Department of Computing
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> # 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

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