# Category: r/math

## Why are natural transformation diagrams commutative ?

I just started learning about category theory. I have no problem understanding the concept of category and of functor, and I can also see how functors make a category, but I struggle with the definition of natural transformations. The part about choosing a morphism in Mor(F(X), G(X)) for each X in the first category makes sense to me, but why does the diagram have to commute ? Is it in order to respect something else ? Or is it just because of convenience ?

submitted by Nevin Manimala Nevin Manimala /u/lonelygenius

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## “Spectral graph theory” by Fan R. K. Chung

What are your opinions on this book? Is it worth reading, or is there some other useful book about spectral graph theory?

submitted by Nevin Manimala Nevin Manimala /u/derrdi

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## Any numerical analysis course out there in the Internet?

Of all the MOOC and online learning platforms I know of, only OCW apparently was able to display a course on numerical analysis, 18.330 Introduction to Numerical Analysis. edX, Udacity and Coursera delivered little to no results.

I am an independent learner and would eagerly learn about the subject. Do you know any interesting and sound course on it? Alternatively, some textbooks to follow? I much appreciate them for their exhaustivity, with the only downside of not imposing a fixed schedule to follow.

submitted by Nevin Manimala Nevin Manimala /u/al_taken

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## “Review of unsteady transonic aerodynamics: Theory and applications” by Oddvar O. Bendiksen [PDF]

## Galois Prime Extensions Correspondence

## Where to find resources on mathematical puzzles like this?

1) 6-sided die (sides: 1, 2, 3, 4, 5, 6), roll and win $x depending on the side facing up. How much are you willing to pay to play this game?

2) If we play a game in which Player 1 picks a number 1-11, and then player 2 can add 1-11 to that (i.e. player 1 picks 5, player 2 can add to make it 6-16), what is the strategy to win this game if Player 1 wants to make 60?

Looking for a collection of similar questions or significantly challenging ones relative to these.

submitted by Nevin Manimala Nevin Manimala /u/letsgobaby

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## What are some cool mathematical coincidences?

## Complex Analysis Summer Study Group?

Hey /r/math, I will be studying Gamelin’s Complex Analysis this summer in preparation for graduate school. While I enjoy studying immensely, I find that it can be a very lonely experience. Would anybody be interested in joining a study group? I was thinking we could create a google drive folder and submit our answers to problems and have a discord or whatsapp or something to discuss further. I would expect that you would know at least some real analysis, and would have a substantial amount of time to devote to solving problems. If I get at least five people interested I’ll start this up. You can comment or PM me.

submitted by Nevin Manimala Nevin Manimala /u/McTestes68

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## Arzelà–Ascoli

Looking over my notes for real at the stuff I didn’t understand, Arzelà–Ascoli was the worst offender.

Wikipedia has a great article on it, but the proof they give (at least from what I can understand) isn’t general enough to deal with compact sets in abitrary metric spaces as opposed to just R^{n.}

Here are the two statements: Consider a sequence of real-valued continuous functions { fn }n ∈ N defined on a closed and bounded interval [a, b] of the real line. If this sequence is uniformly bounded and equicontinuous, then there exists a subsequence { fnk }k ∈ N that converges uniformly.

And the sequential version from my class: Let A be a compact set in a metric space (M, d), and suppose (fk) is a sequence of functions fk : A −→ R which is bounded and equicontinuous. Then (fk) has a uniformly convergent subsequence

Any help would really be apreciated

submitted by Nevin Manimala Nevin Manimala /u/sectandmew

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