Technical University Berlin

This course explores advanced principles of computer networks based on fundamentals of the topic. The topics are protocol mechanisms, principles of implementation, network algorithms, advanced network architectures, network simulation, network measurement as well as techniques of protocol specification and verification. Protocols mechanisms and techniques of protocols used in network protocols include signaling, separation of control and data channel, soft state and hard state, using of randomization, indirection, multiplexing of resources, localization of services, and network virtualization (overlays, VxLANs, peer-to-peer networks). The identification and study of principles that lead to the implementation of network protocols include system principles, reflections on efficiency, and caveats/ case studies. Network architecture examines “the big picture”. It identifies and studies principles that lead the design of network architectures. The course considers substantial questions rather than specific protocol and implementation tricks, which include internet design principles, lessons learned from the internet, architecture of telephone network, and circuit switching versus packet switching (revisited). Protocols cover network algorithms, self stabilization (examples of routing), Kelly's congestion control framework, and closed loop control on the example of TCP. Simulation, oblivious routing and routing in cryptocurrency networks includes principles of discrete event simulation, analysis of simulation results, packet versus flow models, bounding strategies (e.g., Chernoff bounds), and Gaussian distributions.

This course begins with a study of the most classical objects in algebraic geometry: conics and plane curves. Students spend time examining these examples to develop a feeling for how algebraic equations and geometric shapes interact and prove an early version of Bezout's theorem. The central part of the course develops the theory of sheaves and schemes, which provide the natural framework in which to formulate and generalize classical results. The course introduces morphisms of schemes and their fundamental properties, and it studies divisors and line bundles as fundamental tools for encoding geometric information. Students examine the local structure of schemes, including objects such as differential forms. The class also introduces Čech cohomology, both as a computational method and as a bridge to more advanced cohomological techniques. The course concludes with the Riemann-Roch theorem.

This course explores mathematical concepts that are useful and frequently used in machine learning. Students examine linear algebra (vector spaces, scalar products, orthogonal vectors, matrices as linear mappings, determinants, eigenvalue and eigenvectors), analysis (differentiation), and probability theory (multidimensional probability distributions, calculations with expected values and variances). The class also discusses some contemporary applications of mathematics in machine learning. 

This course examines groups, which are best understood as symmetries of mathematical objects. Students explore geometric group theory and the connection between the algebraic properties of a group and the geometric properties of the spaces it acts on.

In this course and through the DAMS Lab group (FG Big Data Engineering), students learn how to conduct research in areas of data engineering, data management, and machine learning systems. Students review scientific literature in these areas as well as how to design, implement, and evaluate prototypes. The lab group offers this project on large-scale data engineering. The course includes tasks in a wide range of components of data management and machine learning systems. Students will have the opportunity to make meaningful contributions to free open-source projects.

The course explores various social and ecological issues that are perpetrated by the current system of exploitation for economic gain. Students are introduced to the "flourishing business model canvas" (by Antony Upward). The components of the canvas are broadly discussed throughout the duration of the module, and familiarization with grand societal challenges and entrepreneurial approaches to them. Students work in teams during lecture time to analyze existing sustainable business models and understand how they are aiming to solve problems while delivering social and ecological value. Other sustainability related issues are discussed in class. Team work, open group discussions and utilization of the business model canvas foster sustainable entrepreneurial competencies such as cooperation, individual reflexivity, and initial strategic and systems thinking.

This project focuses on exploring Berlin through analog hand drawing, and then using drawing and model making methods to design and construct a small building project. The course offers participants an in-depth knowledge of the design professional's important tool of hand drawing, a skill that equips them for their studies and later professional work. It begins with the basics of hand drawing to establish a foundation and then moves on to apply drawing to observe, analyze and design the environment. Students learn drawing forms such as perspective, isometry, section, pictogram, and others. The subject of analysis is the city of Berlin, the city fabric, micro urban situations, and the Design-Build project site. The Design-Build part of the project focuses on the realization of a small building project for a special community in Berlin. The students develop an idea from the design stage to the built project. An examination of the context and discussions with the clients and users form the basis for the final design. In a competitive design workshop, the best and most feasible solution(s) are selected and developed. In collaboration with the users and under the guidance of a craftsman, the design is built and inaugurated. The community is the client for this Design-Build project. They actively participate in guiding the project from the design phase to on-site construction. This project is carried out in an academic environment, engaging in interdisciplinary collaboration between students of various disciplines and the community. Through designing and building together, the students gain insights into the world that the people they are designing for are facing, with the goal of making students more sensitive to the social, cultural and ecological implications of their work. The challenge is to integrate "low-cost" and "high efficiency" requirements with considerations for sustainability, aesthetics, appropriateness, participation, and education. In order to profit from the high potential of these small-scale projects, the focus has to be the quality of the space that is created. This course primarily takes place off campus, with the drawing sessions happening throughout Berlin and the construction activities conducted on-site.

In this course, students learn and apply core principles and concepts in heterogeneous catalysis. Students learn the most important catalytic materials and how to describe their functions, including important applications of heterogeneous catalysts in sustainable energy conversion. Course topics include the scope of future energy supply and its significance for industry and society as well as the environment and various synthetic methods for the preparation of heterogeneous catalysts using various solid-state, solution-and molecular-based approaches. Students learn how to define crystalline and amorphous materials and thin-film technology and gain a basic understanding of the characterization techniques and systematic evaluation of catalysts/thin films using diffraction, microscopic, and analytics. The course covers fundamentals of electrochemistry and how to correlate and explain activity parameters to differentiate catalyst's performances in catalytic oxidation and reduction processes in the rapidly growing fields of water electrolysis, fuel cells, CO2 activation, biomass reforming, and paired electrolysis. Course readings include relevant scientific literature and key publications of leading female and male scientists of the field.

The course introduces the basics of Geometry Processing. It presents mathematical models, data structures and algorithms to represent geometry on modern computer applications, and these are manipulated through practical exercises. The techniques seen in the course are fundamental for applications like 3D modeling, geometry reconstruction from scanned objects, and physical simulation.

In this course, students gain an integrative understanding of the field of Artificial Intelligence (AI), with equal emphasis on data-driven AI (especially machine learning) and model-based AI (especially planning and reasoning). They come to understand AI from the perspectives of decision theory, machine learning, optimization, and classical problem solving. Students learn to independently implement and understand core algorithms from these areas and can identify appropriate problem formulations and AI algorithms for a given application. Course topics include problem formulations and algorithmic approaches from decision theory (including reinforcement learning, multi-armed bandits, control theory), machine learning, optimization, and inference, classical planning, and problem solving. The class also discusses fundamental and recurring algorithmic principles such as dynamic programming, optimization-based vs. sampling-based methods, and decision trees.