Topics in Applied Mathematics

The Topics in Applied Mathematics course provides a rigorous mathematical and statistical foundation for modern artificial intelligence. It covers vector spaces, linear operators, matrix decompositions, Fourier series, SVD, PCA, and least-squares methods, as well as probability theory and descriptive statistics. Students gain essential skills in data preparation, analysis, and uncertainty management for AI applications. The course supports an understanding of machine learning, network modelling, and data processing from a mathematical perspective. It also develops the ability to work with English-language technical literature and communicate results effectively. The course fosters precision, autonomy, and research-oriented thinking for advanced AI studies.
 

Statistical learning theory and kernel methods

The Statistical Learning Theory and Kernel Methods course provides a rigorous theoretical foundation for modern machine learning, with a focus on reproducing kernel Hilbert spaces (RKHS), kernel-based algorithms, and generalisation theory. It covers core concepts such as regularisation, representation theorems, kernelised regression and classification, support vector machines, kernel PCA, and nonparametric estimation. Students gain insight into bias–variance trade-offs, consistency, stability, concentration inequalities, and PAC-style generalisation guarantees. It develops strong analytical and data-processing skills for applying kernel methods across domains such as healthcare, finance, and industry.

Numerical Methods for Optimisation

The Numerical Methods for Optimisation course introduces fundamental optimisation concepts and algorithms widely used in artificial intelligence and computer engineering. It covers single- and multi-parameter optimisation in both constrained and unconstrained settings, including derivative-free and gradient-based methods. Students learn practical techniques for computing and approximating derivatives, as well as specialised approaches such as quadratic and least-squares optimisation. The course develops strong analytical and data-processing skills for real-world AI applications. It supports effective professional communication in English and engagement with current research. The course fosters precision, autonomy, and responsible problem-solving in optimisation-driven AI systems.

Machine Learning

The Machine Learning course provides an in-depth introduction to core machine learning models, algorithms, and their theoretical foundations. It covers key topics such as decision trees, support vector machines and kernel methods, probabilistic and graphical models, neural networks, ensemble techniques, semi-supervised learning, time-series analysis, and text mining. Special emphasis is placed on hyperparameters, model tuning, and the strengths and limitations of different methods across application domains. Students develop skills in data preparation, analysis, and practical problem solving for recognition, recommendation, and generation tasks. The course supports interdisciplinary thinking and application across healthcare, finance, industry, and education. It also fosters continuous learning and engagement with current advances in AI.
 

Principles of artificial intelligence

The Principles of Artificial Intelligence course introduces the fundamental concepts and methods underlying modern AI systems, including problem modelling, search, and reasoning. It places special emphasis on classical AI search and heuristic optimisation methods, covering state-space representations, graph-based problem solving, AND/OR graphs, heuristic search, and strategies such as A*, hill climbing, tabu search, simulated annealing, backtracking, minimax, and alpha–beta pruning. The course also introduces evolutionary algorithms and game-playing techniques.

In addition, it provides an overview of supervised and unsupervised learning, including k-nearest neighbours, decision trees, random forests, deep learning, k-means, and PCA. Students gain insight into explainable, safe, and responsible AI that integrates ethical and legal considerations. The course develops skills in data preparation, interdisciplinary problem solving, and solution planning, and fosters continuous learning, professional communication in English, and research-oriented thinking.
 

Methods and tools for AI applications

The Methods and Tools for AI Applications course provides a mathematically rigorous foundation for modern artificial intelligence. It focuses on mathematical data models in AI, covering linear and generalised linear models, probability theory, likelihood-based estimation and approximation (maximum likelihood, MAP, Bayesian methods), and optimisation techniques. Students learn unsupervised methods such as expectation maximisation and clustering, as well as ensemble models and autoencoders. The course emphasises explainable, safe, and ethically grounded AI development. It develops interdisciplinary problem-solving skills and supports application across domains such as healthcare, finance, industry, and education.
 

Deep Network Developments

The Deep Network Developments course provides an in-depth, practice-oriented introduction to modern deep learning architectures and applications. It follows state-of-the-art (SOTA) methods and introduces them progressively across semesters, ensuring that students continuously build on the latest advances in the field. The course covers DNNs, backpropagation, convolutional neural networks, transfer learning, autoencoders, semantic segmentation, object detection, recurrent neural networks, transformers, and generative adversarial networks. Students gain hands-on experience with PyTorch, backpropagation, and model training for classification, detection, and generation tasks. The course emphasises explainable, safe, and ethically grounded AI development, integrating legal and societal considerations. Students engage with current research and develop customizable, real-world AI systems.

