京都大学 京都大学

Mathematics for Economic and StatisticalAnalysis

Numbering Code G-ECON31 5A106 LE43
G-ECON31 5A106 LE55 		Year/Term 2022 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language English Day/Period Wed.4
Instructor name KAZUMURA TOMOYA (Graduate School of Economics Senior Lecturer)
Outline and Purpose of the Course This is an introductory course in mathematics for economic and statistical analysis. The course covers linear algebra, optimization, and probability, and provides basic mathematical tools often used in economic and statistical analysis. In the course we do not focus on proofs of theorems. We rather focus on how mathematical concepts are used in the context of economics and statistics.
Course Goals By the end of this course, students are expected to understand basic mathematical concepts and be able to use them to solve problems in economic and statistical analysis.
Schedule and Contents This course consists of three topics.

1. Linear algebra (Weeks 1 to 4)
a) Matrices and their basic properties
b) Linear (in)dependence and rank of a matrix
c) Determinant of a matrix
d) Eigenvalues, eigenvectors, and decomposition
e) Quadratic forms and definite matrices

2. Optimization (Weeks 5 to 9)
a) Derivative of functions of one variable
b) Partial derivative and total derivative of multivariable functions
c) Convexity and concavity
d) Optimization: Lagrange multiplier method
e) Dynamic optimization: Dynamic programming and optimal control

3. Probability (Weeks 10 to 14)
a) Probability
b) Random variables
c) Parametric distributions
d) Multivariate distributions


Week 15:Final exam

Week 16:Feedback
Evaluation Methods and Policy Grading will be based on homework (50%) and final exam (50%).
Course Requirements Undergraduate level mathematics for economics.
Study outside of Class (preparation and review) Students are expected to read lecture materials before the class.
Textbooks Textbooks/References Lecture materials will be distributed in class.
References, etc. Linear algebra and optimization:
1. Chiang, A. C. and K. Wainwright (2005) "Fundamental methods of mathematical economics," McGraw Hill Higher Education, ISBN: 978-0071238236.
2. Sundaram, R. K. (1996) "A first course in optimization theory," Cambridge University Press, ISBN: 978-0521497701.
Dynamic optimization:
3. Alogoskoufis, G. "Dynamic macroeconomics," The MIT Press, ISBN: 978-0262043014.
Probability:
4. Hansen, B. E. (2022) "Probability and statistics for economists," Princeton University Press, ISBN: 978-0691235943.
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