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41 個評分

Kirill Bukin

提供方

Mathematics for economists

俄罗斯国家研究型高等经济大学

課程信息

32,330 次近期查看

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

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中級

完成時間大約為26 小時

英語（English）

字幕：阿拉伯語（Arabic）, 法語（French）, （歐洲人講的）葡萄牙語, 中文（簡體）, 意大利語, 越南語, 韓語, 德語（German）, 俄語（Russian）, 土耳其語（Turkish）, 英語（English）, 西班牙語（Spanish）

講師

授課教師評分

4.28/5 （7 個評分）

Kirill Bukin

Associate Professor, Candidate of sciences (phys.-math.)

Faculty of Economic Sciences, Department of Theoretical Economics

23,587 個學生

1 門課程

可分享的證書

完成後獲得證書

100% 在線

立即開始，按照自己的計劃學習。

可靈活調整截止日期

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中級

完成時間大約為26 小時

英語（English）

提供方

俄罗斯国家研究型高等经济大学

HSE University 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.

教學大綱 - 您將從這門課程中學到什麼

週

週 1

完成時間為 4 小時

The basics of the set theory. Functions in Rn

Week 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.

完成時間為 4 小時

12 個視頻（總計 117 分鐘）, 2 個閱讀材料, 1 個測驗

12 個視頻

About the University1分鐘

Promo1分鐘

1.1. Definitions and examples of sets14分鐘

1.2. Operations on sets9分鐘

1.3. Open balls in Rn9分鐘

1.4. Sequences in Rn. Closed sets.10分鐘

1.5. Bounded and compact sets10分鐘

1.6. Functions and level curves in Rn16分鐘

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

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

1.9. Composite function.12分鐘

1.10. Continuity of a composite function3分鐘

2 個閱讀材料

About the University10分鐘

Rules on the academic integrity in the course10分鐘

週

週 2

完成時間為 4 小時

Differentiation. Gradient. Hessian.

Week 2 of the Course is devoted to the main concepts of differentiation, gradient and Hessian.

完成時間為 4 小時

13 個視頻（總計 115 分鐘）

13 個視頻

2.1. Differentiation. Partial differentiation.7分鐘

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

2.3. Tangent plane.7分鐘

2.4. Total differential.7分鐘

2.5. Chain rule for multivariate functions.8分鐘

2.6. Gradient of the function.9分鐘

2.7. Economic applications of the gradient.9分鐘

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

2.9. Chain rule for differentiation.10分鐘

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

2.11. Second-order derivatives.10分鐘

2.12. Young's Theorem.5分鐘

2.13. Hessian matrix.5分鐘

1 個練習

Limits. Derivatives. Continuity1小時

週

週 3

完成時間為 3 小時

Implicit Function Theorems and their applications.

Week 3 of the Course is devoted to implicit function theorems. In this week three different

完成時間為 3 小時

12 個視頻（總計 93 分鐘）

12 個視頻

3.1. Implicit functions.7分鐘

3.2. Implicit Function Theorem.5分鐘

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

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

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

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

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

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

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

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

3.11. Example of application in microeconomics.6分鐘

3.12. Cramer's rule.2分鐘

週

週 4

完成時間為 4 小時

Unconstrained and constrained optimization.

Week 4 of the Course is devoted to the problems of constrained and unconstrained optimization.

完成時間為 4 小時

15 個視頻（總計 112 分鐘）

15 個視頻

4.1. Introduction in optimization.10分鐘

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

4.3. Unconstrained optimization.9分鐘

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

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

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

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

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

4.9. Example of Hessians (part 2).4分鐘

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

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

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

4.13. Constrained optimization.9分鐘

4.14. Lagrangian.5分鐘

4.15. Example of constrained optimization problem.4分鐘

1 個練習

Partial derivatives and unconstrained optimization.1小時

週

週 5

完成時間為 3 小時

Constrained optimization for n-dim space. Bordered Hessian.

Week 5 of the Course is devoted to the extension of the constrained optimization problem to the

完成時間為 3 小時

13 個視頻（總計 99 分鐘）

13 個視頻

5.1. Example of the solution of the constrained optimization.6分鐘

5.2. Weierstrass theorem. Compact sets.7分鐘

5.3. Bordered Hessian.9分鐘

5.4. Constrained optimization in general case (part 1).5分鐘

5.5. Constrained optimization in general case (part 2).6分鐘

5.6. Application of the bordered Hessian in the constrained optimization.7分鐘

5.7. Generalization of the constrained optimization problem for the n variables case.8分鐘

5.8. Example of constrained optimization for the case of more than two variables (part 1).7分鐘

5.9. Example of constrained optimization for the case of more than two variables (part 2).9分鐘

5.10. Example of constrained optimization problem on non-compact set.5分鐘

5.11. Theorem for determining definiteness (positive or negative) or indefiniteness of the bordered matrix.5分鐘

5.12. Example of application bordered Hessian technique for the constrained optimization problem.8分鐘

5.13. Example of violating NDCQ.10分鐘

週

週 6

完成時間為 2 小時

Envelope theorems. Concavity and convexity.

