## Essential Mathematics for Global LeadersⅠ［17S1000］

科目名Course Title 授業言語Language Essential Mathematics for Global LeadersⅠ［17S1000］Essential Mathematics for Global LeadersⅠ English 共通科目（前期課程） 博士課程共通 2.0単位 1～3年

 月曜 3 ～ 4 限 人間文化研究科棟408室

Powerpoint hands-out. Will be distributed at each class.

その他=その他=Attendance, Reports.

Understand background Probability used in Statistics
Use and understand various Null Hypothesis Significance Tests (NHST)
Use confidence intervals
Understand the limitation and caveat of Confidence Intervals and NHST
Understand and use (simple) Linear Regression (単) 線形回帰
Become autonomous to study and learn more Statistical tools.

1. Notions of Probability.　必要な確率論
2. Random Variables. Examples (discrete and continuous).　確率変数（離散と連続）
3. Sampling Distribution, Point estimation. Maximum likelihood. Central Limit Theorem.

4. Null Hypothesis Significant Test帰無仮説検定
One-sample tests: z-test, chi2-test for variance, small and large Student t-tests.
More than one-sample tests: t-test (equal variance), paired data, F-test, chi2 for goodness- of-fit, chi2 for independence, One-way ANOVA).
5. Confidence Intervals. 信頼区間
Comparison with NHST. Case of polling.
6. Linear regression. 線形回帰
7. Additional topics (if time allows): multivariate analysis, non-linear model.

A strong background in Mathematics is not necessary (basically, high-school, 1st year level in Calculus should be enough). Therefore, besides students from Math, Computer Science, Physics, Chemistry, students from Nutrition, Life Science department are also welcome.