Lecture Notes

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====== Aug 23: what is math for physics and engineering? ======

Is math useful for physics? Well, math is born out of physics. As the Russian mathematical physicist [[https://www.math.fsu.edu/~wxm/Arnold.htm | V.I. Arnold says]].

Is math useful for chemistry? I don't know much about chemistry, except that electron rotates around nuclei, and one needs some wavefunction to describe the quantum states of electron. So chemistry needs physics, hence needs math? 

Is math useful for computer science?
  * Shannon's information theory is about probability
  * AI needs probability
  * gradient descent, neural network, needs calculus and linear algebra. 

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So, why do //you// take this course? (sure, it might be required to get your degree). Here are my questionaire. I would like to know more about you:

1. What do you find interesting or exciting about the field(i.e. major) that you are in? 

2. What direction do you want to explore, to learn? 

3. What kind of math do you need to do that? 


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A little story. I was a physics undergrad, but I was deeply attracted by fancy words, like 'manifold' 'Riemannian geometry', 'Einstein', 'entropy', so I took some math classes then. In grad school, as experimental physicist student, I often hear people say 'confidence interval', 'p-value', so I audited a stat class. So one motivation for me to learn stuff, is to know what other people are talking about. Curiosity? Or FIFO (fear of missing out)? 

So, what are you curious about? excited about? Can you tell us about it? I am all ears. 

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How about ChatGPT? Suppose AI can answer all the questions that I ask in this class, perfectly, do we still need to learn math and do math 'by hand'? 

Yes, doing math by hand is like 
  - hiking a trail instead of flying a drone over it
  - making a pottery instead of buying in a store
  - eat in a restraurent, rather than reading the review

You need to know how to do it yourself, before letting someone or some tool to do it for you. 

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That's about it. Tomorrow I will talk about some review of linear algebra. 

   * what is a vector space? 
   * what is a linear map? 
   * what is a matrix? matrix multiplication? 

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Oh, in case you are bored in class, read this [[http://www.paulgraham.com/greatwork.html | How to do great work]], which I believe all of you have potential to do.
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