About this Course
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Intermediate Level

Approx. 34 hours to complete

Suggested: 8 weeks of study...

English

Subtitles: English
User
Learners taking this Course are
  • Economists
  • Financial Analysts
  • Financial Advisors
  • Data Scientists
  • Accountants
User
Learners taking this Course are
  • Economists
  • Financial Analysts
  • Financial Advisors
  • Data Scientists
  • Accountants

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 34 hours to complete

Suggested: 8 weeks of study...

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
4 hours to complete

The basics of the set theory. Functions in Rn

11 videos (Total 116 min), 1 quiz
11 videos
1.1. Definitions and examples of sets14m
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
2
5 hours to complete

Differentiation. Gradient. Hessian.

13 videos (Total 115 min), 2 quizzes
13 videos
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
1 practice exercise
Limits. Derivatives. Continuity1h
Week
3
4 hours to complete

Implicit Function Theorems and their applications.

12 videos (Total 93 min), 1 quiz
12 videos
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
4
5 hours to complete

Unconstrained and constrained optimization.

15 videos (Total 112 min), 2 quizzes
15 videos
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
1 practice exercise
Partial derivatives and unconstrained optimization.1h
4.7
4 ReviewsChevron Right

Top reviews from Mathematics for economists

By MISep 1st 2019

The Best Course for Economists and Mathematicians and Coursera is an excellent platform for learners.

Instructor

Avatar

Kirill Bukin

Associate Professor, Candidate of sciences (phys.-math.)
Faculty of Economic Sciences, Department of Theoretical Economics

About National Research University Higher School of Economics

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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

Frequently Asked Questions

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