又一張

又搵得返以前嘅作品：

New Note

新增 differentiation II，主要是 Taylor Series。

Tutorial Notes 建立中 ...

topic 順序到時再定。

1. set, informal logic and function
2. countability
3. infimum and supremum
4. sequences
5. continuous functions
6. differentiation I
7. differentiation II
8. riemann integral I
9. riemann integral II
10. riemann integral III
11. Midterm/Final Review

Record a useful code:

\newtheorem{ex}[thm]{Example}

\usepackage{xparse}

\ExplSyntaxOn

    \NewDocumentEnvironment{exam} { o }

     {\IfNoValueTF{#1}

     {\begin{ex}\begin{oframed}}{\begin{ex}[#1]\begin{oframed}}

     \ignorespaces

     }

     {\end{oframed}\end{ex}}

\ExplSyntaxOff

Teaching Evaluation~

一 sem 一度，evaluation 報告有 11 種評分---都不重要～每次焦點都在於最後的那些 comment (如有)。把 Math3033 兩個 section 的 comment 放在一起：

What was good about the TA?

1. Best TA ever!
2. TA is very cute and smart. He is also very responsible. Even though there are only a few students coming to the tutorial, he is still working hard and explains everything in a very detailed way. I like him~
3. Tutorial notes were pertinent and posted online.
4. the ta has a very good understanding in this course. the examples he gave during tutorial were good,which boarder my horizon in the field. the ta was also willing to answer questions,nevertheless,he was so funny which made the tutorial much enjoyable. I enjoyed his tutorial.
5. Clear explanation of materials Sometimes provide an interesting atmosphere for learning
6. He is a very responsible TA.
7. Solid knowledge

How might the TA improve?

1. Better time control over students' presentations.
2. The exercises should be more related to the exams.
3. Materials used might be a bit difficult

有些 comment 蠻長的～這一年度我把 tutorial notes 裁減得異常精簡，所以學生對 tutorial notes 沒甚麼意見，以前 notes 太長或內容太豐富反而有學生會美言幾句 (有點矛盾 ...)。每一個 sem 學生總會在 "good" 那一欄提到 solid knowledge，而這一個 sem 意外地沒有人對我的英語有意見。

Improvement 那有兩點是沒法辦到的。presentation 的時間我已盡量控制，已盡力令他們不能超時，也設法幫他們加速 (如有人嘗試把一段長長的數式用英語讀一遍，我會叫他/她直接稱它為 "this expression")。其次是 exercise 不可能和考試有很大關聯 --- 因為 kin li 會把 notes 的所有問題掃一眼，出題盡量和 exercise 不相似 (當然基本概念必定一樣，但解題的技巧就不同)。最後是，material 的難度真的簡單得不能再簡單了 -w-。

To be used in tutorial

The following is a standard result for functions of bounded variation. If $g$ is continuous then we can still show this without resorting to any known result for functions of bdd variation:

Problem. Let $g\in C[a,b]$ and let $\Lambda:C[a,b]\to \mathbb R$ be a linear function given by \[
\Lambda(f)=\int_a^b f(x)g(x)\,dx.
\] Show that \[
\|\Lambda\|:=\sup\left\{\left|\int_a^b f(x)g(x)\,dx\right|:
f\in C[a,b], \sup_{x\in [a,b]}|f(x)|\leq 1\right\}=\int_a^b |g(x)|\,dx.\]