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

Fremen

Computer science is pretty huge these days, so it depends what you're interested in. I work in a machine learning/AI research group - if I was going to pick subjects that would be most useful to me, I'd think about

Numerical analysis/ Advanced numerical analysis
Financial Mathematics
Mathematical Modelling in Biology and Medicine
Linear and Dynamic Programming
Linear algebra
Analysis

though I'm not sure what "methods of applied mathematics" involves.

Computer science has gone through a big shift over the last 20 years or so. Big chunks of it rely heavily on probability theory, so I've thrown financial maths in there for some exposure to it.

I guess 'Analysis' is Rudin-style hardcore real analysis. It won't bring any immediate benefit, but if you go into research it could pay off. Knowing a bit of measure theory can be pretty handy if you end up studying probability.

Of course, these are just the courses that would be most useful to *me*. Someone who ends up doing compiler design might want a completely different list of topics (though I suspect not). The number theory course might be useful if you ended up working in cryptography, say.

Edit: can't stress how important linear algebra is for me. I'd take that above anything else.

Metro10

Thanks very much Fremen.

In case anyone's interested in the module descriptions of the "Methods of Applied Mathematics", "Numerical Analysis", and "Advanced Numerical Analysis" modules which you mentioned, I've shown them below.

Fremen wrote: »

though I'm not sure what "methods of applied mathematics" involves.

Description of Methods of Applied Mathematics

PART A

Linear algebra:
matrix algebra; Gaussian elimination; LU-factorization; matrix inversion; vector spaces; solution of m equations in n unknowns; linear independence, null spaces, row and column spaces; inner products of vectors; fundamental theorem of linear algebra; projections and the least-squares approximation; determinants; complex matrices; eigenvalues and eigenvectors; matrix diagonalisation, positive definite matrices.

PART B

Complex functions:
algebra; analytic functions; Cauchy-Riemann equations; Cauchy's theorem; infinite series; Taylor's theorem; Laurent expansions; theory of residues; evaluation of integrals using the residue theorem.

Ordinary differential equations:
series solution; Bessel functions and other special functions.

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.

Fremen wrote: »

Edit: can't stress how important linear algebra is for me. I'd take that above anything else.

Thanks very much for that. Yes, that does seem to be quite a fundamental module.

Fremen

I'd think about dumping analysis for methods of applied maths then. That's a solid course.

Metro10

Fremen wrote: »

I'd think about dumping analysis for methods of applied maths then. That's a solid course.

Thanks again Fremen.