Mathematics Expert in Data Analytics and Machine Learning

postgraduate specialization program

Why this training?

The fact that you are reading this website already indicates that you want to be among the winners of the socio-economic transformations generated by artificial intelligence. Moreover, you are even aware that you can make the most of the possibilities offered by artificial intelligence if you well understand and are able to use and shape AI technologies. This training of the Institute of Mathematics of Eötvös Loránd University will help you not only to have the existing artificial intelligence technologies available to you, but also to have the necessary knowledge and skills to accommodate the artificial intelligence technologies that will be created in the next decade.

The focus of the training is machine learning, its techniques and solutions from the fields of statistics and deep learning, as well as data science and big data. This is complemented by an internationally unique mathematical foundation so that, building on this, students can have a truly deep understanding of machine learning technologies. We are convinced that there is a strong need on the market for experts having deeper mathematical education.

Our program is intended for graduates who have learned the basics of university-level mathematics and who would like to gain deeper knowledge and competencies in the field of data science and artificial intelligence.

  • 00days until application deadline for Fall 2021

Summary of the program

We have incorporated the suggestions of leading experts from companies, who will employ our graduates into the curricula of our program. 

The program consists of 60 credits, classified as Fundamental background knowledge (at least 6 credits are needed from this group), Core courses (at least 12 credits) and Special courses (at least 18 credits). A course of about 20-24 contact hours is worth 6 credits – the students are supposed to take 5 such courses on average per semester. Most of the courses are elective, the few obligatory ones are typeset in bold in the next table.

Fundamental background knowledge
(6-24 credits)







Core courses
(12-27 credits)







Special courses
(18-27 credits)







Graph Theory and Algorithms (6)

Network Science (6)

Data Analysis for Time Series (6)

Basics in Linear Algebra and Numerical Methods (6)

Statistical Learning (6)

Advanced Modeling for Big Data and AI (6)

Optimisation (6)

Mathematical Modeling Practice (6)

Deep Learning (9)

Python for Data Science (6)

Data Mining Models and Algorithms (9)

Project Work (6)

Courses

Graph Theory and Algorithms (Fall Semester)

The aim of the course is to present the basic concepts of graph theory and complexity theory, to show the difference between polynomial and exponential running time algorithms.
In the practices the students will learn to formalize real world problems about networks in the language of graphs and algorithms.

Course description
Course coordinator: Péter Csikvári

Basics in Linear Algebra and Numerical Methods (Fall Semester)

The students get familiar with the basic linear algebraic notions and operations and some corresponding efficient numerical methods.
They will use the related subroutines in Matlab or Python and understand their role in the architecture of neural networks.

Course description
Course coordinator: Ferenc Izsák

Optimisation (Fall Semester)

The students learn the basics of combinatorial optimisation, including elements of linear programming, understanding the main ideas of LP solving techniques.
They will be able to recognize convex programming problems, and will be familiar with the gradient descent algorithm.

Course description
Course coordinator: Kristóf Bérczi

Python for Data Science (Fall Semester)

This is a quick introduction to Python Basics (standard library), efficient data manipulating (NumPy, Pandas), data visualization (Matplotlib).

The students will be familiar with the machine learning basics (scikit-learn).

Course description
Course coordinator: Máté Fellner

Network Science (Fall Semester)

The aim of the course is to give an introduction to the modelling methods of large networks.

The students will understand the basic measures of models and the role of linear algebra in network science.

Course description
Course coordinator: Péter Csikvári

Statistical Learning (Fall Semester)

The students learn regression and classification, the variance-bias trade-off.

They will understand regularization: Ridge regression and Lasso and become familiar with generalized additive models, decision trees and support vector machines.

Course description
Course coordinator: Vilmos Prokaj

Mathematical Modeling Practice (Fall Semester)

It is a team work on problems, presented by experts of the partner companies, which can be tackled by artificial intelligence. The students will get continuous supervision and feedback in order to be able to create a practically relevant solution.

Course description
Course coordinator: András Zempléni

Data Mining Models and Algorithms (Spring Semester)

The aim of the course is to teach the basic approach and methodology of data mining.

The students will know the models, algorithms and tools to solve main tasks of data mining; planning and implementing simple data mining projects.

Course description
Course coordinator: András Lukács

Data Analysis for Time Series (Spring Semester)

The students learn the most important notions of time series, needed for building more complex models.

They become able to use the related subroutines in R or Python and understand their role in the architecture of neural networks.

Course description
Course coordinator: László Márkus

Advanced Modeling for Big Data and AI (Spring Semester)

The aim of the course is to understand the mathematical theory of learning; knowledge of models and algorithmic techniques for analysing data of high volume and complexity.

The students will also master methods for special types of data and domain of problems.

Course description
Course coordinator: András Lukács

Deep Learning (Spring Semester)

The students gain understanding of neural networks; knowledge and ability to use several types of deep neural networks (e.g. convolutional networks, long-short term memory networks etc.)

In the practices the students apply neural networks for different types of data.

Course description
Course coordinator: András Lukács

Project Work (Spring Semester)

The main aim of the course is to apply the learned methods for real life problems; to shed light on hidden relations within datasets, using mathematically well-founded methods. The problems to be solved will be based on our partners’ suggestions who will provide (possibly anonimised) data and supervision or alternatively on public data sets, under our teachers’ supervision.

Course description
Course coordinator: András Zempléni

Lecturers

All-focus

András Zempléni

Program coordinator, associate professor at the Department of Probability Theory and Statistics.

