Imperial College London

In this course, students use advanced mathematical methods to establish convexity in complex problems. In addition, students specify necessary and sufficient conditions for optimality, classify optimization algorithms as first or second order, determine appropriate optimization algorithms for given problems given the size and structure of the optimization models, and apply sensitivity analysis to optimization problems using Lagrange multipliers.

This course builds upon the knowledge and understanding gained by the students in the Separation Processes 1 course. This is  achieved by both broadening the content to encompass a wider range of separation processes and deepening the student’s understanding of the processes covered in Separation Processes 1. This is primarily achieved by building upon knowledge of distillation and extraction processes and design, introducing more complex variables and via the introduction of new separation processes such as adsorption. 

This course provides a comprehensive overview of the key contemporary issues in global economics and the leading models deployed by global economics institutions such as the WTO, United Nations, IMF and World Bank, as well as by global companies.

This course develops intellectual and practical skills in the use of modal logics for knowledge representation and automated reasoning in Artificial Intelligence. The first part of the course focuses on general modal logic: modal and temporal operators, Kripke frames and models, and the basics of the model theory of modal logics, including the notions of satisfaction and validity, their computational complexity, as well as invariance under bisimulation. The second part of the module introduces the language of Alternating-time Temporal Logic (ATL), an extension of the temporal logics CTL and LTL, which allows for the expression of game-theoretical notions such as the existence of a winning strategy for a group of agents.

This course explores the advanced mathematical techniques required to understand, design, and implement modern statistical machine learning algorithms and inference mechanisms.

In this course, students learn to explain the behavior and properties of fluids (static and dynamic), solve problems involving incompressible flows, and apply these basic principles in flow measurements and other flow (e.g. pipe) related problems, and (ii) to develop a basic understanding of conductive, diffusion and convective heat and mass transport, emphasizing first principles analysis, and apply it to a broad range of contexts.

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.