graphics (3D vector manipulation)
+ vector notation
+ vector addition, multiplication, dot and cross products
+ vector equations and intersections of lines/planes
+ vector spaces and linear in/dependence

[Matrices/Linear algebra (3)] for Computer Graphics,
Performance Modelling, Digital Libraries, Computational Techniques

Motivated by: Computer Graphics (3D transformations) and
PageRank algorithm (eigenvector/eigenvalue)
+ matrix notation
+ three dimensional transformations (rotation, scaling, skewing)
+ matrix addition, multiplication, determinant, inverse
+ linear in/dependence
+ solution of linear equations by Gaussian elimination
+ eigenvectors, eigenvalues, characteristic equation

[Calculus (2)] for Computational Techniques (Computational Finance,
Operations Research)

Motivated by: Computer Graphics (differential algorithms) and
Optimisation (maxima/minima over surfaces)
+ review of differentiation
+ differentiation as limit of gradient
+ fundamental theorem of calculus
+ stationary points
+ partial derivatives and the chain rule
+ recurrence relations and solution

[Analysis (5)] 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 and the Hessian
+ finite precision arithmetic and effect on computations
+ introduction to fixed point problems

[Complex Numbers (1)] for Computer Graphics,
Computer Vision, Performance Modelling

+ complex numbers and argand diagram
+ Curra+ibCurr, Currcis \thetaCurr, Currr\exp(-i\theta)Curr notations