Week 6 of the Course is devoted to envelope theorems, concavity and convexity of functions.

完成時間為 2 小時

11 個視頻（總計 85 分鐘）

11 個視頻

6.1. Envelope Theorem.8分鐘

6.2. Envelope Theorem for constrained optimization.4分鐘

6.3. Examples of the Envelope Theorem application (part 1).7分鐘

6.4. Examples of the Envelope Theorem application (part 2).6分鐘

6.5. Interpretation of the Lagrangian multiplier.10分鐘

6.6. Relaxing assumptions using second order conditions.8分鐘

6.7. Concave and convex functions.7分鐘

6.8. Concave and convex functions in n-dimensional case.7分鐘

6.9. Inequality for concave function in n-dimensional space.9分鐘

6.10. Criteria of concavity and convexity of the function in n-dimensional space.5分鐘

6.11. Properties of concave functions.7分鐘

週

週 7

完成時間為 3 小時

Global extrema. Constrained optimization with inequality constraints.

Week 7 of the Course is devoted to identification of global extrema and constrained optimization

完成時間為 3 小時

11 個視頻（總計 96 分鐘）

11 個視頻

7.1. How to identify global extrema? (part 1)11分鐘

7.2. How to identify global extrema? (part 2)10分鐘

7.3. How to identify global extrema? (part 3)12分鐘

7.4. How to identify global extrema? (part 4)10分鐘

7.5. Constrained optimization with inequality constraints.8分鐘

7.6. Binding constraints. Complementary slackness conditions.5分鐘

7.7. Constrained optimization problem with inequalities for n-dimensional space.7分鐘

7.8. Constrained optimization problem with inequalities. Theorem.6分鐘

7.9. Example of solving constrained optimization problem with inequalities (part 1).9分鐘

7.10. Example of solving constrained optimization problem with inequalities (part 2).10分鐘

7.11. Example of solving constrained optimization problem with inequalities (part 3).3分鐘

週

週 8

完成時間為 3 小時

Kunh-Tucker conditions. Homogeneous functions.

Week 8 of the Course is devoted to Kuhn-Tucker conditions and homogenous functions. This

完成時間為 3 小時

9 個視頻（總計 80 分鐘）

9 個視頻

8.1. Kuhn-Tucker conditions.7分鐘

8.2. Solving consumer choice problem using Kuhn-Tucker conditions (part 1).9分鐘

8.3. Solving consumer choice problem using Kuhn-Tucker conditions (part 2).11分鐘

8.4. Solving minimization costs problem using Kuhn-Tucker conditions (part 1).9分鐘

8.5. Solving minimization costs problem using Kuhn-Tucker conditions (part 2).7分鐘

8.6. Homogeneous functions.6分鐘

8.7. Homogeneous functions. Two propositions.5分鐘

8.8. Income-consumption curve.10分鐘

8.9. Euler's Theorem.12分鐘

1 個練習

Kuhn-Tucker conditions. Concavity, convexity.1小時

審閱

4.2

11 條評論

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4 stars
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3 stars
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1 star
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來自MATHEMATICS FOR ECONOMISTS的熱門評論

由 MI 提供2019年8月31日

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

由 CG 提供2020年12月29日

This course is very tough for me. I want to leave this course. Please, do the needful.

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Mathematics for economists

Mathematics for economists

課程信息

講師

Kirill Bukin

提供方

俄罗斯国家研究型高等经济大学

教學大綱 - 您將從這門課程中學到什麼

週 1

The basics of the set theory. Functions in Rn

週 2

Differentiation. Gradient. Hessian.

週 3

Implicit Function Theorems and their applications.

週 4

Unconstrained and constrained optimization.

週 5

Constrained optimization for n-dim space. Bordered Hessian.

週 6

Envelope theorems. Concavity and convexity.

週 7

Global extrema. Constrained optimization with inequality constraints.

週 8

Kunh-Tucker conditions. Homogeneous functions.

審閱

來自MATHEMATICS FOR ECONOMISTS的熱門評論

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熱門在線課程

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Mathematics for economists

Mathematics for economists

課程信息

講師

Kirill Bukin

提供方

俄罗斯国家研究型高等经济大学

教學大綱 - 您將從這門課程中學到什麼

週 1

The basics of the set theory. Functions in Rn

週 2

Differentiation. Gradient. Hessian.

週 3

Implicit Function Theorems and their applications.

週 4

Unconstrained and constrained optimization.

週 5

Constrained optimization for n-dim space. Bordered Hessian.

週 6

Envelope theorems. Concavity and convexity.

週 7

Global extrema. Constrained optimization with inequality constraints.

週 8

Kunh-Tucker conditions. Homogeneous functions.

審閱

來自MATHEMATICS FOR ECONOMISTS的熱門評論

常見問題

Coursera Footer

熱門在線課程

熱門在線專項課程

在線證書

在線學位課程

Coursera

社區

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