2025/2026

Abstract Mathematics 1

Type: Minor

Delivered by: International College of Economics and Finance

Open to: students of all HSE University campuses

Instructors: Dmitri Piontkovski

Language: English

Course Syllabus

Abstract

Abstract Mathematics is a two-semester course for the third year bachelor’s programme students who selected specialization Economics and Mathematics. The course is taught in English. For the theory itself there are no pre-requisites except for an aptitude for logical reasoning. However, many examples will reference concepts from Calculus, Statistics, Mathematics for Economists and Linear Algebra courses from the 1st and 2nd years of the ICEF bachelor’s programme. The emphasis of the course is on the theory rather than on the method. One central topic of the course is formal mathematical reasoning. The students will practice formulating precise mathematical statements and proving them rigorously. These skills are essential for the current specialization, they often remain in shadows in other math courses where the focus is on solving problems through calculation. The second central topic of the course is the abstract mathematical structures from algebra (groups, fields, etc.), analysis, topology (topological spaces, manifolds), and mathematical logic. We will develop some of these theories roughly to the extent of standard 1st and 2nd -year courses of the mathematical departments. The awareness of the theoretical foundations of these classical theories is key in understanding the contemporary theoretical research and the synergies between different areas of mathematics and its applications.