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Higher School of Economics

Mathematics for Economists

Higher School of Economics via XuetangX

Overview

本课程是未来经济学家本科教育的重要组成部分,对于想要获得数学知识的研究生来说也很有帮助。该课程使学生能够将数学知识和专长应用于经济学问题。学习本课程的先决条件是掌握单变量微积分知识和线性代数基础,包括矩阵运算和联立方程组的基本理论,了解一些向量空间的知识对于理解本课程也有帮助。


课程内容涵盖多变量微积分,包括有约束和无约束优化。课程旨在教导学生掌握比较静态问题和利用已掌握的数学工具进行优化问题的解决。每周都会布置家庭作业。


本课程的目标是帮助学生在数学领域获取知识,并使他们准备好分析模拟和真实的经济情况。


在这门课上,学生可以通过具体的例子和练习来学习如何使用和应用数学。此外,这门课程还向学生展示了什么构成严谨的证明,并且帮助学生训练和提高提出证明的能力。通过这门课程,你会发现数学并不只是照本宣科的“菜谱”。正相反,对数学概念的深入探索有助于我们理解现实生活中的不同情况。


如您对本课程有任何意见和建议,欢迎联系[email protected]


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.


Please feel free to contact us via [email protected].


Syllabus

  • Introduction. Information about the course
    • WEEK 1: The basics of the set theory. Functions in Rn
      • WEEK 2: Differentiation. Gradient. Hessian
        • WEEK 3. Implicit Function Theorems and their applications
          • WEEK 4: Unconstrained and constrained optimization
            • WEEK 5. Constrained optimization for n-dim space. Bordered Hessian
              • WEEK 6: Envelope theorems. Concavity and convexity
                • WEEK 7. Global extrema. Constrained optimization with inequality constraints
                  • WEEK 8. Kunh-Tucker conditions. Homogeneous functions

                    Taught by

                    Kirill Bukin

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