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Mathematics for economists

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Course Summary

This course is designed to teach mathematics specifically for economists, with topics ranging from calculus to optimization theory. Students will learn how to apply mathematical concepts to solve economic problems and interpret economic models.

Key Learning Points

Learn mathematical concepts specifically tailored for economists
Apply mathematical concepts to solve economic problems and interpret models
Gain a deeper understanding of calculus, linear algebra, and optimization theory

Learning Outcomes

Apply mathematical concepts to real-world economic problems
Create and interpret economic models using mathematical analysis
Develop a deeper understanding of calculus, linear algebra, and optimization theory

Prerequisites or good to have knowledge before taking this course

Basic understanding of algebra
Familiarity with calculus

Course Difficulty Level

Intermediate

Course Format

Online
Self-paced

Similar Courses

Statistics for Economists
Microeconomics Principles

Related Education Paths

Notable People in This Field

Nassim Nicholas Taleb
Paul Krugman

Related Books

Description

This course is an important part of the undergraduate stage in education for future economists. It's also useful for graduate students who would like to gain knowledge and skills in an important part of math. It gives students skills for implementation of the mathematical knowledge and expertise to the problems of economics. Its prerequisites are both the knowledge of the single variable calculus and the foundations of linear algebra including operations on matrices and the general theory of systems of simultaneous equations. Some knowledge of vector spaces would be beneficial for a student.

The course covers several variable calculus, both constrained and unconstrained optimization. The course is aimed at teaching students to master comparative statics problems, optimization problems using the acquired mathematical tools. Home assignments will be provided on a weekly basis. The objective of the course is to acquire the students’ knowledge in the field of mathematics and to make them ready to analyze simulated as well as real economic situations. Students learn how to use and apply mathematics by working with concrete examples and exercises. Moreover this course is aimed at showing what constitutes a solid proof. The ability to present proofs can be trained and improved and in that respect the course is helpful. It will be shown that math is not reduced just to “cookbook recipes”. On the contrary the deep knowledge of math concepts helps to understand real life situations. Do you have technical problems? Write to us: coursera@hse.ru

Outline

The basics of the set theory. Functions in Rn
About the University
Promo
1.1. Definitions and examples of sets
1.2. Operations on sets
1.3. Open balls in Rn
1.4. Sequences in Rn. Closed sets.
1.5. Bounded and compact sets
1.6. Functions and level curves in Rn
1.7. Domain and limit of a function. Continuous functions.
1.8. Continuity of a function. Weierstrass theorem.
1.9. Composite function.
1.10. Continuity of a composite function
About University
Rules on the academic integrity in the course

Differentiation. Gradient. Hessian.
2.1. Differentiation. Partial differentiation.
2.2. Example of differentiation. Cobb-Douglas function.
2.3. Tangent plane.
2.4. Total differential.
2.5. Chain rule for multivariate functions.
2.6. Gradient of the function.
2.7. Economic applications of the gradient.
2.8. Equation of a circumference. Smooth curves.
2.9. Chain rule for differentiation.
2.10. Linear approximation. Example of tangent plane for particular function.
2.11. Second-order derivatives.
2.12. Young's Theorem.
2.13. Hessian matrix.
Limits. Derivatives. Continuity

Implicit Function Theorems and their applications.
3.1. Implicit functions.
3.2. Implicit Function Theorem.
3.3. Applications of the Implicit Function Theorem (part 1).
3.4. Applications of the Implicit Function Theorem (part 2).
3.5. Gradient is perpendicular to a level curve of a function.
3.6. Implicit function theorem for the function of many variables.
3.7. Example of application of the IFT for the function of many variables.
3.8. Implicit Function Theorem for the system of implicit functions. Jacobian matrix.
3.9. Example of application IFT for the system of implicit functions (part 1).
3.10. Example of application IFT for the system of implicit functions (part 2).
3.11. Example of application in microeconomics.
3.12. Cramer's rule.