Deep Reinforcement Learning

The Deep Reinforcement Learning course provides a rigorous introduction to modern reinforcement learning theory and its deep learning–based extensions. It covers core topics such as Markov Decision Processes, dynamic programming, Monte Carlo and temporal-difference methods, policy gradients, and function approximation. Students learn value-based, policy-based, and model-based deep RL, as well as meta-learning and multi-agent reinforcement learning. The course includes hands-on development with tools such as OpenAI Gym and Deep Q-Learning for real-world applications. It emphasises ethically grounded, reliable, and human-centred AI systems. Students engage with current research and develop skills for building adaptive, cooperative, and scalable intelligent agents.
 

New results in the machine learning seminar

The New Results in Machine Learning Seminar exposes students to the latest research advances in artificial intelligence and machine learning. Each session focuses on the presentation and critical discussion of a recent scientific paper, covering topics such as neural networks, reinforcement learning, ethical AI, and real-world AI applications. The seminar develops skills in scientific reading, research interpretation, and professional communication in English. Students learn to evaluate emerging methods, identify innovation directions, and formulate research milestones. It fosters collaborative learning, ethical awareness, and responsible AI development. Assessment is based on presentation quality, active participation, and understanding of the discussed materials.

Graph Neural Networks

The Graph Neural Networks course provides an in-depth introduction to machine learning on graph-structured data and modern GNN architectures. It covers graph representation methods, spectral graph theory, classic approaches such as DeepWalk and Node2Vec, and classic core GNN models, including GCN and GAT. Students learn message-passing techniques, graph convolutions, and applications such as node classification, link prediction, and graph classification. The course also addresses advanced topics such as position-aware and identity-aware GNNs, adversarial attacks, and scalability and interpretability challenges. Students gain hands-on experience with PyTorch Geometric and develop skills in research analysis, interdisciplinary applications, and professional English communication.
 

Research methodology

The Research Methodology course equips students with the essential skills for conducting high-quality research in artificial intelligence and data science. It covers research planning, scientific writing, publication standards, and the evaluation processes used in academic conferences and journals. Students learn how to develop research proposals, define milestones, and structure R&D&I projects, including Horizon Europe–style work plans. The course introduces collaborative tools (e.g., GitHub), LaTeX and BibTeX, and best practices for presentations, publications and technical reports. It also addresses ethical issues, data protection, and responsible research conduct. Students study how to prepare their thesis topic and a research plan, and to foster research-oriented thinking and professional communication in English.
 

Legal and ethical aspects of DS and AI

The Legal and Ethical Aspects of Data Science and AI course introduces the regulatory, legal, and ethical foundations of modern AI and data-driven systems. It covers data protection, privacy law, intellectual property, contract law, and the legal circulation and transferability of data, with a strong focus on EU regulations, including the EU AI Act, as well as international legal frameworks. Students gain insight into ethical AI principles, bias mitigation, and responsible system design. The course addresses sector-specific challenges in finance and healthcare. It develops skills in professional communication, interdisciplinary collaboration, and responsible data handling. Students learn to integrate legal compliance and ethical standards into real-world AI applications.

I Learn with Prompt Engineering

The I Learn with Prompt Engineering course introduces students to the principles and practice of designing effective prompts for large language models. It covers direct prompting, prompt patterns, extended prompting techniques, and creative learning strategies using LLMs. Students learn to craft precise, well-structured prompts to support learning, research, and problem-solving while improving their scientific English proficiency. The course emphasises ethical and responsible use of generative AI in education. It supports autonomous, self-paced learning and personal skill development. Students gain practical experience in tailoring, refining, and sharing prompts for academic and professional purposes.

Preparation course for master's studies and developing learning skills

The Preparation Course for Master Studies and Developing Learning Skills supports students – especially international entrants – in successfully integrating into the academic environment of the ELTE Faculty of Informatics. The course develops communication, learning, and academic English skills essential for university studies and professional self-development. It introduces the Hungarian higher education system and ELTE’s teaching and learning culture, helping students orient themselves effectively. Students learn time management, stress management, learning methodology, and soft and entrepreneurial skills. The course emphasises teamwork, a proactive mindset, and social integration through practical training and outdoor programs. It fosters responsible behaviour, collaboration, and ethical awareness in academic and professional contexts.
 

