University of Copenhagen

This course is a first introduction to algebraic topology, the area of mathematics in which algebra is used to study topological spaces. It defines the fundamental group and singular homology and studies their basic properties and applications. The course introduces foundational competencies in algebraic topology. Important concepts include homotopy, homotopy equivalence, fundamental group, covering space, chain complex, and homology. Prerequisites include knowledge about general topology and abelian groups, as obtained through courses such as Topology and Algebra 2, and Advanced Vector Spaces.
 

This course is an introduction to computability theory and Gödel's incompleteness theorems. The first half of the course focuses on computability theory, and includes Recursive and primitive recursive functions; Turing machines and computable functions; basic results in computability theory including Kleene's Normal Form Theorem, the s-m-n Theorem, Kleene's Recursion Theorem, Recursively enumerable sets, the halting problem and decision problems in general; as well as hierarchy theory, relative computability, and Turing degrees. The second part of the course focuses on Gödel's first incompleteness theorem, and includes Axiom systems for number theory, representable relations and functions, arithmetization of syntax, the Fixed-Point Lemma, and Gödel's first incompleteness theorem, as well as Gödel's second incompleteness theorem.

This course provides an opportunity to rediscover classics, to explore contemporary economic and business issues, and to consider and discuss different approaches to anthropological work in economy and business. It provides classic and new knowledge within economic and business anthropology, develops a curiosity, overview, and understanding of the field and related fields, allows and encourages use of economic and business anthropology in the analysis of student's own empirical data, planned fieldwork, theoretical debates, or current issues. Topics include markets, capitalism, exchange, money, debt, leadership, organization, design, and consumption, as well as additional concepts of interest to students.

This course constructs a philosophical framework for the interdisciplinary examination of gender. Against a historical outline of the development of contemporary gender studies, it examines biological, sociological, and psychological perspectives on gender. These theoretical perspectives are put into discussion with ethical issues concerning sexuality, self hood, personal identity, and autonomy. The course develops skills to make sense of the interdisciplinary examination of gender and discuss the historical, theoretical, and ethical aspects of what it means to exist with a gender identity. It provides a philosophical foundation for thinking critically about the complexity of human experience of gender. The most important elements of this philosophical foundation are a sense of history, conceptual clarity, and an understanding of interdisciplinary methodology. 

The course links knowledge on marine environment and organisms with applied cases, where such knowledge is required (e.g. climate change, eutrophication, pollution). The course is based on several themes representing specific applied issues, which provide the frame for understanding and assessing the potentials, limitations, and environmental effects of human activities on marine ecosystem structure and function. The cases are presented in a scientific context, where an understanding of the underlying basic physiological and ecological processes provide the foundation for evaluating, predicting, and managing environmental effects of human activities on marine systems. Each theme involves lectures, student presentations, and theoretical exercises. Students work in groups and deliver a written report for each theme.

This course provides an understanding of the challenges associated with the transition from fossil-based fuels to renewable energy, considering both the supply and demand side of energy markets. This includes the technological challenges of introducing renewable energy in the energy system and the regulatory challenges of designing optimal policies to facilitate the transition. While the course generally deals with the several energy markets, special emphasis is placed on electricity markets due to the significant role of electricity in a carbon neutral energy system. The course applies theory and analytical tools from microeconomics, macroeconomics, and econometrics. A large part of the course is also based on numerical structural models of the energy system.

This course offers contemplative reading and discussion of the works of Copenhagen’s most radical author, Søren Kierkegaard (1813-1855). Kierkegaard's thoughts about the struggle for meaning take us through unusual philosophical territory. His works—which are as novelistic as they are philosophical—treat themes like the existential meaning of anxiety and despair, beauty and boredom, humor and seriousness, the sicknesses and health of the soul, the joy and pain of embodiment, and, finally, commitment and love.

This course address how the economy works and how it affects individuals and society by focusing on a critically important domain of the economy—namely, financial markets. Overall, the course provides a sociological understanding of why we have financial markets, who the key financial actors are, how financial markets are evolving, as well as how finance and financial logics affect individuals and society. More specifically, it introduces recent sociological discussions of two aspects of finance. The first concerns “financialization,” that is, the growing use and importance of financial logics in otherwise non-financial fields. One example of this is when production companies generate more revenue from finance operations than from their core production activities. Another dimension of financialization relates to the everyday life of ordinary citizens who are increasingly embedded in financial logics. For example, the course discusses inequalities pertaining to the ability to obtain loans (credit). The second aspect of the course focuses on the inner workings of contemporary financial markets. In addition to discussing the backdrop to the 2008 financial crisis, particular emphasis is given to understanding how financial markets have transformed in light of automated trading, that is, fully automated algorithms acting in markets without direct human involvement. It covers the main elements in present-day markets, including trading firms, financial exchanges, so-called dark pools, and financial regulation, as well as discusses the kinds of financial crashes automated trading might give rise to. The course draws upon a combination of classical sociological analyses and theories of financial markets (from Max Weber to Wayne Baker); more recent sociological discussions of performativity in markets; financialization literature; and social studies of science-inspired analyses of automation.

This course explores the key problems that the oceans are contemporarily facing and how global governors, law enforcement agencies, and other actors intend to address them. The course is organized in three blocks. In the first part, it revisits the contemporary foundations of ocean governance, including international organizations and the law of the sea. It then revisits the key contemporary ocean discourses. In part two, the course investigates major issues on the ocean agenda, such as shipping, fishing, piracy, smuggling, or deep seabed mining and how international actors address them. Following an independent writing period, the course concludes with a workshop where case studies are presented. The course is assessed on the basis of participation and the independent project.

This course explores the factors that have triggered the evolution of environmental law and governance beyond state (since the development of the UN Sustainable Development Goals), and how the theoretical approaches of environmental studies developed in that context. Additionally, it reflects on how and to what extent environmental law and governance can be resilient and adaptive in facing global challenges.