Unconstrained and constrained optimization.
4.1. Introduction in optimization.
4.2. Global max. Local max. Saddle point.
4.3. Unconstrained optimization.
4.4. Critical point. Taylor's formula.
4.5. Quadratic forms. Positive definiteness. Negative definiteness.
4.6. Sylvester's criterion (part 1).
4.7. Sylvester's criterion (part 2).
4.8. Examples of Hessians (part 1).
4.9. Example of Hessians (part 2).
4.10. Sufficient condition for a critical point to be a local maximum, a local minimum and neither of both.
4.11. Examples of finding and classification of critical points (part 1).
4.12. Examples of finding and classification of critical points (part 2).
4.13. Constrained optimization.
4.14. Lagrangian.
4.15. Example of constrained optimization problem.
Partial derivatives and unconstrained optimization.

Constrained optimization for n-dim space. Bordered Hessian.
5.1. Example of the solution of the constrained optimization.
5.2. Weierstrass theorem. Compact sets.
5.3. Bordered Hessian.
5.4. Constrained optimization in general case (part 1).
5.5. Constrained optimization in general case (part 2).
5.6. Application of the bordered Hessian in the constrained optimization.
5.7. Generalization of the constrained optimization problem for the n variables case.
5.8. Example of constrained optimization for the case of more than two variables (part 1).
5.9. Example of constrained optimization for the case of more than two variables (part 2).
5.10. Example of constrained optimization problem on non-compact set.
5.11. Theorem for determining definiteness (positive or negative) or indefiniteness of the bordered matrix.
5.12. Example of application bordered Hessian technique for the constrained optimization problem.
5.13. Example of violating NDCQ.

Envelope theorems. Concavity and convexity.
6.1. Envelope Theorem.
6.2. Envelope Theorem for constrained optimization.
6.3. Examples of the Envelope Theorem application (part 1).
6.4. Examples of the Envelope Theorem application (part 2).
6.5. Interpretation of the Lagrangian multiplier.
6.6. Relaxing assumptions using second order conditions.
6.7. Concave and convex functions.
6.8. Concave and convex functions in n-dimensional case.
6.9. Inequality for concave function in n-dimensional space.
6.10. Criteria of concavity and convexity of the function in n-dimensional space.
6.11. Properties of concave functions.

Global extrema. Constrained optimization with inequality constraints.
7.1. How to identify global extrema? (part 1)
7.2. How to identify global extrema? (part 2)
7.3. How to identify global extrema? (part 3)
7.4. How to identify global extrema? (part 4)
7.5. Constrained optimization with inequality constraints.
7.6. Binding constraints. Complementary slackness conditions.
7.7. Constrained optimization problem with inequalities for n-dimensional space.
7.8. Constrained optimization problem with inequalities. Theorem.
7.9. Example of solving constrained optimization problem with inequalities (part 1).
7.10. Example of solving constrained optimization problem with inequalities (part 2).
7.11. Example of solving constrained optimization problem with inequalities (part 3).

Kunh-Tucker conditions. Homogeneous functions.
8.1. Kuhn-Tucker conditions.
8.2. Solving consumer choice problem using Kuhn-Tucker conditions (part 1).
8.3. Solving consumer choice problem using Kuhn-Tucker conditions (part 2).
8.4. Solving minimization costs problem using Kuhn-Tucker conditions (part 1).
8.5. Solving minimization costs problem using Kuhn-Tucker conditions (part 2).
8.6. Homogeneous functions.
8.7. Homogeneous functions. Two propositions.
8.8. Income-consumption curve.
8.9. Euler's Theorem.
Kuhn-Tucker conditions. Concavity, convexity.

Summary of User Reviews

Read reviews of Mathematics for Economists course on Coursera. Learners are praising the course for being comprehensive and informative.

Key Aspect Users Liked About This Course

Comprehensive and informative course material

Pros from User Reviews

The course content is well-structured and covers a wide range of topics
The lectures are engaging and easy to follow
The course is taught by experienced instructors with a deep understanding of the subject matter

Cons from User Reviews

Some learners found the course to be too challenging, especially for those without a strong mathematical background
The quizzes and assignments can be time-consuming and difficult to complete
A few learners felt that the course could benefit from more interactive elements such as live discussions or group projects

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