Your instructors:
Simon Board (Econ) and
Yigal Newman (Finance)
We plan to have 26 lectures of 1.5 hours (8:30-10:00 and 10:30-12:00). The
first three days will be spent on basic mathematical concepts, while the
following two weeks will be split between economics and statistics. Below
is an outline of what we plan to discuss, so let one of us know if you
would like to make any changes in emphasis or content. After all, the
purpose of this course is to prepare you for the coming term.
Note: the number of classes is in brackets
Maths (6)
- Basic calculus and analysis (2)
- Rules of calculus. Sequences, convergence, topology in euclidean
space.
- Vectors and Matrices (1)
- Basic matrix operations, matrix inversion, special matrices, solutions
of systems of linear equations.
- Static Optimization (1)
- First and second order conditions, Lagrange multipliers.
- Differential Equations (1)
- Linear and nonlinear first order, linear second order.
- Useful Topics (1)
- Correspondences, fixed point theorems, envelope theorems, implicit
funciton theorem.
Economics (10)
- Consumer Theory (2)
- Axioms to utility functions. Source: Kreps and MWG.
- Utility functions to demand functions. Source: MWG.
- General Equilibrium (2)
- Setup, existence, welfare theorems. Source: MWG.
- Uniqueness, uncertainty, core. Source: MWG.
- Partial Equilibrium (1)
- Externalities, coase theorem. Source: MWG.
- Game Theory (5)
- A game, expected utility, dominance and nash. Source: Osborne and
Rubinstein.
- Subgame perfection and baysian nash equilbrium. Source: Osborne and Rubinstein.
- Industrial Organisation. Monopoly, oligopoly, product differentiation.
Source: Tirole.
- Knowledge functions, email game, common knowledge, no trade theorem.
Source: Osborne and Rubinstein.
- Asymmetric information. Market failure, signalling, revelation
principle. Source: MWG.
Statistics (10)
- Probability basics: Probability space, probability function, and
axioms of probability (1)
- Conditional probability and independence (1)
- Discrete random variables and vectors, distribution functions and
expectation of a random variable. Examples: Binomial, Poisson, geometric
(2)
- Continuous random variables, density functions. Examples: uniform,
Normal, exponential, gamma (2)
- Joint distributions and conditional distributions; variance,
covariance and correlation of random variables (1+)
- Transformations of random variables, moment generating functions and
conditional probability (1)
- Central limit theorems, the law of large numbers, stochastic
inequalities (Markov, Chebychev) (1)
- Some more math (time permitting): First order differential equations,
Markov chains
Back to Home or
the PhD Programme
Date: September 2001