灰

今天如常地搞 workshop，由一開始的 5 人，減少至今天的 3 人。有一班 (3 個) 原打算今天來的，但因為種種原因今天不想來。沒差，3 個就 3 個，氣氛還算不錯，一氣呵成把第 4 課講完。

希望下一次 workshop 人數不會比今天更低。以下為 ``syllabus"。

Some Example from the net

Drawing midway arrow:

\usepackage{tikz}
\usetikzlibrary{decorations.markings}

fix the comma in mathptmx

\usepackage{mathptmx}

\mathcode`,"8000

\begingroup

\lccode`\~`\,\lowercase{\endgroup

\def~{\mathpunct{\textrm{,}}}}

\usepackage{eucal}

\begin{document}

\showoutput

,$,$

\end{document}

Tikz 的軟件

無意中發現一套名為 tikzedt 的軟件。

http://www.tikzedt.org/quicktour.html

很方便，不用自己預先設計座標，也把一些搜尋需時的指令放在一個清單上。

為了熟習一下，自製的 vector 版小丑神頭像誔生！

http://ihome.ust.hk/~cclee/document/siuchausang.pdf

Record some code

Equations share the same numbering with theorems with ntheorem package

\newtheorem{thm}{Theorem}[section]
\numberwithin{equation}{section}
\makeatletter
\let\c@equation\c@thm
\makeatother

**********

change the font of sections, subsections, chapter to \sf
\usepackage{sectsty}
\allsectionsfont{\sffamily}

Updated notes in analysis (PW: My ITSC)

I am expanding the notes last year (still working in progress, and should be finished at the beginning of July):
http://ihome.ust.hk/~cclee/document/WorkshopinAnalysis.pdf

Last year I stopped at littlewood's 3 principles (last section in measurable functions). Having the preparation last year, I plan to quickly go through abstract outer measure and measure (skip some of the proofs which can be copied word by word) and go directly into some important extension theorem on "pre-measure" and "pre-sigma algebra" (in my case, semi-ring), they will be used in the construction of product measure.

My schedule is the following sequence:

Basic Measure Theory
1. Outer measure and Measure
2. Integration
3. Construction of particular measure, go back to R^n
4. ???
5. ???
6. Duality of L^p space on sigma-finite measure space
(possibly need Radon–Nikodym, so 4, 5 may be signed measure and relevant theorems, that's will be big task).

Measure and Topology
7. Brief review of topology material (if necessary)
8. Facts and measure on locally compact Hausdorff space
9. Try to prove the Riesz-Markov theorem
http://en.wikipedia.org/wiki/Riesz_representation_theorem

Hopefully (???) if I have time I plan to apply knowledge in functional analysis and the Riesz-Markov theorem to show Haar measure always exists on compact group, which is unique up to a +ve-constant.

The workshop will begin at the middle of July, and as before, I would ask Kin Li to book me a room. If you are to-be year 2 students and also want to join us, it would be better to digest the material in chapter 2 and 3. We will apply some of the technique implicitly.

Workhop in Analysis

正準備第二次 workshop 的 notes。上一個暑假邊教邊製作 notes，進度緩慢之餘，到後期沒有動力由頭 develop 那些已經用慣的 theorem (所以沒有教 integration)。有了上次經驗，今次 workshop 在 abstract outer measure, measure 還有 measurable function 的 proof 不用重覆再教 (照抄可也)，所以 focus 可放在 extension of set function 和 integration。因為所認識的同學都有學 topology，我打算一起學 locally compact hausdorff space 和在這類 space 上的 measure theory。一年前很``粗略"地讀過一次，故大概知道這些 theory ``發生甚麼事"。正打算以 rudin 的 approach 學學看...。