Elementary Papers at ArXiv

Question

Inspired by this question, at MO i am asking this question.

Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i would like to see some interesting papers and articles to learn something new. If the paper is very much advanced then its of no use to me since i haven't learnt enough Math. I have been searching around for past two hours and i couldn't find a single paper which i could comprehend. Article which i would like to see:-

Interesting proofs of some Elementary number Theory results.
Interesting identity involving Infinite series.
Interesting articles in Basic Abstract Algebra ( concerning Groups and Rings.)
Your favorite article. ( Make sure its elementary enough!)

The best example of what type of articles i am looking for can be found in the answer given by Bill here:

Characterizing continuous functions based on the graph of the function

This is an interesting article. I really enjoyed reading it since i could understand it.

@Chandru1: Should this be tagged as big-list as well? Have flagged this for CW. — , Feb 10 '11 at 07:07
Why ArXiv? Lots of people have their papers online for free on their homepage. — Yuval Filmus, Feb 10 '11 at 07:25
To second Yuval's comment: why arXiv? You should get yourself to a library and browse the American Mathematical Monthly. — Willie Wong, Feb 10 '11 at 12:03
The American Mathematical Monthly has a lot of wonderful elementary-level articles. I second Willie Wong's suggestion. — Cheerful Parsnip, Feb 10 '11 at 15:16
Well, the thing(s) about the Monthly is that it is not free and it is not easily available online. A couple of years ago I became a member of the MAA for the first time, mostly because I was looking forward to the online access to the Monthly articles. But I was so disappointed by the limited, slow and buggy nature of their online archives that I actually cancelled my membership. Their response was interesting, essentially: "We understand and hope you will try us again later on when we get things in better order." Does anyone know if it has gotten better recently? — Pete L. Clark, Jul 08 '11 at 21:12
By the way, along with other people, I think a small perturbation makes for a much better question: Where can one find (freely, online) mathematical articles with a fighting chance to be understood by high school students and undergraduates? Maybe I'll ask this myself... — Pete L. Clark, Jul 08 '11 at 23:45

score 5 · Answer 1 · answered Feb 10 '11 at 11:37

5

A similar paper to Yuval's answer, which is also quite elementary, is Doyle (and Conway)'s Division by Three. I don't think it requires any advanced knowledge, and is rather interesting.

answered Feb 10 '11 at 11:37

Cheerful Parsnip

27,278

This is a lovely paper. – CommonerG Dec 30 '15 at 14:07

score 4 · Answer 2 · answered Jul 08 '11 at 20:21

4

I thought that What is special about the divisors of 24? was creative and fairly approachable.

answered Jul 08 '11 at 20:21

Charles

32,122

2

I saw this article and thought it was more or less equivalent to a popular question on this site! (But I recommend other papers by the same author: he is a serious mathematician who is clearly very committed to good exposition, so really it's all good.) – Pete L. Clark Jul 08 '11 at 21:14
1

@Pete: Which question? – Charles Jul 09 '11 at 05:10
1

$@$Charles: http://math.stackexchange.com/questions/855/for-any-prime-p-3-why-is-p2-1-always-divisible-by-24. – Pete L. Clark Jul 09 '11 at 05:27

score 4 · Answer 3 · answered Jul 09 '11 at 03:48

Depending on your tastes, there's a nice paper called Recounting the Rationals, by Calkin and Wilf. (Get it here, here, here or here.) I mention it as answer to your question because there's a blog post about it which says

If you are just learning to read math papers, or you think you might like to learn to read them, [this paper] would be a good place to start. It is serious research mathematics, but elementary. It is very short. The result is very elegant. The proofs are straightforward. The techniques used are typical and widely applicable; there is no weird ad-hockery. The discussion in the paper is sure to inspire you to tinker around with it more on your own. All sorts of nice things turn up. […] Check it out.

You should read the paper directly, but if you get stuck or would like more detail, there's also a six-part series about it (! 1, 2, 3, 4, 5, 6), Wikipedia, articles for further reading, etc.

score 2 · Answer 4 · answered May 19 '16 at 06:24

2

I enjoyed this one very much: How to compute $\sum 1/n^2$ by solving triangles

answered May 19 '16 at 06:24

Larara

1,492

score 2 · Answer 5 · answered Dec 19 '13 at 13:54

It is in the nature of modern mathematics to be fairly technical and therefore inaccessible to a novice, but the category "math.HO' at the arxiv sometimes contains papers readable by a non-expert. For example, I just looked through the recent papers in that category and found an interesting piece on "unity and disunity of mathematics" and there are many others.

score 1 · Answer 6 · answered Feb 10 '11 at 07:25

1

That's a bit of a stretch, but the beautiful paper Seven Trees in One by Andreas Blass (which has a faulty ArXiv version) is perhaps possible to understand up to section 4 (which is exactly where my understanding stops). The first three sections are not really difficult, even though they mention some abstract non-sense (which you can skip), some enumerative combinatorics (which you can also skip), and some really basic definitions in abstract algebra, which are unfortunately too "basic" to include in a normal course; but all you need to know about them is how to calculate within them. You also need to know some very basic set theory (mainly $\aleph_0^2 = \aleph_0$).

answered Feb 10 '11 at 07:25

Yuval Filmus

57,157

1

Hmm, I read the word "topos" in that article. I'm not convinced it "is perhaps possible to understand" it ;) – fosco Feb 10 '11 at 08:02
1

Topoi are only mentioned in section 4. Up to there it's truly elementary. – Yuval Filmus Feb 10 '11 at 10:02
What is faulty about the arXiv version? This is not a rhetorical question; I am being curious. – darij grinberg Jan 31 '14 at 21:40
The page is not set up properly, so the bottom lines go out of bounds. – Yuval Filmus Jan 31 '14 at 23:06

score 1 · Answer 7 · answered Dec 19 '13 at 12:45

1

If you like pizza, you might wanna look at: http://arxiv.org/abs/0812.2870

answered Dec 19 '13 at 12:45

roman

822

score 1 · Answer 8 · answered Dec 19 '13 at 15:24

1

I stumbled upon This one: http://arxiv.org/pdf/1312.3839.pdf which might fit the bill. The title is: "On the antiderivative of inverse functions" and at least parts of it is elementary.

answered Dec 19 '13 at 15:24

kjetil b halvorsen

6,625

Dave L. Renfro · Answer 9 · 2021-04-01T04:52:31.207

0

Sometime in the near future I plan on posting a paper in the General Mathematics section that may be what you're looking for, but for the time being you can find the paper here.

edited Apr 01 '21 at 04:52

answered Jul 08 '11 at 21:57

Dave L. Renfro

36,843

In case anyone wondered what happened to that manuscript (whose original URL I gave is now a dead link, so I've replaced it with one that currently works), I put a fair amount of effort into trying to get an endorsement after originally writing this answer, for example see this 1 June 2011 sci.math post, and I finally gave up. – Dave L. Renfro Apr 01 '21 at 04:55

Elementary Papers at ArXiv

9 Answers9

Linked