Imperial College London

This course teaches students to evaluate geometric machine learning as a tool to model common learning frameworks. Students design optimizers on Riemannian manifolds to implement smooth constrained optimization; synthesize discrete operators on graphs from their continuous versions; and modify learning models to operate on constrained domains and outcomes. As part of the course, students implement deep learning on unstructured domains such as graphs, point sets, and meshes, as well as mechanisms to yield structured output from learning models.

This course extends the statistical ideas introduced in the first year to more complex settings. Mathematically, the central concept is the linear model, a framework for statistical modelling that accommodates multiple predictor variables, continuous and categorial, in a unified way. There is a focus on fitting models to real data from a variety of problem domains, using R to perform computations. 

Students apply knowledge of core chemical engineering to the design and evaluation of solutions for industrially relevant problems in an authentic context.  The course enables students to confidently undertake open-ended research in later courses. Students also explore business ethics on 3 levels (the Corporate, the social, and the theoretical) in order to develop an understanding of the moral structure of competing obligations and responsibilities inherent in various situations and issues.

This course explores the classical theory of games involving concepts of dominance, best response, and equilibria, where it proves Nash’s Theorem on the existence of equilibria in games. Students learn the concept of when a game is termed zero-sum and prove the related Von Neumann’s Minimax Theorem. The course explores cooperation in games and investigates the interesting Nash bargaining solution which arises from reasonable bargaining axioms. Students also explore the concept of a congestion game, often applied to situations involving traffic flow, where they see the counterintuitive Braess paradox emerge and prove Nash’s theorem in another context. 

In this course, students develop the skills required to identify hazards, to estimate the magnitude of the consequences (typically fires, explosions and toxic releases) and the probability of such an event occurring. Additionally, a fundamental approach for the systematic assessment and reduction of risk is established. Such an approach is essential to minimize harm, the resulting loss of money and reputation, and to meet national regulatory requirements.

The course provides an overview of data center technologies, the infrastructure needed to run a variety of workloads, and the design decisions when engineering scalable distributed applications. Students analyze the full system stack for managing and scheduling data-center resources. Further, they discuss the design principles for scalable systems; investigate concepts and techniques to build large scale systems, with a focus on distributed storage, coordination, computation and resource allocation. They get an overview of NewSQL and NoSQL technologies, learn new data models, their associated query languages and systems, and discuss new storage technology and its impact on query execution and data management systems in general.

In this course, students use probability theory to model uncertainty; design simple probabilistic models that facilitate prediction; conduct sound scientific analysis of data, and study the mathematical foundations of probabilistic modelling with Markov chains and simulation.

This course focuses on mobile robotics, emphasizing practical algorithms for navigation, all based around real hardware and tested in the real world. Key elements are: wheeled locomotion, motor control, and motion calibration; outward-looking sensors for behavioral control loops; probabilistic localization using particle filtering; advanced use of sensors for place recognition, occupancy mapping and planning; and an introduction to Simultaneous Localization and Mapping. The course is intensively practical, and all the key methods students learn are tested on robots they build.

This course teaches students to use MATLAB for data processing, visualization, simulation, and analysis; apply probability models, estimate their parameters and test their fit to data; apply reliability theory to devices and networks; and perform predictive modelling tasks using regression and time series analysis.