Computational Intelligence

The Computational Intelligence course introduces biologically inspired and soft computing approaches to artificial intelligence. It covers fuzzy systems and fuzzy inference, neuro-fuzzy models, spiking neural networks, evolutionary algorithms, and swarm intelligence techniques. Students learn how these methods support learning, optimisation, and decision-making in complex, real-world systems. The course emphasises hybrid intelligent systems, explainable and safe AI, and human-centred interaction. It develops skills in data preparation, system design, and interdisciplinary problem solving. Students engage with current AI research and apply computational intelligence methods across diverse application domains.

Advanced Deep Network Developments

The Advanced Deep Network Developments course provides a research-oriented, in-depth exploration of state-of-the-art deep learning methods and architectures. It covers core foundations such as automatic differentiation, optimisation, and modern design patterns, alongside advanced architectures including Transformers and attention-based models. Students study generative methods and representation learning, with an emphasis on variational autoencoders, diffusion models, and latent-space structures. The course integrates human-centred AI, focusing on interpretability, explainability, and human-in-the-loop learning. Applications include human–machine interaction and affective computing for emotion recognition and user modelling. Students engage with cutting-edge research and develop adaptable, ethically grounded AI systems.
 

AI Project Lab I. & AI Project Lab II.

The AI Project Lab I & AI Project Lab II courses provide hands-on experience solving real-world artificial intelligence problems in a research-and-development setting. Students work individually or in teams on projects based on real data from industrial and academic partners of the Faculty of Informatics. The course covers both basic and applied AI research under the supervision of experienced AI scientists. Students develop skills in data preparation, experimentation, and professional English reporting. Weekly consultations support continuous progress and high-quality outcomes. As a course requirement, students summarise their research in a TDK paper and present it at the Faculty Student Research Conference (TDK). Together with AI Project Lab II, the course fulfils the program's internship requirement.
 

Introduction to Data Science

The Introduction to Data Science course provides a foundational overview of core data science concepts, models, and methodologies essential for artificial intelligence applications. It covers descriptive techniques such as clustering and frequent pattern mining, as well as predictive models for classification and regression. Special emphasis is placed on model validation, hyperparameters, overfitting–underfitting, and the bias–variance trade-off. Students learn data quality and preprocessing techniques, including handling noise, missing values, and normalisation. The course also introduces recommendation systems and the CRISP-DM data mining process. Students develop practical skills in data preparation, analysis, and result interpretation across application domains
 

Advanced Software Technology

The Advanced Software Technology course introduces modern principles and practices across the full software development lifecycle, with a strong focus on AI-driven systems. It covers idea formation, MVP design, project execution, and contemporary development methodologies. Students learn to build maintainable architectures and to apply tools and techniques for sustainable, scalable software processes. The course emphasises innovation, ethical system design, and industrial reliability. Learning is team-based and coach-supported, with continuous assessment reflecting both team performance and individual contribution. Students develop skills essential for leading complex AI and software projects.

Logic Programming

The Logic Programming course introduces declarative programming as one of the core paradigms of artificial intelligence, focusing on reasoning, symbolic representation, and problem solving. It covers the principles of logic programs, recursive relations, search trees, and control strategies, with special emphasis on finite and efficient search. Students gain practical experience with Prolog including its execution model, optimisation techniques, and meta-logical constructs. The course develops skills in formal problem modelling, abstraction, and human-centred AI system design. It emphasises correctness, efficiency, and ethical system behaviour. Students learn to apply logic-based methods in recognition, reasoning, and decision-support systems.
 

Affective computing

The Affective Computing course introduces the interdisciplinary foundations of emotion-aware artificial intelligence, integrating insights from psychology, cognitive science, and computer science. It focuses on modelling, recognising, and responding to human emotions through facial expressions, eye tracking, body pose analysis, and physiological signals. Students study key theories of human emotions and practical methods for detecting affective states such as stress and drowsiness, including in driving scenarios. The course introduces benchmark datasets and state-of-the-art deep learning tools for affective analysis. It emphasises ethical, human-centred AI and responsible system design. Students develop skills for building adaptive and emotionally intelligent human–computer interaction systems.

