I'm going to be doing a Bachelor of Science (Computer Science) combined with a Bachelor of Art (Mathematics).
I'd like to work in the games industry and since I love maths I thought 3D graphics looked interesting. Anyway I was wondering what maths units would be most useful for 3D graphics. The list is below.
Also how do 3D graphics programmers score in job security, salary, et cetera (especially in comparison to other jobs in game design)?
I'll start with third year (by then I will have covered ODE's, linear algebra, and stuff):
MATH3101 - Bifurcation and Chaos
Modelling with nonlinear systems of ODE's. Stability and bifurcation theory including the Hopf bifurcation and limit cycles. Homoclinic & heteroclinic orbits and Mel'nikov theory. Stability, bifurcation theory and chaos in I-dimensional Maps. Period doubling. Feigenbaum's approach to chaos. Properties of chaos. The Lorenz Equations.
MATH3102 - Methods & Models of Applied Mathematics
Elements of vector analysis. Sturm-Liouville theory. Fourier transform & Green's functions. Generalised functions. Modelling with scalar & vector fields: perfect fluid flow & potential theory; convection-diffusion equations & spread of pollutants; elastic continua and vibrations.
MATH3202 - Operations Research & Mathematical Planning
Applications of optimisation in operations research. Linear programming & non-linear programming. Use of optimisation packages.
MATH 3203 - Visualisation & Modelling in Scientific Computing
Visualisation as a key tool for the synthesis and analysis of biological, physical and engineering models. The use of the graphical interfaces of MATLAB and other visualisation packages such as OpenDX. Aspects of high performance computing. A brief introduction to parallel computing.
MATH3301 - Graph Theory & Geometry
Topics from graph theory & relevant algorithms. Planarity. Factorisation of graphs. Graphs with interesting automorphism groups. Euclidean, projective & other geometries.
MATH3302 - Coding & Cryptography
Error correction & detection. Hamming, BCH, Reed-Solomon & cyclic codes. Cryptographic methods for encryption, decryption & authentication. DES, IDEA, RSA. Applications: CD players, EFTPOS, etc.
MATH3303 - Abstract Algebra & Number Theory
Important facets of modern algebra & number theory, with emphasis on computational algorithms.
MATH3306 - Set Theory & Mathematical Logic
The course will introduce students to aspects of set theory and formal logic. It will include topics in Set Theory: the Zermelo-Fraenkel Axioms, Axiom of Choice, Transfinite arithmetic, Zorn's Lemma, Ordinal numbers, Cardinal numbers and an introduction to model theory; topics in Propositional & predicate calculus: semantics, soundness & completeness of formal languages, recursive functions & computability, Godel's incompleteness theorems.
MATH3404 - Optimisation Theory
Calculus of variations: critical points; Euler equations; transversality; corner conditions; Hamilton equations; Jacobi equations; Legendre sufficient condition; Weierstrass E-function. Control theory: Lagrange, Mayer & Bolza problems; Pontryagin maximal principle, legendre transformations, augmented Hamiltonians, transversality, bang-bang control, linear systems.
MATH4202 - Advanced Techniques in Numerical Linear Algebra
State of the art techniques in the application of numerical linear algebra in advanced scientific computation.
MATH4205 - Advances in Scientific Visualisation and Graphics
This course discusses advanced concepts in the area of data visualisation and computer graphics. Topics include multi-variate and multi-dimensional datasets, rendering algorithms, animation, haptics, sonification, immersive environments. The course strives to provide a snapshot on the current state of the art in visualisation and will be supported by recent research papers with real-world applications, spanning the physical sciences, engineering and computer science. Students will develop a topic of their choice by completing an individual project.
I guess that one is obviously going to be useful.
MATH4301 - Advanced Algebra
Topics from groups, rings, fields, algebraic number theory, category theory & homological algebra, with applications to quantum algebras.
MATH4302 - Combinatorial Designs
Selected topics from design theory, Latin squares, finite geometrics.
MATH4303 - Advanced Combinatorics
Topics from computational combinatorics & algorithms, cryptography, advanced graph theory.
MATH4405 - Measure Theory
Lebesgue integral & measure. Monotone convergence. Fatour & Lebesgue dominated convergence theorems. Modes of convergence. Bounded variation. Absolute continuity. Signed measures. Generation of measures. Radon-Nikodym & Riesz representation theorems.
MATH4406 - Control Theory
Topics from: state space control; linear systems; calculus of variations & Pontryagin principle; optimal control, quadratic optimisation, Riccati equations; stability; LQG, Kalman filtering; frequency domain theory; Matrix transfer functions, realisations; coprime factorisation; robust control.
If I've skipped something basic like the analyses, differential equations, number theory, it's because I'll be taking them regardless.
Thanks!