Maths modules relevant to Comp Sci?

[Metro10]

If taking a Mathematics & Computer Science BSc, which of the following maths modules would be most relevant to Computer Science?

APPLIED MATHEMATICS
Methods of Applied Mathematics
Numerical Analysis
Classical Mechanics
Fluid Mechanics and Electromagnetism
Electromagnetic Theory
Quantum Theory
Advanced Numerical Analysis
Partial Differential Equations
Tensor Field Theory
Financial Mathematics
Calculus of Variations and Hamiltonian Mechanics
Mathematical Modelling in Biology and Medicine
Linear and Dynamic Programming


PURE MATHEMATICS
Complex Variables
Linear Algebra
Elementary Number Theory
Analysis
Group Theory
Geometry

 

[Jim2007]

Well given that this is a forum about money, I expect we all say Financial Maths

I'd suggest you ask the question on one of the computer tech. forums.

Jim.

 

[z107]

Computer science is pretty broad.
For software development for business, I would use these:
- Linear Algebra
- Financial Mathematics
- Numerical Analysis (Not 100% sure what this is)
- Linear and Dynamic Programming (Not sure what this is either, but it has 'programming' in the title.

It really depends on what you want to do. They all sound fun (well, apart from financial mathematics).

 

[Metro10]

Thanks umop3p!sdn.

Yes, the Linear Algebra module appears to be quite a fundamental module.

- Numerical Analysis (Not 100% sure what this is)
- Linear and Dynamic Programming (Not sure what this is either, but it has 'programming' in the title.

Just to clarify the content of the Numerical Analysis and Linear Dynamic Programming modules, I've listed their descriptions below.


Description of Linear & Dynamic Programming

Dynamic programming; stochastic problems; allocation, production-inventory and optimal route problems, including some non-dynamic programming algorithms. Linear programming: primal, dual and revised simplex methods, duality, post-optimal analysis, transportation and assignment problems, network flow problems.

Description of Numerical Analysis

Introduction: review of basic calculus; Taylor's theorem and truncation error; storage of non-integers; round-off error; absolute and relative errors; Richardson's extrapolation.

Equations in one variable: Bisection, False-position, Secant and Newton-Raphson methods; fixed point and one-point iteration; Aitken's delta-squared method; roots of polynomials.

Interpolation and polynomial approximation: Lagrangian interpolation; Neville's algorithm; other methods.

Approximation theory: norms; least-squares approximation; minimax approximation; linear least-squares; orthogonal polynomials; discrete least-squares.

Numerical differentiation and finite-difference methods: Formulae for first and second derivative; finite-difference operators and formulae.

Numerical quadrature: Newton-Cotes formulae; composite quadrature; Romberg integration; adaptive quadrature; Gaussian quadrature.

Initial-value ordinary differential equations: errors; Taylor-series methods; Runge-Kutta methods; predictor-corrector methods.

Solution of linear equations: Gauss elimination; pivoting; LU decomposition; norms; condition number; ill-conditioned linear equations; iterative refinement; iterative methods.

Computing practical and project: weekly practicals; word-processed project-report.

Description of Advanced Numerical Analysis

Approximation theory: norms, weighted least-squares approximation, polynomial minimax approximation, Chebyshev polynomials and Chebyshev expansions, rational Pade approximation, rational minimax approximation, piecewise polynomial approximation, Lagrange and Newton interpolation and splines.

Matrix eigenvalues/eigenvector analysis: vector and matrix norms, matrix algorithms, Givens' and Householder zeroising transformations, Power Method and inverse iteration, Jacobi method, Householder reduction to tridiagonal form, QR method.

Numerical integration: review of basic techniques, interpolatory quadrature, Gaussian quadrature, applications of orthogonal polynomials and the Christoffel-Darboux identity to Gaussian quadrature, errors, integration over infinite intervals.

Practials: three practical assigments, to implement in MATLAB Chebyshev series and the minimax approximation, the Pade approximation, and the Power Method.