Exeter College, Oxford University

This course introduces the key principles of mathematical modelling, which then are explored through several real-world examples in disease modelling, environmental planning, and population dynamics. The techniques of calculus are essential, although core concepts such as differential equations are revisited. Students also touch on the mathematical models used in data science, particularly the techniques of principal component analysis and clustering, both essential tools in machine learning models.  

Climate change exemplifies the sort of planetary challenge facing humankind in the 21st century. In this course, students explore how that kind of challenge can be understood as a scientific, political, social, and moral problem, to better understand our place in the world under conditions of multiple and interlocking crises. The course introduces the Anthropocene, as both a proposed geological phenomenon and a critical tool to rethink the relationship between humans and the planet. Pursuing this question require students to question some established distinctions—between human/animal, nature/culture, biology/society, life/nonlife, and Globe/Earth. Through anthropological materials, historical and contemporary accounts of life in the aftermath of industrial transformation, colonization and anthropogenic change, the course considers the types of knowledge, forms of collaboration, political engagement, and social practice that might help us better apprehend the fragility of the planet and articulate a shared responsibility to its future.  

The course is divided into two main sections. Following a brief historical introduction to the discipline, students explore classical concepts and theories of IR, including power and anarchy (realism), cooperation and human rights (liberalism), norms and identity (constructivism), followed by critical perspectives on global politics such as class and dependencies (Marxism), gender and the patriarchy (feminism), and exploitation and orientalism (postcolonialism). In the second section of the course, students investigate pressing global issues like terrorism, AI, and the climate crisis, which have fundamentally altered the conduct of international politics. Finally, the course concludes with a discussion of future (im)possibilities for global politics. 

The course provides the opportunity to engage with an issue that is of vital importance to the discipline of history as we know it, particularly at a time when regimes and practices of establishing and communicating truth based on evidence and objectivity are contested. Philosophers and anthropologists have argued that archives inherently select and organize their materials in ways that necessarily obscure fundamental elements of historical experience, with special reference to empire, colonialism, race, and slavery. The challenge that this radical critique poses to contemporary historians is carefully discussed. At the same time, special attention is given to the work of a growing number of historians, who have transformed the archive into a subject of historical research. 

This is an introduction to quantum computer science, intended primarily for computer scientists, physicists, electrical engineers, and mathematicians. It introduces a large number of ideas with an emphasis on building familiarity with the main concepts, and some general knowledge of terminology and methods. Mathematical methods are employed in a practical way, on a "need-to-know" basis. 

This course explores modern numerical algorithms through three connected tasks: large scale linear algebra, optimization for data science, and deep learning.  The first six lectures discuss how to approximately solve massive scale linear algebra tasks using techniques not covered in linear algebra courses. The second six lectures discuss optimization algorithms with a focus on large data science tasks. Numerical optimization is one of the most useful skills as so many tasks from science to business can be cast as optimization problems. The six seminars focus on deep learning, the key algorithmic advance driving the recent advances in machine learning and artificial intelligence. The lectures on numerical linear algebra and optimization ground this course in well understood numerical algorithms which students can study in detail, while the deep learning seminars give students the opportunity to explore the excitement driving the AI revolution. 

Students research a self-chosen topic and develop an extended research essay under the direct tutelage of an appointed mentor. Students engage in conversation with teachers who are experts in the subject being studied. These tutorials allow students to develop their own ideas under the direct supervision of a tutor.

This course introduces students to the mathematical theory of fluids via the Navier Stokes Equations. The equations can be used to successfully model almost any fluid on Earth, but our mathematical understanding of them remains limited. So much so, that a $1-million prize exists for anyone that can help to further our understanding of problems involving vortex reconnection, turbulence, and whether or not the equations are "well-posed." We will look at examples in inviscid flow theory which provide insight into physical phenomena such as flight, vortex motion, and water waves. Students also explore the basic fluid dynamics necessary to build mathematical models of the environment in which we live, focusing on problems such as climate change, pollution, or the spread of infectious aerosol droplets within our buildings.