University of London External Programme Graduate Diploma in Mathematics

[chestnut.cc]

I'll be applying this forthcoming cycle for MA, MSc, MPhil eco... I'm an economics undergraduate at a leading institution in India with statistics and math minors... the thing is both these minors have a more applied focus... covering multivariate calculus, linear algebra, linear optimization, a bit of game theory in the math part... real analysis is something im planning on working through by attending bsc math classes... but i wont get any formal transcript for any of those classes... so i was wondering if i ought to register for the graduate diploma in mathematics... Here are some of the course details:

Abstract Mathematics:

Topics covered are: Logic, integers, sets and functions, prime numbers, relations,
real and complex numbers, greatest common divisor and modular arithmetic,
EMFSS unit information – 116 Abstract mathematics
2 University of London External Programme
infimum and supremum, sequences, limits of sequences, functions and limits of
functions, continuity, groups.

Advanced Linear Algebra:

Topics covered are: Vector spaces, linear independence, basis, dimension, linear
transformations, similarity, eigenvalues and eigenvectors, diagonalization, systems
of difference and differential equations, powers of matrices, Markov chains, inner
products, orthogonality, quadratic forms, orthogonal diagonalization, complex
matrices, direct sums and projections, least squares, spectral theory.

Advanced Calculus:

Topics included are: Functions of several variables, linear approximations and
tangent planes, directional derivatives and the gradient, Edgeworth box and
contract curves, concave and convex functions, inverse functions, local inverses
and critical points, the Riemann integral, multiple integration, improper integrals,
manipulation of integrals, introduction to the Laplace transform.

Game Theory:

Topics covered are:
Combinatorial games and Nim.
Game trees with perfect information, backward induction.
Extensive and strategic (normal) form of a game.
EMFSS unit information – 40 Game Theory
Nash equilibrium.
Commitment.
Mixed strategies and Nash equilibria in mixed strategies.
Finding mixed-strategy equilibria for two-person games.
Zero sum games, maxmin strategies.
Extensive games with information sets, behaviour strategies, perfect recall.
The Nash bargaining solution.
Multistage bargaining.

Optimization Theory:

Introduction and review of relevant parts from real analysis, with emphasis on
higher dimensions.
Weierstrass' Theorem on continuous functions on compact set.
Review with added rigour of unconstrained optimisation of differentiable
functions.
Lagrange’s Theorem on equality constrained optimisation.
EMFSS unit information – 42 Optimisation theory
2 University of London External Programme
The Kuhn-Tucker Theorem on inequality constrained optimisation.
Finite and infinite horizon dynamic programming.

Advanced Statistics 2:

Syllabus
Data reduction; Sufficiency, minimal sufficiency. Likelihood.
Point estimation; Bias, consistency, mean square error. Central limit theorem. Rao-
Blackwell theorem. Minimum variance unbiased estimates, Cramer-Rao bound.
Properties of maximum likelihood estimates.
Interval estimation; Pivotal quantities. Size and coverage probability.
Hypothesis testing; Likelihood ratio test. Most powerful tests. Neyman-Pearson
lemma.

Queries:

1. How feasible is this for someone with a background of Multivariate Calc and Linear Algebra? In short, is this biting of more than you can chew?

2. Would it be simply better to wait and check out MA, MSc, MPhilcourse structures to see how to squeeze in the relevant courses in the future?

[asianeconomist]

If you're looking towards MPhil courses in Oxbridge, then you'll not be able to fit in any math courses in your curriculum as they tend to have a pretty rigid structure. The MSc @ LSE is more flexible in this regard.

Also, although it's not very relevant at this point, I have heard from other Indian applicants that Cambridge doesn't take UGrads straight to their MPhil. Rather, they are required to first complete the diploma.

[chestnut.cc]

Yes that seems to be true... they say so on their site... also they seem to emphasize only metrics and there are no other maths courses... hence i was looking to find a way to squeeze in more math... now if i rem you mentioned learning most of the stuff on your own... which is what i think i will do... along with attending bsc math classes... but i would like some sort of transcript for that if poss... hence the query... so in that regard... how feasible is doing all of the above or even part of it in a single year?

[filroz]

Originally Posted by asianeconomist

The MSc @ LSE is more flexible in this regard.

It is not. You have 3 core subjects and 1 option, all are econ not math subjects (see here).