Бакалавриат
2024/2025
Научно-исследовательский семинар "Анализ данных в естественных науках"
Статус:
Курс по выбору (Прикладной анализ данных)
Направление:
01.03.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
4-й курс, 1-3 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
4
Course Syllabus
Abstract
The specialization seminar offers the opportunity to study subjects and sections of mathematical statistics related to the application of differential equations, machine learning, probability theory and mathematical for modeling various solutions of a wide range of theoretical and applied problems. These tasks include analysis and forecasting of time series, automatic detection of trend changes, forecasting “black swan” events, and analysis of stable configurations in the community. The computational methods used are standard for machine learning: clustering, pattern recognition, dimension reduction. The purpose of the research seminar is to expand the research horizons of students. It is assumed that at the end of the course, the student will be able to prepare a research paper or grant application. To do this, the student will be involved in the following activities: attending classes (it is obligatory), analyzing a large number of sources in a foreign area for the student in order to learn how to highlight mathematical problems in non-mathematical articles, completing part of a group project, preparing presentations and discussion (peer review) of other people's projects and presentations. Prerequisites Knowledge of basic mathematics: analysis, linear algebra, probability theory, - algorithms, programming fundamentals, the ability to understand computational packages
Learning Objectives
- Be able to prepare and conduct a presentation with a report on a scientific topic, as well as conduct an academic discussion on the materials of the report.
- To be able to independently choose and study modern scientific articles, find relevant literature.
- Be able to write scientific texts.
Expected Learning Outcomes
- Be able to prepare and conduct a presentation with a report on a scientific topic, as well as conduct an academic discussion on the materials of the report.
- Methods for verifying empirical results: hypothesis testing, bootstrap, randomization, etc.
- Methods of mathematical modeling based on (stochastic) differential equations, probability theory.
- Modern computational methods used in related fields, in particular, when forecasting time series and solving inverse problems (Fourier analysis, wavelets, regression, SSA, dimension reduction, moving averages, neural networks, filters, etc. - understanding the advantages and disadvantages each of the methods.
- To be able to independently choose and study modern scientific articles, find relevant literature. Be able to write scientific texts.
Course Contents
- Scientific modeling and machine learning description.
- Forward problem solution using generative modeling.
- Uncertainty estimation for machine-learning based solution.
- Diploma topic defence
- Scientific papers presentation
- Selected scientific topics context analysis
- Kolloquium
Assessment Elements
- ReviewsDuring module 2 there must be at least one presentation per each group, an obligatory colloquium will be conducted at the end of the module, and a defence of the chosen BSc thesis topic.
- PresentationsDuring module 1 there must be at least one presentation per each group and an obligatory colloquium will be conducted at the end of the module.
- AuditoringDuring module 3 there must be at least one presentation per each group and an obligatory colloquium will be conducted at the end of the module.
Bibliography
Recommended Core Bibliography
- Ernest P. Chan. (2021). Quantitative Trading : How to Build Your Own Algorithmic Trading Business. Wiley.
- Gabaix, X., Gopikrishnan, P., Plerou, V., & Stanley, H. E. (2003). A theory of power-law distributions in financial market fluctuations. Nature, 423(6937), 267. https://doi.org/10.1038/nature01624
- Irene Aldridge. (2013). High-Frequency Trading : A Practical Guide to Algorithmic Strategies and Trading Systems: Vol. 2nd edition. Wiley.
- Joel Hasbrouck. (2007). Empirical Market Microstructure : The Institutions, Economics, and Econometrics of Securities Trading. Oxford University Press.
- Mike Elvin. (2004). Financial Risk Taking : An Introduction to the Psychology of Trading and Behavioural Finance. Wiley.
Recommended Additional Bibliography
- 9781491912140 - Vanderplas, Jacob T. - Python Data Science Handbook : Essential Tools for Working with Data - 2016 - O'Reilly Media - https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=1425081 - nlebk - 1425081
- Christopher M. Bishop. (n.d.). Australian National University Pattern Recognition and Machine Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.EBA0C705