Computer Science

The course covers the translation between biology and mathematics; population models and spatial models, simulations: Deterministic versus stochastic simulations of mathematical models; weaknesses, strengths, and applicability; the Gillespie algorithm for stochastic simulations: Naive implementation and possible optimizations for large systems; cost functions; optimization methods including local optimization, thermodynamic methods, particle-swarm optimization, and genetic algorithms; and sensitivity analysis: Estimation of the uncertainty of determined parameter values. Strategies to achieve robustness. Admission to the course requires 90 credits Science studies, including knowledge equivalent to BERN01 Modelling in Computational Science, 7.5 credits or FYTN03 Computational physics, 7.5 credits and English 6/B. Admission to the course also requires knowledge in programming in Python equivalent to NUMA01, 7.5 credits or similar knowledge in Matlab, C++ or the like programming language.

The course provides an overview of current applications of formal methods to modern AI systems, including the verification, certification, and monitoring of agent-based systems and solutions. The course is structured in four parts. The first part focuses on basic modal logic, its syntax and semantics based on Kripke frames and models, as well as the model theory of modal logic, including the notions of satisfaction and validity. The second part gives students the foundations for the specification of strategic behaviors of agents in multi-agent systems (MAS), including the formalism of Concurrent Game Structures as a mathematical representation of MAS. In the third part, students consider the role played by formal methods in modern AI systems, specifically reinforcement learning (RL). In the fourth part, the course introduces the language of Alternating-time Temporal Logic (ATL), an extension of the temporal logics CTL and LTL, which allows students to express 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.

Students are introduced to data science and its practice: how it works and how it can produce insights from social, political, and economic data. It combines accessible knowledge of data science as a field of study with practical knowledge about data science as a career path. By combining case studies in applications of both with the study of the content of data science, it covers data science that is both pedagogic but accessible, as well as fundamentally applied and practical. The course combines three perspectives: inferential thinking, computational thinking, and real-world relevance.

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.

 

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's aim is to develop an understanding of large language models (LLM) as well as their evaluation and to practice reading, understanding, and presenting research work. As part of the class, methods for the selection of data and LLMs, data preparation, application and evaluation of LLMs are developed and put into practice. The use cases are examples from the field of natural language processing, e.g. translation, summary of text, or information extraction.

This advanced topics course covers reinforcement learning, search, and test-time scaling of large language models that are expected to drive the next generation of AI systems. 

Topics include: Basics of RL (Markov Decision Process and Policy evaluation), Basics RL (Imitation learning, Deep policy gradient methods), Basics of RL (Deep Q-Learning, Rainbow DQN); Symmetric alternating Markov games, Monte Carlo tree search, expert iteration, and AlphaGo; Imperfect information games, Counerfactural regret minimization, and Pluribus; NLP basics (RNN, beam search, tokenizers); NLP basics (Transformers, encoder-decoder architectures); Instruction fine-tuning, Scaling laws of LLM pre-training; Reinforcement learning with human feedback, direct policy optimization, Group Relative Policy Optimization (GRPO); Chain of thought, Process reward models, Prover-verifier games; In-context learning, Scaling LLM Test-Time Compute; DeepSeek-R1. 

This advanced undergraduate course delves deeply into Internet technology. It covers the structure of the Internet and its protocol applications in detail. Students examine the basic design principles, implementation, and operating principles of computer networks used in modern Internet and cloud/data centers, and study in detail the design principles and functions of the transport layer, network layer, link layer, and physical layer, including client-server models, web, video streaming, and smart phone network applications. If time permits, the course includes ultra-low latency/ultra-bandwidth networking issues in data centers. An understanding of the OSI protocol and basic concepts of data communication is required. 

All engineering disciplines today employ machine learning for monitoring systems and fault detection, for data-based decision support as well as for leveraging new potentials in the environment of big data. This module teaches the fundamentals of standard machine learning techniques as well as their implementation using standard libraries in the Python programming language based on real-world engineering examples. It focuses on the complete data science process from data exploration over modeling to inference and production.