Mathematics for Economists

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Международный институт экономики и финансов

Статус:

Курс обязательный

Когда читается:

1-й курс, 1, 2 модуль

Преподаватели

Демешев Борис Борисович

Паламарчук Екатерина Сергеевна

Course Syllabus

Abstract

The objective of the course is to equip the students with the essential mathematical background for Economics, Econometrics and Finance: preliminaries on linear algebra, multivariate calculus, probability theory and statistics, dynamic optimization, and stochastic calculus. Prerequisites include undergraduate level mathematics: Calculus (both single and multi-dimensional), Linear Algebra, Probability theory and Mathematical Statistics, Ordinary Differential Equations.

Learning Objectives

• Get acquainted with the essential mathematical tools for Economics, Econometrics and Finance
• Develop skills at solving differential equations and systems of differential equations
• Understand the dynamics induced by systems of differential equations
• Become familiar with basic methods on optimal control theory and dynamic programming and their applicability in economic theory
• Become familiar with Brownian and Wiener stochastic processes and Ito’s integral, both at a preliminary theoretical level, and in terms of simple applications

Expected Learning Outcomes

• Apply statistical methods to economic tasks
• Solve problems of calculus of variations as well as optimal control theory
• Become familiar with the main elementary notions related to matrices and linear algebra that are employed in Economics and Econometrics
• Become familiar with the main elementary ideas and techniques for constrained optimization that are employed in Economics
• Solve elementary ordinary differential equations and understand the dynamics induced by a system of equations
• Understand the balancing of intertemporal trade-offs via the Euler equation and the recursive formulation of the problems via Bellman's equation
• Solve problems of calculus of variations and optimal control theory, and interpret the multiplier function as a reflection of incentives

Course Contents

• Theory of probability and statistics
• Elements of linear algebra
• Elements of calculus
• Differential Equations
• Dynamic Optimization in Continuous Time
• Dynamic Optimization in Discrete Time
• Uncertainty, information, and stochastic calculus

Assessment Elements

• Homework (Section 7)
• Homework (Sections 4,5,6)
• Test (Sections 2,3)
• Exam (Section 7)
• Homework (Sections 2,3)
• Quizzes (Section 1)
• Test (Sections 4,5,6)
• Test (Section 1)

Interim Assessment

• 2025/2026 1st module
  0.041 * Homework (Sections 2,3) + 0.25 * Homework (Sections 4,5,6) + 0.005 * Quizzes (Section 1) + 0.16 * Test (Section 1) + 0.124 * Test (Sections 2,3) + 0.42 * Test (Sections 4,5,6)
• 2025/2026 2nd module
  0.6 * 2025/2026 1st module + 0.35 * Exam (Section 7) + 0.05 * Homework (Section 7)

Bibliography

Recommended Core Bibliography

• Dynamic optimization : the calculus of variations and optimal control in economics and management, Kamien, M. I., 2012
• Econometric methods, Johnston, J., 2007
• Economic growth, Barro, R. J., 2004
• Introduction to modern economic growth, Acemoglu, D., 2009
• Mathematics for economists, Simon, C. P., 1994

Authors

• Demeshev Boris Borisovich
• ZASORIN ALEKSANDR IGOREVICH
• PALAMARCHUK EKATERINA SERGEEVNA