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Master 2022/2023

# 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: Boris Demeshev, Alexander Zasorin, Peio Zuazo-Garin
Master’s programme: Financial Economics
Language: English
ECTS credits: 6
Contact hours: 86

### 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 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

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

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

• 2022/2023 1st module
0.005 * Quizzes (Section 1) + 0.124 * Test (Sections 2,3) + 0.041 * Homework (Sections 2,3) + 0.25 * Homework (Sections 4,5,6) + 0.42 * Test (Sections 4,5,6) + 0.16 * Test (Section 1)
• 2022/2023 2nd module
0.85 * Exam (Section 7) + 0.15 * Homework (Section 7) #### 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