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Regular version of the site
Master 2021/2022

Mathematics for Economists

Type: Compulsory course (Financial Economics)
Area of studies: Economics
When: 1 year, 1, 2 module
Mode of studies: offline
Open to: students of one campus
Instructors: Kirill Bukin, Boris Demeshev, Victor A Lapshin, Alexander Zasorin, Peio Zuazo-Garin
Master’s programme: Financial Economics
Language: English
ECTS credits: 7
Contact hours: 112

Course Syllabus


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

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

Expected Learning Outcomes

  • Apply multidimensional calculus, optimization to economic problems
  • 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

Course Contents

  • Multidimensional calculus, basics of optimization
  • Convex analysis and Kuhn-Tucker theorem
  • Linear Algebra
  • Theory of probability and statistics
  • Differential Equations
  • Dynamic Optimization in Continuous Time
  • Dynamic Optimization in Discrete Time
  • Uncertainty, information, and stochastic calculus
Assessment Elements

Assessment Elements

  • non-blocking home assignments
  • non-blocking refersher test
  • blocking Final exam
    Online format.
  • non-blocking Midterm Examination
Interim Assessment

Interim Assessment

  • 2021/2022 1st module
    0.25 * home assignments + 0.33 * refersher test + 0.42 * Midterm Examination
  • 2021/2022 2nd module
    0.15 * home assignments + 0.4 * Final exam + 0.25 * Midterm Examination + 0.2 * refersher test


Recommended Core Bibliography

  • Dynamic optimization : the calculus of variations and optimal control in economics and management, Kamien, M. I., 2012
  • Economic growth, Barro, R. J., 2004
  • Introduction to modern economic growth, Acemoglu, D., 2009
  • Mathematics for economists, Simon, C. P., 1994
  • Statistics for business and economics, Newbold, P., 2003

Recommended Additional Bibliography

  • Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004