Offered By

National Research University Higher School of Economics

About this Course

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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....

Start instantly and learn at your own schedule.

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Suggested: 8 weeks of study...

Subtitles: English...

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 8 weeks of study...

Subtitles: English...

Week

1Week 1 of the Course is devoted to the main concepts of the set theory, operation on sets and functions in Rn. Of special attention will be level curves. Also in this week introduced definitions of sequences, bounded and compact sets, domain and limit of the function. Also from this week students will grasp the concept of continuous function....

10 videos (Total 114 min), 1 quiz

1.2. Operations on sets9m

1.3. Open balls in Rn9m

1.4. Sequences in Rn. Closed sets.10m

1.5. Bounded and compact sets10m

1.6. Functions and level curves in Rn16m

1.7. Domain and limit of a function. Continuous functions.13m

1.8. Continuity of a function. Weierstrass theorem.13m

1.9. Composite function.12m

1.10. Continuity of a composite function3m

Week

2Week 2 of the Course is devoted to the main concepts of differentiation, gradient and Hessian.
Of special attention is the chain rule. Also students will understand economic applications of the
gradient....

13 videos (Total 115 min), 2 quizzes

2.2. Example of differentiation. Cobb-Douglas function.9m

2.3. Tangent plane.7m

2.4. Total differential.7m

2.5. Chain rule for multivariate functions.8m

2.6. Gradient of the function.9m

2.7. Economic applications of the gradient.9m

2.8. Equation of a circumference. Smooth curves.13m

2.9. Chain rule for differentiation.10m

2.10. Linear approximation. Example of tangent plane for particular function.10m

2.11. Second-order derivatives.10m

2.12. Young's Theorem.5m

2.13. Hessian matrix.5m

Limits. Derivatives. Continuitym

Week

3Week 3 of the Course is devoted to implicit function theorems. In this week three different
implicit function theorems are explained. This week students will grasp how to apply IFT
concept to solve different problems....

12 videos (Total 93 min), 1 quiz

3.2. Implicit Function Theorem.5m

3.3. Applications of the Implicit Function Theorem (part 1).10m

3.4. Applications of the Implicit Function Theorem (part 2).7m

3.5. Gradient is perpendicular to a level curve of a function.11m

3.6. Implicit function theorem for the function of many variables.6m

3.7. Example of application of the IFT for the function of many variables.8m

3.8. Implicit Function Theorem for the system of implicit functions. Jacobian matrix.10m

3.9. Example of application IFT for the system of implicit functions (part 1).8m

3.10. Example of application IFT for the system of implicit functions (part 2).7m

3.11. Example of application in microeconomics.6m

3.12. Cramer's rule.2m

Week

4Week 4 of the Course is devoted to the problems of constrained and unconstrained optimization.
Of special attention are quadratic forms, critical points and their classification....

15 videos (Total 112 min), 2 quizzes

4.2. Global max. Local max. Saddle point.9m

4.3. Unconstrained optimization.9m

4.4. Critical point. Taylor's formula.12m

4.5. Quadratic forms. Positive definiteness. Negative definiteness.7m

4.6. Sylvester's criterion (part 1).7m

4.7. Sylvester's criterion (part 2).5m

4.8. Examples of Hessians (part 1).7m

4.9. Example of Hessians (part 2).4m

4.10. Sufficient condition for a critical point to be a local maximum, a local minimum and neither of both.7m

4.11. Examples of finding and classification of critical points (part 1).6m

4.12. Examples of finding and classification of critical points (part 2).4m

4.13. Constrained optimization.9m

4.14. Lagrangian.5m

4.15. Example of constrained optimization problem.4m

Partial derivatives and unconstrained optimization.m

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more.
Learn more on www.hse.ru...

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