He has over 30 years of teaching experience, including courses at insurance companies or major international firms and several Bsc and MSc courses, some of them in English. He has been the coordinator of the Applied Project course for MSc students in Applied Mathematics for more than 10 years. He is the founder and head of the Applied Statistical Services Group, which provides statistical consultancy for companies.

He was a visiting researcher at the University of Sheffield and TU Munich. He publishes regularly in journals like Quality and Reliability Engineering, Journal of Statistical Theory and Applications etc. He has written several lecture notes in Probability Theory and Mathematical Statistics, including computational aspects. He started working on data science and machine learning two years ago.

Courses: Mathematical Modelling Practice and Project Work

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Kristóf Bérczi

He is a senior lecturer of the Department of Operations Research, Mathematics Institute of Eötvös Loránd University, and also a member of the MTA-ELTE Egerváry Research Group on Combinatorial Optimization.

He obtained his PhD from Eötvös Loránd University, and held post-doc positions at the EGRES research group and the Hungarian Academy of Sciences. He has over 10 years of teaching experience. His main research interest is combinatorial optimization, with particular interest in matroid theory and approximation algorithms.

Course: Optimisiation

csikvari_peter

Péter Csikvári

He is an associate professor of the Department of Computer Science, Mathematics Institute of Eötvös Loránd University, and the head of the Counting in Sparse Graphs Lendület Research Group of Alfréd Rényi Institute of Mathematics.

He obtained his PhD from Eötvös Loránd University, and held post-doc positions at Alfréd Rényi Institute of Mathematics and Massachusetts Institute of Technology (MIT). He has over 10 years of teaching experience.

Courses: Graph Theory and Algorithms and Network Science

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Imre Fekete

He is an assistant professor of the Department of Applied Analysis and Computational Mathematics at Eötvös Loránd University, and also a member of the MTA-ELTE Numerical Analysis and Large Networks Research Group.

He obtained his PhD from Eötvös Loránd University. He held postdoc position at KAUST Numerical Mathematics Group. He was a short term visiting researcher at Public University of Navarre and Lund University. His research interests include theoretical and computational aspects of time discretisation techniques for ordinary, partial and neural differential equations.

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Máté Fellner

He has finished his university studies in mathematics (BSc) in 2017, and applied mathematics (MSc) in 2019 from Eötvös Loránd University (ELTE). Currently, he is a research fellow of the PIT research group of bioinformatics under the supervision of Vince Grolmusz at ELTE.
He is a founder and lead programmer at Lain Consulting, a company that has a specialization in artificial intelligence consulting.

His main research interests are programming and machine learning, data mining in large biological databases, and medical data processing.

Course: Python for Data Science

Ferenc Izsák

Ferenc Izsák

He is an associate professor at the Department of Applied Analysis and Computational Mathematics at Eötvös Loránd University.

In the past 20 years, he was teaching students in several majors ranging from biology over physics to pure mathematics. Over 7 years he was working as a research associate at the University of Twente in the Netherlands. His scientific interests include modeling issues, construction, analysis and efficient implementation of numerical algorithms for real-life problems. He established research collaboration with a number of his former students. He also became active in the analytic and practical study of neural networks with a special emphasis on their use in numerical methods.

Course: Basics in Linear Algebra and Numerical Methods

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András Lukács

He is a senior researcher and lecturer of data science and algorithms at the Department of Computer Science. He obtained his CSc degree in mathematics from the Hungarian Academy of Sciences. He organizes and manages the Artificial Intelligence and Data Science Research Group at the Institute of Mathematics, Eötvös Loránd University. 

He has deep expertise in data science and artificial intelligence, solving problems and use-cases from a wide range of domains, keeping up a good balance of mathematical and engineering approach, covering the full value chain of AI. His expertise was called in several R&D projects from the fields of telecommunication, finance, security and life sciences.

Courses:  Data Mining Models and Algorithms, Advanced Modelling for Big Data and AI and Deep Learning

markus_laszlo

László Márkus

He is an associate professor at the Department of Probability Theory and Statistics. He has over 30 years of teaching experience, including courses at major international firms, six sigma and design of experiments trainings at various companies, and several BSc and MSc courses, in part in English, some of them in the US.

He has his Ph.D. from Lomonosov Moscow State University. He was a post-doc fellow in Meijo University Japan and a Fulbright scholar at the University of Connecticut. He has run applied research projects funded by large insurance companies, banks, and financial services companies, as well as government-funded fundamental research projects. He has written lecture notes in financial mathematics. His research includes the use of machine learning techniques in mathematical finance.

Courses: Data Analysis for Time Series

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Vilmos Prokaj

Vilmos Prokaj is an associate professor at the Department of Probability and Statistics. He received his degree in Mathematics from Eötvös Loránd University, Budapest. After graduation he spent a year at the Rényi Institute. He has teaching experience in Statistics, Probability and Stochastic Processes. He was visiting professor at the University of California, Santa Barbara in 2014-15.

Course: Statistical learning

takacs_kristof

Kristóf Takács

He graduated in mathematics (BSc) in 2015, applied mathematics (MSc) in 2017, and actuarial and financial mathematics (MSc) in 2019 from Eötvös Loránd University (ELTE). Currently, he is a PhD student in mathematics and computer science at ELTE.

He joined the Protein Information Technology research group as a research fellow in 2017. His main research interest is data mining in large biological databases, regarding proteins and enzymes with special attributes applicable in solving practical problems.

He is also working as an instructor of several university courses since 2015.

Contact

Address:
Pázmány Péter sétány 1/C
H-1117 Budapest, Hungary

Phone:
(+36 1) 381 2202

Email:

ai.training@ttk.elte.hu