Mathematics for Economics and Business

Bachelor 2021/2022

Category 'Best Course for New Knowledge and Skills'

Type: Compulsory course (HSE University and Kyung Hee University Double Degree Programme in Economics and Politics in Asia)

Area of studies: Foreign Regional Studies

Delivered by: Faculty of World Economy and International Affairs

Where: Faculty of World Economy and International Affairs

When: 1 year, 1, 2 module

Mode of studies: offline

Open to: students of one campus

Instructors: Ivan Deseatnicov

Language: English

ECTS credits: 3

Contact hours: 60

Full Syllabus

Abstract

No Pre-requisites required but familiarity with basic algebra and calculus is assumed. Anyone who interested in basic mathematics is always welcome. The course consists of three parts. In the first, we introduce some concepts from linear algebra. The second part is devoted to multivariate calculus constrained static optimization. The last section provides an introduction to differential equations and dynamic systems. This course covers the basic mathematical tools that are used in classical and modern economics analysis and econometrics. By the end of this course, students are expected to master a number of derivations techniques, and this mastering comes only at the price of doing a sizable number of exercise. The instructor is there to help you through the learning process.

Learning Objectives

To introduce the key mathematical theories that are applied in economic analysis such as equilibrium analysis, linear algebra, and calculus
To develop the mathematical maturity so that students are not intimidated by mathematical notations and abstractions
To develop intuition, creativity, critical thinking and problem-solving skills of students

Expected Learning Outcomes

Lessons learned by students: a. Student understands the meaning of market equilibrium b. Student can solve one and two-commodity market equilibrium models
Lessons learned by students: a. Students can apply Kuhn-Tucker conditions for Nonlinear programming b. Students know economic applications of nonlinear programming
Lessons learned by students: a. Students can apply the envelope theorem for unconstrained optimization b. Students know the Roy’s identity and Shephard’s lemma
Lessons learned by students: a. Students can distinguish the ingredients of a mathematical model b. Students understand the real-number system c. Students understand the concept of sets d. Students can identify relations and functions
Lessons learned by students: a. Students can find differentials and total derivatives b. Students can find derivatives of implicit functions c. Students can conduct a comparative statics analysis of general-function models
Lessons learned by students: a. Students can find extreme values of a function of two variables b. Students can solve the problem of multiproduct firms
Lessons learned by students: a. Students can find relative maximum and minimum of a function b. Students know Maclaurin and Taylor series
Lessons learned by students: a. Students can find stationary values b. Students understand quasiconcavity and quasiconvexity c. Students know homogeneous functions
Lessons learned by students: a. Students know logarithmic and exponential functions b. Students can find derivatives of logarithmic and exponential functions
Lessons learned by students: a. Students understand the concept of a derivative b. Students can identify continuity and differentiability of a function
Lessons learned by students: Students can perform various matrix and vector operations; Students know different types of matrices; Students understand the concept of nonsingularity; Students can calculate determinants of different orders; Students can apply the Gaussian method to solve system of linear equations and to find an inverse matrix; Students can find the inverse matrix by expansion of s determinant by alien cofactors; Students can solve the system of linear equations by Cramer’s rule

Course Contents

Introduction
Equilibrium Analysis
Linear Models and Matrix Algebra
Differentiation and Comparative Statics
Comparative Statics of General Function Models
Optimization and Equilibrium
Exponential and Logarithmic Functions
Multivariable optimization
Optimization with Equality Constraints
Non-Linear Programming and Kuhn-Tucker conditions
Duality and the Envelope Theorem

Assessment Elements

Assignments
Attendance
COMMUNICATION CRITERIA In case any urgent issue arises, better address it to the instructor directly. Most of the non-urgent issues might be resolved by contacting teaching assistant (TA), either via e-mail or via any other means announced later. For instance, if for some reason you want to leave during the classes, address to the instructor. Being absent / late for the classes, inquire deadlines for Home Assignments, any technical issues – better address to TA.
Midterm test
Final Exam
Platforms: Zoom, Socrative и Gradescope

Interim Assessment

2021/2022 2nd module
0.11 * Attendance + 0.29 * Midterm test + 0.4 * Final Exam + 0.2 * Assignments

Bibliography

Recommended Core Bibliography

Sydsæter, K., & Hammond, P. J. (2016). Essential Mathematics for Economic Analysis (Vol. Fifth edition). Harlow, United Kingdom: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1419812

Recommended Additional Bibliography

Jacques, I. (2015). Mathematics for Economics and Business (Vol. 8th ed). Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419610

Course Syllabus