2023年12月10日发(作者：2016宁夏一模数学试卷)

FUNDAMENTALS OF ECONOMIC MATHEMATICS

SYLLABUS

I. Course Description

The studying course Mathematics for Economists is an important part in economical

education. The course has to give students skills of implementation of mathematical

knowledge and practice to economic problems both theoretical and applied ones. Its

prerequisites are both knowledge and skills of one variable calculus and linear algebra

including general theory of systems of linear equations and matrix algebra.

The course covers several variables calculus and selected topics of theory and application of

deferential and divergence equations. The contents of the course have to teach students to

investigate different comparative-static problems, optimization problems and dynamic

problems with developed mathematical tools.

II. Textbook and Other Required Materials:

III. Objectives:

By the end of the autumn semester a student has to know the principal results of several

variable calculi, including calculation of partial derivatives of both explicit and implicit

functions, solving both unconstrained and constrained optimization problems. A student has

to be able to apply calculus to different comparative static problems, to find maximizes and/or

minimizes of several variable functions; to apply the Lagrange multipliers approach to

constrained optimization problems.

By the end of the spring semester a student has to know the principal methods of dynamic

analysis of economic processes, main concepts and results of differential and difference

equations. A student has to be able to find solutions of linear differential and difference

equations, analyze their stability. A student has to have skills of implementation above

mentioned mathematical concepts to solution of microeconomics\' and macroeconomics\'

problems.

IV. Methods of Instruction

The course program consists of lectures, classes and regular students\' work without assistance.

The latter means thinking over lectures\' material, their extension and doing of assignments

given by the teacher. During each term there will be two mid-session exams. V. Attendance Procedure

Attendance, promptness, and participation in all accounting classes are prerequisites to

success both in relation to a student\'s grade and to a student\'s ultimate success in the

business world. Poor attendance, arriving late consistently, and lack of participation can affect

a student\'s grade. If you come to class late, make sure you notify your instructor after class

that you attended class; otherwise, you will be marked absent.

VI. Methods of Evaluation

The exam will take place sometime after the end of the math part .It will consist of both

theory and exercises. More weight will be given to exercises. In every lecture, a set of

compulsory exercises will be handed out to be answered by next week. You are strongly

advised to understand well the theory before attempting the exercises. There is one thing I

expect at the exams: You have to be able to solve exercises. The material we cover here is

crucial to most aspects of economic theory. It is almost impossible to understand most of

other areas of economic analysis (micro, macro, I.O. to mention just a few) unless you have a

grasp of both static and dynamic mathematical tools. That is why exercises (both exam and

weekly ones) will take up about 70% of the total mark for mathematics, whereas theory will

be given the remainder. Beware though. You cannot solve exercises unless you have

understood well the theory.

VII. Course Outline:

1. Relations, Orderings and Cardinality

2. Topology, Continuity and Metric Spaces

3. Compactness

4. Complete Metric Spaces and Banach Fixed Point Theorem

5. Hemi-Continuity and the Maximum Theorem

6. Brouwer and Kakutani Fixed Point Theorems

7. Characteristic Roots

8. Difference and Differential Equations

9. Inner Product and Orthogonality

10. Hyperplanes and Strong Separation

11. Cones and Farkas Lemma

12. Minkowski Separation and Support

13. Constrained Optimization and the Implicit Function Theorem

14. The Lagrangian and Kuhn-Tucker

15. Value Function and Envelop Theorems

16. Market Demand and the Slutsky Decomposition

17. Intro to Dynamic Programming (I)

18. Intro to Dynamic Programming (II) International Journal on Mathematical Economics such as

i. Journal of Mathematical Economics

ii. Journal of Economics Theory

iii. Journal of Economics and Business

iv. Journal of Mathematical Finance

v. Journal of Econometrics

vi. Mathematical Social Sciences

vii. Economics Modelling

viii. Economics Letters

ix. Economics Theory

x. Game Theory


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