AI Robotics

The AI Robotics course provides a comprehensive introduction to intelligent robotic systems, integrating artificial intelligence with classical robotics. It covers robot architectures, sensing and perception, kinematics, dynamics, motion planning, control, and trajectory generation. Students learn to design and program robotic systems in state-of-the-art simulation environments and apply AI methods to perception, decision-making, and multi-agent coordination. The course emphasizes human–robot interaction, ethical and sustainable robotics, and interdisciplinary collaboration. Students develop practical and theoretical skills for deploying AI-driven robotic solutions in real-world applications. It prepares students for advanced research and industrial roles in autonomous and intelligent systems.

Embodied Intelligence

The Embodied Intelligence course explores how artificial intelligence emerges from the interaction between computation, physical bodies, and real-world environments. It covers embedded systems, sensorics, actuators, and microprocessors, alongside mobile and industrial robotics modelling and simulation. Students study cognitive robotics and selected applications where perception, action, and learning are tightly integrated. The course emphasises human-centred and ethically grounded design of intelligent physical systems. Students develop interdisciplinary skills for deploying AI in embodied, real-world scenarios. It prepares students for work in robotics, autonomous systems, and physical AI.
 

3D Computer Vision

The 3D Computer Vision course focuses on enabling machines to perceive and interpret the three-dimensional world from visual data. It covers camera models, calibration, feature detection, stereo and monocular vision, and simultaneous localisation and mapping (SLAM). Students learn how to reconstruct geometry, motion, and scene structure from images and videos using modern AI-based methods. The course integrates pattern recognition with real-world vision applications in robotics, healthcare, and industry. Emphasis is placed on practical case studies and research-driven techniques. Students develop strong foundations for careers in autonomous systems, robotics, and spatial AI.

3D point cloud processing and analysis

The 3D Point Cloud Processing and Analysis course focuses on understanding and analysing three-dimensional data acquired from sensors such as LiDAR, depth cameras, and 3D scanners. It introduces point cloud filtering, nearest neighbour search, model fitting, and geometric feature extraction as core techniques. Students learn both classical and deep learning–based methods for point cloud segmentation, recognition, and classification. The course emphasises the role of 3D data as a complement to 2D vision in perception systems. Applications span robotics, autonomous driving, digital twins, healthcare, and industrial inspection. Students gain practical skills for building robust 3D AI pipelines.

Computational Linguistics

The Computational Linguistics course introduces the theoretical foundations and practical methods of Natural Language Processing. It covers the full linguistic pipeline from tokenisation and morphology through syntax, parsing, and semantics. Students learn core models such as n-grams, bag-of-words, word sense disambiguation, and word vector representations. The course also explores lexical resources, including WordNet and FrameNet, as well as key applications such as information retrieval, sentiment analysis, and knowledge extraction. Emphasis is placed on formalising language-related problems and solving them using computational and AI-based approaches.

Natural Language Processing and Language-based Foundation Models

The Natural Language Processing and Language-based Foundation Models course provides a comprehensive introduction to modern Natural Language Processing (NLP) and large language–based foundation models, with a strong focus on human–machine interaction and generative AI systems. It covers the full NLP pipeline, from classical computational linguistics (tokenisation, POS tagging, parsing, semantics) to contemporary deep learning–based language modelling.

Students learn traditional methods such as bag-of-words, word sense disambiguation, and latent semantic analysis, as well as modern representation learning with word vectors and contextual embeddings. The course places special emphasis on neural language models, including RNNs, Seq2Seq architectures, attention mechanisms, and Transformer-based models such as BERT and GPT.

Advanced topics include efficient attention mechanisms, state-of-the-art Large Language Models (LLMs), training and fine-tuning techniques (e.g. adapters, LoRA, RLHF), prompt engineering, and LLM tooling. The course also introduces multimodal foundation models, modality fusion, and language grounding, with applications in speech-to-text systems and conversational agents.

Ethical, legal, and societal aspects of NLP and foundation models are integrated throughout, alongside paper-reading seminars and applied mini-projects, enabling students to gain hands-on experience with state-of-the-art NLP and multimodal technologies.
 

Cognitive Science

The Cognitive Science course provides a comprehensive introduction to the theoretical foundations and modern research directions of Cognitive Science, with a strong emphasis on its relevance to artificial intelligence and human-centred system design. It explores how humans perceive, learn, think, remember, communicate, and interact socially, and how these processes can inspire and inform intelligent systems.

