Lecturer: Roger Tribe

Term(s): Term 2

Status for Mathematics students:

Commitment: 10 x 3 hour lectures + 9 x 1 hour support classes

Assessment: Assessed homework sheets (15%) and Summer exam (85%)

Formal registration prerequisites: None

Assumed knowledge: Basic probability theory: random variables, law of large numbers, Chebycheff inequality, distribution functions, expectation and variance, Bernoulli distribution, normal distribution, Poisson distribution, exponential distribution, de Moivre Laplace theorem e.g. ST111 Probability A & ST112 Probability B.

Some basic skills in analysis: MA258 Mathematical Analysis III or MA259 Multivariate Calculus or ST208 Mathematical Methods or MA244 Analysis III. The module works in Euclidean vector space ${R}^n $ , so norm, basic inequalities, scalar product, linear mappings and matrix algebra (eigenvalues, eigenvectors, singular values etc) are relevant.

Useful background: Know what a a probability measure/distribution is. Earlier probability modules will be of some use but not necessary. The framework is some mild probability theory (e.g. ST202 Stochastic Processes). Know what the Central Limit Theorem is (de Moirvre Laplace for general random variables).

Synergies: In general the module is a mathematical basis for machine learning, data science and random matrix theory. The following modules provide some synergies and connections:

• MA359 Measure Theory
• MA3K1 Maths of Machine Learning
• MA3H2 Markov Processes and Percolation Theory

There are also strong links and thus suitable combinations to the following modules:

• MA4K4 Topics in Interacting Particle Systems
• MA4F7 Brownian Motion
• MA482 Stochastic Analysis
• MA427 Ergodic Theory
• MA424 Dynamical Systems
• MA4L2 Statistical Mechanics
• MA4L3 Large Deviation Theory

Leads to: The following modules have this module listed as assumed knowledge or useful background:

• MA3K1 Mathematics of Machine Learning

Additional Resources