Mathematics and Statistics for International Development Engineering Mathematics and Statistics for International Development Engineering

文字サイズ小中大

担当教員: 山下幸彦

使用教室: 木7-8(S611)

単位数: 講義：2 演習：0 実験：0

講義コード: 70042

シラバス更新日: 2015年2月12日

講義資料更新日: 2015年2月12日

学期: 後期

概要

講義概要

Please take the presentation slide of this lecture from

http://www.ide.titech.ac.jp/~yamasita/MMS/

Linear algebra (eigenvalue problem, singular value decomposition, generalized inverse matrix),
statistics (estimation and test),
and optimization technique (gradient method, conjugate gradient method, and quasi-Newton method) are lectured.

講義の目的

The objective of this course is to provide fundamental optimization technique
and statistics to handle various quantities with respect to international development.
In order to understand those knowledges, basic mathematics for them is also provided.

講義計画

1. Introduction
2. Eigenvalue decomposition and singular value decomposition
3. Generalized inverses of matrix
4. Probability (Definition of Random variable)
5. Estimator (Maximum likelihood estimator and Bayesian estimator)
6. Cramer-Rao lower bound
7. Principle component analysis
8. Regression
9. Testing
10. Statistical learning theory
11. Maximum gradient method and Conjugate gradient method
12. Newton method and Quasi-Newton method
13. Lagrange’s method and Karush–Kuhn–Tucker condition
14. Dual problem
15. Penalty method

教科書・参考書等

Copy of slide is prepared

成績評価

Attendance
Homework
Report