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Math Basics for Computer Science and Machine Learning [pdf]

cis.upenn.edu

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Re: Math Basics for Computer Science and Machine Learning [pdf]

#41

Post by emmanueloga_ »

In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval.

The point is, understanding integrals and derivatives doesn't require one to memorize all the mechanical rules. Using software to compute those functions can be a huge time saver. No one should go with pen an paper double checking if that polynomial integral is correct or not!

With a book almost 2000 pages long, I wonder if this books leans more heavily on the mechanical-rules side of math. In my mind, is the difference between writing a book such that you can write your own wolfram alpha, or writing a book so you can just use it.

Re: Math Basics for Computer Science and Machine Learning [pdf]

#43

Post by MAXPOOL »

emmanueloga_ wrote: post #41

In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval. The point is, understanding integrals and derivatives doesn't require one to memorize all the mechanical rules.…

You don't need to memorize rules when studying math. Just like you don't need to spend any time to memorize syntax for programming languages. You automatically remember things you use a lot.

Once you have spent countless hours doing exercises to the extent that you understand the math, you already remember the rules. If you have not spent countless hours doing exercises, you don't understand anything at this level.

You don't hire a programmer who has read all the books and 'understands' programming but has never programmed. It's the same with math. You don't just read a math book from start to finish. You can use wolfram alpha for visualizing functions, not for learning math.

Re: Math Basics for Computer Science and Machine Learning [pdf]

#44

Post by djaychela »

meuk wrote: post #42

Whoah, this covers a lot. I was expecting some linear algebra, calculus, and discrete math, but there's actually some stuff in there I don't know after doing a masters in math.

That makes me feel somewhat better - I saw the title of 'Maths Basics' and thought 'Great!'... then I saw it's 1,962 pages - if that's the basics, how much is the intermediate and advanced bit?

Re: Math Basics for Computer Science and Machine Learning [pdf]

#45

Post by worldsayshi »

jointpdf wrote: post #25

“Math Basics” is quite the misnomer—it gives the impression that one would need to study all of the contents of this book to be an effective practitioner in CS or ML. Memorizing every definition and theorem in this book would be neither necessary nor sufficient for that purpose. Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math book like this (do the math). This is mor…

A friend with a math msc aluded at this, that it's kind of a math meme to call material "basic" or "introduction to" for rather advanced stuff.

I feel like it's some kind of misguided intellectual humility. Kind of feels vaguely related to how so many Haskell packages are version "0.*".

Re: Math Basics for Computer Science and Machine Learning [pdf]

#46

Post by langitbiru »

PopeDotNinja wrote: post #34
jointpdf wrote: post #25

“Math Basics” is quite the misnomer—it gives the impression that one would need to study all of the contents of this book to be an effective practitioner in CS or ML. Memorizing every definition and theorem in this book would be neither necessary nor sufficient for that purpose. Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math book like this (do the math). This is mor…

This is book 1962 pages long. If this is basic, how long is the advanced book?!

It reminds me of Introduction to Algorithms, a classic book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest. It is over 1000 pages long. But they call it "Introduction..." :)

Re: Math Basics for Computer Science and Machine Learning [pdf]

#47

Post by plinkplonk »

MAXPOOL wrote: post #43
emmanueloga_ wrote: post #41

In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval. The point is, understanding integrals and derivatives doesn't require one to memorize all the mechanical rules.…

You don't need to memorize rules when studying math. Just like you don't need to spend any time to memorize syntax for programming languages. You automatically remember things you use a lot. Once you have spent countless hours doing exercises to the extent that you understand the math, you already remember the rules. If you have not spent countless hours doing exercises, you don't understand anything at this level. Y…

+ 100. I can't upvote this enough.

Programmers have spent countless hours practising programming to the point where they have forgotten how difficult it was in the beginning. A non programmer might think of programming as "memorizing hundreds of rules" to get anything done, but one doesn't learn programming by sitting around explicitly memorizing hundreds of rules and then begin to program.

Actually writing programs with a minimal set of 'rules' memorized and then adding more as needed is how one typically learns programming.

Re: Math Basics for Computer Science and Machine Learning [pdf]

#48

Post by kebman »

graycat wrote: post #28
SKILNER wrote: post #17

Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.

Here's what he is doing. He wants to start with the set of real numbers, intuitively the points on the line, usually denoted by R, maybe typed in some special font. Then he wants to define, say, addition of real numbers. So, given two real numbers, x and y, that might be equal, he wants to define x + y. So, here he wants to regard addition, that is, +, as an operation . Then, as is usual for defining operations, he w…

Here you go: ℝ

Re: Math Basics for Computer Science and Machine Learning [pdf]

#49

Post by kebman »

plinkplonk wrote: post #47
MAXPOOL wrote: post #43

Earlier quoted context omitted.

You don't need to memorize rules when studying math. Just like you don't need to spend any time to memorize syntax for programming languages. You automatically remember things you use a lot. Once you have spent countless hours doing exercises to the extent that you understand the math, you already remember the rules. If you have not spent countless hours doing exercises, you don't understand anything at this level. Y…

+ 100. I can't upvote this enough. Programmers have spent countless hours practising programming to the point where they have forgotten how difficult it was in the beginning. A non programmer might think of programming as "memorizing hundreds of rules" to get anything done, but one doesn't learn programming by sitting around explicitly memorizing hundreds of rules and then begin to program. Actually writing programs…

I've been teaching programming for five or six years now. I always start with HTML, then add CSS, and then add JavaScript. That way they experience mastery all the way, and see how they can be creative with the code. It's so great to see a pupil "get it" -- and sometimes even pupils that "suck at math" or even pupils who have problems spelling the most basic sentence correctly. In fact I've found that there's a strange correlation where pupils who have dyslexia often seem to be better than others at programming.
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