Master
2022/2023

# Mathematics for Economists

Type:
Compulsory course (Financial Economics)

Area of studies:
Economics

Delivered by:
International College of Economics and Finance

When:
1 year, 1, 2 module

Mode of studies:
offline

Open to:
students of one campus

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 module0.005 * 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 module0.85 * Exam (Section 7) + 0.15 * 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