| 週次 |
授課內容 |
| 第1週 |
Product space: Product measure, Fubini’s theorem
|
| 第2週 |
Holiday(Peace Memorial day) |
| 第3週 |
Product space: Convolution
|
| 第4週 |
The Radon-Nikodym theorem: Hahn decomposition theorem, The Radon-Nikodym theorem
(MID report1) |
| 第5週 |
The Radon-Nikodym theorem: Lebesgue decomposition theorem, Bounded linear functional
|
| 第6週 |
Fourier transforms: The inversion theorem, The Plancherel theorem |
| 第7週 |
Holiday(Observed holiday for NCHU Anniversary & Sports meet) |
| 第8週 |
Online class: Banach spaces: The Hahn-Banach theorem
(MID report2) |
| 第9週 |
Banach spaces: Baire’s theorem and consequences |
| 第10週 |
Hilbert spaces: Inner products, Orthonormal sets |
| 第11週 |
Hilbert spaces: Fourier series |
| 第12週 |
MIDTERM |
| 第13週 |
Probability: Definition, Independence(Lecture) |
| 第14週 |
Probability: Weak/Strong law of large numbers, Conditional expectation(Presentation) |
| 第15週 |
Probability: Martingales, Weak convergence(Presentation) |
| 第16週 |
Online Class: Probability: Characteristic functions(Lecture)] |
| 第17週 |
Probability: Central limit theorem, Kolmogorov extension theorem(Presentation) |
| 第18週 |
Probability: Brownian motion(Lecture) |