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How to Read Mathematics

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Re: How to Read Mathematics

#11

Post by whatshisface »

catnaroek wrote: post #8
vinchuco wrote: post #5

I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.

Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.

That's true, but there are many situations where you don't know if you really need to understand it until you've skimmed it or otherwise have read enough to know what's in it.

Re: How to Read Mathematics

#12

Post by vinchuco »

catnaroek wrote: post #8
vinchuco wrote: post #5

I disagree with 'do not read too fast': Skim all. Skim again the next day. But the third time, get pencil and paper and take notes, and effort. If it's neither uncomfortable nor exciting, you're doing it wrong.

Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.

Context matters https://en.wikipedia.org/wiki/Principia_Mathematica

Re: How to Read Mathematics

#13

Post by criloz2 »

sillysaurus3 wrote: post #9
catnaroek wrote: post #8

Earlier quoted context omitted.

Just... no. If you actually have to understand it (rather than, say, peer-review it), then make a honest attempt to understand it right from the beginning. For instance, suppose it takes you 30 minutes to skim through a chapter of a math book. Then you've wasted 30 minutes you could've spent understanding the chapter's first section.

What if everyone learns differently?

haha true, I envy people that just sit down read a book/chapter/article/blog linearly and then comes enlightened, I can't, I need to first Skim almost 90% of the material, and then start again from the bottom, reading the last part and trying to figure out how the first part is connected or are important for understand what is written.

I think that people that read it linearly don't miss important info, but I just can't

Re: How to Read Mathematics

#14

Post by CamperBob2 »

zitterbewegung wrote: post #3

How I read Mathematics. First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf. First you want to see if this paper is even worth read…

How I read Mathematics. First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf.

Short of bugging the author, you can also go to Wikipedia's entry for SciHub and see what their latest known domain suffix and/or IP address is.

Re: How to Read Mathematics

#15

Post by nicklaf »

Iv wrote: post #4
zitterbewegung wrote: post #3

How I read Mathematics. First try to find the paper. First use http://front.math.ucdavis.edu . If you can't find it then use google scholar. If that fails then go on the authors academic website. If that fails then see if the author is live and try to contact them. Then repeat for their grad students. If all else fails post it to r/math or HN and ask for the pdf. First you want to see if this paper is even worth read…

Also a very good advice I had received a long time ago but that I had dismissed until recently: some articles are just badly written. The author sometimes forget to mention what B actually is, changes the meaning of the multiplication operator implicitly, assumes the formula given is inside an integral.... I could go on. A maths article is an article. A lot are imperfect, quite a few are bad. Some times it is not the…

I remember reading this exact piece of advice, but have been trying to remember where.

Would anybody be able to provide the blog post I believe we both read, which says almost exactly what Iv wrote? I could have sworn Michael Nielson wrote it, but I was unable to produce it last time I searched. So I am following OP's advice and am asking here. :P

Re: How to Read Mathematics

#16

Post by sulam »

I’m curious if anyone has advice on how to understand all the symbols used in math papers. Frequently I find this is the first barrier for me in reading them.

Re: How to Read Mathematics

#17

Post by kalid »

sulam wrote: post #16

I’m curious if anyone has advice on how to understand all the symbols used in math papers. Frequently I find this is the first barrier for me in reading them.

Shameless plug, I write about math on BetterExplained.com

For each symbol, I try to make an analogy. For "e", for example, I have the notion of "continuous growth". The formal definition is this:

https://betterexplained.com/ColorizedMath/content/img/E_(mat...

"The base for continuous growth is the unit quantity earning unit interest for unit time."

Once you see the role of each part of the definition, the idea snaps into place. I just wrote about it here: https://betterexplained.com/articles/colorized-math-equation...

Hope that helps!

Re: How to Read Mathematics

#18

Post by catnaroek »

sulam wrote: post #16

I’m curious if anyone has advice on how to understand all the symbols used in math papers. Frequently I find this is the first barrier for me in reading them.

Remember that these symbols stand for something, i.e., they must be defined somewhere. Make sure that you can either remember the definition or consult it whenever you need it.

Re: How to Read Mathematics

#19

Post by catnaroek »

kalid wrote: post #17
sulam wrote: post #16

I’m curious if anyone has advice on how to understand all the symbols used in math papers. Frequently I find this is the first barrier for me in reading them.

Shameless plug, I write about math on BetterExplained.com For each symbol, I try to make an analogy. For "e", for example, I have the notion of "continuous growth". The formal definition is this: https://betterexplained.com/ColorizedMath/content/img/E_(mat... "The base for continuous growth is the unit quantity earning unit interest for unit time." Once you see the role of each part of the definition, the idea snaps…

> For each symbol, I try to make an analogy.

Analogies are utterly unhelpful without a thorough understanding of the actual definitions.

Re: How to Read Mathematics

#20

Post by kalid »

catnaroek wrote: post #19
kalid wrote: post #17

Earlier quoted context omitted.

Shameless plug, I write about math on BetterExplained.com For each symbol, I try to make an analogy. For "e", for example, I have the notion of "continuous growth". The formal definition is this: https://betterexplained.com/ColorizedMath/content/img/E_(mat... "The base for continuous growth is the unit quantity earning unit interest for unit time." Once you see the role of each part of the definition, the idea snaps…

> For each symbol, I try to make an analogy. Analogies are utterly unhelpful without a thorough understanding of the actual definitions.

Analogies on their own are limited if you don't continue to the technical definition. They are a raft to cross the river.
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