University of Edinburgh

The syllabus first covers abstract vector spaces and linear transformations. It then introduces rings and modules, their quotients, and the first isomorphism theorem. The multilinear algebra of determinants is studied, together with eigenvectors and eigenvalues, culminating in the Cayley-Hamilton theorem and the Perron Frobenius Theorem. This is followed by an introduction to inner product spaces and the Spectral Theorem. The course then moves on to normal forms for linear transformations and particularly the Jordan Normal Form. Throughout the course, we will also work with a computer algebra system (e.g. Maple) to learn about programming skills and data structures which are useful in Pure Mathematics and beyond. In lab sessions, we will use these skills to investigate topics that are relevant to the theory being developed in lectures and workshops. Students will also carry out a group project which will require some computer algebra work and a short group presentation. Linear Algebra 1. Basic concepts in abstract linear algebra, abstract vector spaces, bases, linear maps, dimension, images and kernels. 2. Linear transformations, choice of basis, Smith normal form. Rings and Modules 1. Basic definitions and examples of rings, homomorphisms, kernels, images. 2. Polynomials, their Euclidean algorithm, roots and algebraically closed fields. 3. Basic definitions and examples of modules, homomorphisms, kernels, images. 4. Quotient rings, modules and vector spaces; the first isomorphism theorem. Determinants and Eigenvalues 1. Multilinear forms; characterizations of determinant. 2. Eigenvalues and eigenvectors; diagonalizable and triangularizable linear mappings; Cayley-Hamilton Theorem. 3. Perron-Frobenius Theorem and applications. Inner Product Spaces and Quadratic Forms 1. Basic definitions and examples of inner product spaces. 2. Orthogonal projection; Gram-Schmidt; 3. Adjoints of linear transformations; spectral theorem for finite dimensional inner product spaces. Jordan Normal Form 1. The Jordan Normal Form. 2. Applications of the Jordan Normal Form.

This course introduces students to the Persian language. The course teaches how to read and write the Persian script and introduces the main features of Persian grammar together with a basic vocabulary in an interactive communicative setting. It provides students with the key tools to understand, speak, read, and write elementary Persian. Translation exercises are given as homework and Persian poetry and prose readings are also regularly discussed and analyzed. Students are also exposed to Persian history and culture through sample readings, writings, discussions, and other cultural activities.

This course imparts basic information about the legal system of Scotland (within the framework of the United Kingdom), including the principal sources and divisions of the law, court structures, legal history, civil and criminal procedure, and the law and institutions of the European Union. Students develop basic legal skills and are encouraged to think critically about the law, legal institutions, and the process of law-making.

The course introduces students to classic themes and concepts in colonial studies, post-colonial studies, cultural studies, and political economy, through accounts of cultural, political, and economic change in the social anthropology of Africa, Latin America, South Asia, and the Pacific. Key themes include colonialism and post colonialism, capitalism, sovereignty, globalization, political violence, science and technology, consumption, and religion.

This course offers a theoretical and practical study of the diversity of living organisms and the evolutionary forces that created it. The course examines the form and function of micro-organisms, animals, and plants in terms of their behavioral, physiological, and structural adaptations to habitat, and how these evolved. The course also covers genetics, and how organisms combat attacks from pathogens. Students study biological diversity; gain first-hand experience in the laboratory learning how to handle living organisms; and learn to observe and record accurately and make sensible deductions. There is a particular focus on scientific writing: how to use the scientific literature and assess biological data, how to explain what you have observed, and how to write in good scientific English.

The course encourages students to grow and extend their practice both within and out of the confines of the college environment and reach a broader, more diverse audience. Students are encouraged to reflect on their art practice in relation to the wider current and historic contexts. They work independently in conjunction with a number of cross-school studio critiques, project space presentations, and regular tutorial support. External exhibition opportunities, invited artists, gallery visits, lectures, and workshops contribute to learning. Students test how artworks are installed, received, and understood professionally by participating in an external exhibition and collaborating with their peers across the school in the development and implementation of other external opportunities.

The first half of the course introduces major theories of economic sociology and their relationship to mainstream economics. The course begins with the field of behavioral economics and asks how far its theories take us towards a sociological perspective. This lays the groundwork for examining the idea of embeddedness, which has been economic sociology's main metaphor for socializing our view of markets since the 1980s. The course then looks at the alternative theoretical perspectives which have developed in the decades since, including the idea of "markets as politics" and the notions of "calculation" and "performativity." The second half of the course focuses on the application of these concepts to case studies of neoliberalism, carbon markets, financial models, and regulation. For example, the course asks if economic theory is not just modelling the economy but also playing a large role in shaping it and what this means for a society. Students also look at the sociological mechanisms involved in the uptake of mathematical financial models and their possible role in economic crises.

Foundation German 3 is the follow-up to the 40 hour Foundation German 2 course or Intermediate German. Students who have successfully completed the Foundation German 2 course or the Intermediate German course or have an equivalent knowledge (Higher or AS level) are ideally suited for this course.