An Infinitely Large Napkin
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An Infinitely Large Napkin
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Re: An Infinitely Large Napkin
#2Adding this here as it may be of related interest for those who enjoyed the massive math cheat sheet on the front page recently.
Evan Chen, a math student at MIT, wrote up what would be considered field notes for higher mathematics. The full PDF is here[1], complete with a dependency graph showing what you need to know before reading any particular section.
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1. https://usamo.files.wordpress.com/2019/02/napkin-v15-2019022...
Re: An Infinitely Large Napkin
#3This is supposed to be aimed at high school students.
I majored in math in college, and yet there were things which I could not decipher in the first few pages of chapter 1. For example, on page 43, what is "nonzero residues modulo p"? I guess you start with something, divide by p, and get a remainder, or residue. But what is that something? Going back to page 41, I see the hint that Z is the set of integers. I vaguely kind of remember that this was a thing that you learned once and just used forever. I had long forgotten that Z is the set of integers. I don't really see where this is clearly stated in this book.
If I was writing this for a high school student to skim through, I would make a big deal that Z is the set of integers, and Z is going to be used many times going forward, and it will always mean the same thing, the set of integers.
Someone who just learned all this stuff would be able to skim through it.
But the way it's written now, it's going to take a lot of intense work for a high school student, or someone who majored in math many years ago, to work through the whole thing.
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Edit: I see now. The prerequisites are in Appendix E. Technically, it's in there. But it's still problematic. High school books can just be read from beginning to end. For college level texts, it's OK to tuck things in Appendix E, and require the reader to go back and forth. So, no, I still would not say this is really aimed at the high school level.
Re: An Infinitely Large Napkin
#4This is supposed to be aimed at high school students. I majored in math in college, and yet there were things which I could not decipher in the first few pages of chapter 1. For example, on page 43, what is "nonzero residues modulo p"? I guess you start with something, divide by p, and get a remainder, or residue. But what is that something? Going back to page 41, I see the hint that Z is the set of integers. I vague…
The fact that Z denotes the set of integers is a sort of mathwide standard. It comes up a lot (number theory, group theory) Did you major in some specific area of maths? Or is it just the span of years between?
Re: An Infinitely Large Napkin
#5This is supposed to be aimed at high school students. I majored in math in college, and yet there were things which I could not decipher in the first few pages of chapter 1. For example, on page 43, what is "nonzero residues modulo p"? I guess you start with something, divide by p, and get a remainder, or residue. But what is that something? Going back to page 41, I see the hint that Z is the set of integers. I vague…
The fact that Z denotes the set of integers is a sort of mathwide standard. It comes up a lot (number theory, group theory) Did you major in some specific area of maths? Or is it just the span of years between?
Many, many years. Also, it's a thing in college. I don't think they talked about this much in high school when I was there. If they did, they started each book with a review, "Z is the set of integers".
Re: An Infinitely Large Napkin
#6Earlier quoted context omitted.
The fact that Z denotes the set of integers is a sort of mathwide standard. It comes up a lot (number theory, group theory) Did you major in some specific area of maths? Or is it just the span of years between?
Many, many years. Also, it's a thing in college. I don't think they talked about this much in high school when I was there. If they did, they started each book with a review, "Z is the set of integers".
I agree with you that for anyone who recently took math in college, it's obvious that Z is the set of integers. But for someone just learning it? Not so much.
Re: An Infinitely Large Napkin
#7This is supposed to be aimed at high school students. I majored in math in college, and yet there were things which I could not decipher in the first few pages of chapter 1. For example, on page 43, what is "nonzero residues modulo p"? I guess you start with something, divide by p, and get a remainder, or residue. But what is that something? Going back to page 41, I see the hint that Z is the set of integers. I vague…
The fact that Z denotes the set of integers is a sort of mathwide standard. It comes up a lot (number theory, group theory) Did you major in some specific area of maths? Or is it just the span of years between?
There's also the shifting of high school curriculum over time. I don't have kids so I haven't kept up with it, but from what I've picked up in the news maths education has changed radically in the 30 years since I was in school. Definitions and techniques in this article may be considered common knowledge now, since testing is more standardized at a national level.
Re: An Infinitely Large Napkin
#8[deleted]
Re: An Infinitely Large Napkin
#9Thank you, this is awesome, very readable.
Re: An Infinitely Large Napkin
#10This is awesome, thanks! My learning style is to read summaries of things and then go deeper where I feel like. I'm not a fan of reading 20 pages of proofs that don't teach me anything new, only to reach half a page that takes me 3 hours to get through. A book which is basically a massive cheat sheet is perfect for reading as if I'm skimming a much larger work.