Why Mathematics?

• Math is useful
• Math trains your mind

believe vs feel

Essense of learning — real story

A function \(f(x)\) is continuous at a point \(c\) if …

Textbook version:

for any \(\epsilon > 0\), there is \(\delta > 0\)
such that
any \(x\) with \(|x - c| < \delta\) also satisfies \(|f(x) - f(c)| < \epsilon\)

Student version：

\(\epsilon > 0\), \(\delta > 0\), \(|x - c| < \delta\), \(|f(x) - f(c)| < \epsilon\)

delivery vs learning outcome

How to make the content fun?

fun programming applications

Theory ––––––––––––––-> Applications

Fun \(=\) learned something

https://www.youtube.com/watch?v=ZQ12ESNoy5k

https://www.youtube.com/watch?v=_L8roj-8HfM

• Video 1 by Jephian Lin: teaching only
• Video 2 by Eddie Woo: teaching \(+\) learning

Any questions?

• no questions
• don't understand, don't want to ask
• I don't know where I don't understand.

Group discussion

• groups of 2 –>
• groups of 4 –>
• unexpected answers
• free-rider

What happens?

• Charisma
• Fluent English
• Logical delivery

rapport \(+\) clear instruction

\(=\)

Mathematics is discussable!

ICQs

Instruction Checking Questions

Where are we going at the next intersection?

CCQs

Concept Checking Questions

If you would like to enjoy the beautiful views, which route would you choose?

Rapport

The first clas is IMPORTANT!

Not your fault…

• clear instruction
• rapport
• students
• classroom
• course content

But there are rooms for improvement –> PDCA

First class: Build the mindset

• M istakes make you smarter.
• A sk questions.
• T hink carefully.
• H elp each other.

We are bound to learn together.

First class: Scaffolded self instroduction

• How are you?
• My name is _____ .
• My major is _____ .
• Assign the group.
• ChatGPT: Please tell me some applications of linear algebra in _____ .

Activities: Run the definition

Activities: Collaborative computation

• Each group get a different exercise.
• The final answer depends on each group's result.

\({\bf u}_1 = \begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\), \({\bf u}_2 = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}\)

\({\bf v}_1 = \begin{bmatrix} 5 \\ 9 \\ 13 \\ 17 \end{bmatrix} = c_1\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} + c_2\begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}\)

\(c_1 = ?\), \(c_2 = ?\)

Activities: Yes-No jigsaw

• Is this set linear independent? Case of yes
• Is this set linear independent? Case of no

Why we need so many teachers?

• Push students to work hard
• Motivate students to learn more
• Offer customized advice based on the needs

Be a student again

If you got a chance to learn the subject again, how would you learn it…?