Students study key cognitive domains including perception, attention, learning and curiosity, memory, language, and social cognition, approached from multiple perspectives: behavioural, computational, and neuroscientific. The course examines fundamental questions such as how cognitive abilities develop, how they differ across species, what neural mechanisms support them, and what happens when they malfunction.

Special attention is given to the implications of cognitive models for AI, particularly in human–machine interaction, adaptive systems, and explainable and responsible AI. By integrating insights from psychology, neuroscience, linguistics, and computer science, the course equips students with a multidisciplinary perspective essential for designing AI systems that align with human cognition and behaviour.
 

Multi-Agent Systems

The Multi-Agent Systems course focuses on the design and analysis of intelligent systems composed of multiple interacting autonomous agents. It covers agent architectures, agent-oriented programming, and the foundations of distributed artificial intelligence. Students learn how agents coordinate, communicate, compete, and collaborate in dynamic environments, including scenarios with self-interested or partially controlled participants. The course introduces multi-agent learning, swarm intelligence, and social systems through simulation-based analysis of system dynamics. Emphasis is placed on strategic interaction, robustness, and scalability of agent-based systems. Students gain practical foundations for building AI solutions in robotics, smart infrastructure, finance, logistics, and complex adaptive systems.

Game Theory

The Game Theory course provides a rigorous foundation for modelling and analysing strategic interactions among rational agents in artificial intelligence systems. It covers decision science, equilibrium concepts, and their connections to optimisation and fixed-point theory. Students study finite and continuous games, zero-sum and non-zero-sum games, leader–follower (Stackelberg) models, and cooperative games including the Shapley value and the core. The course also explores social choice mechanisms, bargaining solutions, and conflict resolution strategies. Emphasis is placed on real-world applications in economics, markets, security, engineering, and environmental decision-making. Students develop analytical tools essential for multi-agent AI, autonomous systems, and strategic AI-driven decision support.

Collective Intelligence

The Collective Intelligence course explores how intelligent behaviour can emerge from the interactions of many simple agents, without centralised control. It introduces key concepts such as emergence, self-organisation, and the tension between local and global optima through classic problems like the Prisoner’s Dilemma and the Tragedy of the Commons. Students study formal methods for analysing decentralised systems, including system dynamics, cellular automata, and agent-based modelling.

The course covers market-based mechanisms and heterogeneity in economic systems, as well as biologically inspired swarm intelligence and ant colony optimisation. Evolutionary game theory and replicator dynamics provide insight into cooperation, competition, and stability in adaptive populations. Network science and mechanism design are also introduced to understand interaction topologies and to design incentive-compatible systems. The course equips students with theoretical and practical tools for designing scalable, robust, and socially-aware multi-agent AI systems.
 

Thesis Consultation

Thesis Consultation is a joint, supervisor–student guided course that supports the systematic development of the MSc thesis through a clearly defined work schedule and regular consultations. Students and supervisors collaboratively define the thesis topic, requirements, and architecture, and continuously monitor progress through agreed milestones. The course ensures that at least 60–70% of the implementation is completed under supervision, leading to a high-quality, well-prepared thesis ready for submission and defence at the final exam.

Erasmus Mobility

The Erasmus Mobility block offers students of the ELTE Faculty of Informatics a structured opportunity to gain international academic and professional experience during their studies. This unified mobility framework enables students to spend a semester or a shorter period at one of ELTE’s prestigious partner universities in Europe or beyond, or to complete a professional internship abroad supported by Erasmus+.

A key feature of this mobility block is that the courses taken and successfully completed at the host institution during the mobility period can be fully recognised and credited toward the student’s current degree programme at the ELTE Faculty of Informatics, ensuring academic continuity and seamless integration into the curriculum.

The programme includes long-term study mobility for partial study abroad, professional internships available both during studies and after graduation, and short-term doctoral research mobility for PhD students. In addition, international credit mobility opportunities beyond Europe are periodically announced.

Through Erasmus+, students gain not only advanced academic knowledge and international work experience, but also intercultural competence, professional networks, and a strong foundation for an international career, while remaining fully embedded in their ELTE degree programme.

More information about the actual open calls at ELTE: 

https://www.elte.hu/erasmus-kreditmobilitas