From here and there, I sometimes encounter mathematical papers that are readable by me, an undergraduate student in Mathematics, which don't go into much specializations in specific fields, which I usually find quite interesting. Some examples are: D.I.E paper, DwD paper and this one. I would be glad if someone could provide me with a list of such papers to read or point to a source which does.

• Many papers in the MAA journals (The Monthly, Mathematics Magazine, College Math Journal) would qualify. – Gerry Myerson Dec 6 '16 at 8:14
• @GerryMyerson It would be better any of these were available for free reading. – bat_of_doom Dec 6 '16 at 8:20
• They are, if your university library has a subscription. – Gerry Myerson Dec 6 '16 at 11:10
• Here's a link to scads of papers written by undergraduates as part of the University of Chicago REU program: math.uchicago.edu/~may/REU2016 I found this by just typing $$\rm{ reu\ papers\ math}$$ into Google, there's probably lots more out there. – Gerry Myerson Dec 7 '16 at 0:26
• REU papers aren't always well-written enough to be "readable by undergraduates"; you'd have to sift the chaff from the wheat just as much as with research papers (in my experience). That said, May's page is a great resource, if you are willing to do that sifting. – darij grinberg Dec 14 '16 at 10:38

See the following link: MAA awards

You will find a long list of awarded expository articles published by MAA journals (like the College Mathematics Journal, the Mathematics Magazine, and the American Mathematical Monthly). Among these awards I recommend the Paul R. Halmos - Lester R. Ford Awards and the Carl B. Allendoerfer Awards.

From my experience :

1. I hear Mathematical Intelligencer is good but I have never read it.

2. I have heard that reading things that you don't completely understand is good for mathematicians so I also recommend the Notices of the AMS.

3. Plus is a math themed magazine. I feel doubtful it would prepare you for graduate school in any way.

4. College Mathematics Journal

5. Mathematics Magazine

6. American Mathematical Monthly.
Also the Pi Mu Epsilon Journal would make a very good read. I would also recommend reading Mathematical Spectrum.

I would suggest

Manjul Bhargava, The factorial function and generalizations. Amer. Math. Monthly 107 (2000), no. 9, 783--799

It's quite likely that the function $f:[1707, 2016] \cap \mathbb{N} \to [0,1] \cap \mathbb{Q}$ given by

$$f(t) = \frac{\text{# of published research papers written in year} \ t \ \text{readable by current undergraduate students}}{\text{# of published research papers written in year} \ t}$$

is decreasing. Therefore, it would perhaps be in your interest to look for older research papers. Moreover, reading older papers helps provide some historical context as to how mathematics got to where it is today. I feel that this is indispensable for an undergraduate to know.

(Fun fact: Euler was born in $1707$)

If you're interested in applied mathematics, the SIAM Review publishes annual articles on current and significant research, which are often written by preeminent scholars in the field (and accompanied by a great number of references). Although it is not free, most institutions have subscriptions to it. In addition, if you are an undergraduate, you may be able to get a free student membership to SIAM, which grants access to the Review.

Although some articles are not written at an undergraduate level, I find that the Survey and Review papers often are. Here are some recent, well-written reviews and surveys likely to be of interest:

My two tips would sound more-less like this: 1) Try to read some articles concerning metrics, or functional equations, basic number theory, as they do not require deep, intensive research to understand the very idea behind the given reasoning. 2) Don't divulge into some fuzzy logic, pde or stuff which generally requires a lot of theoretical basis.

You can use http://www.ams.org/mrlookup to find something which would catch your interest.

Thomas J. Osler (yes, THAT Osler for those who are into long distance running) has a lot of papers freely available that would be suitable. By looking up the homepages of the authors listed in the bibliographies of these papers, you should find a few other people who have similar freely available lists of papers. Keep repeating this, and very soon you'll get a large number of papers.

(To address concern raised in comment) My intent is to show you "how to fish" rather than "giving you a fish". The idea is to search for people and not just for papers. Look at the authors of papers (in whatever areas of math you're interested in) that are published in the journals in which Osler's papers appear (these are journals that tend to publish the kinds of papers you are interested in), and visit these people's homepages. For most journals, you don't need to have university library access or get past paywalls to look at the table of contents (to see the titles and the authors of the papers in the journal).

• Most of the papers from the site are related to applied analysis and some of them are from perhaps algebra-precalculus. What I intended to ask was papers from every field, such as number-theory, linear and abstract algebra, combinatorics, graph-theory, etc. which don't use terms and results studied explicitly by graduate students. Examples can be found above. – bat_of_doom Dec 6 '16 at 16:35
• (After edit)Well, what I meant to say in this analogy that the fish-pond is kind of trivial, and just manipulates things learnt in high-school. I do have mathematics professors in my college too and if I were to look at any papers I could start from there too. But, as I said most of them require specializations. In the link provided by you, most of them are (nearly) elementary. – bat_of_doom Dec 15 '16 at 5:22
• What about Alexander Abian's papers? Quite a few of them are accessible without a lot of background knowledge, and they're not focused on manipulation like Thomas J. Osler's papers are. Indeed, I've cited many of Abian's papers since 1999 (mostly in sci.math, before 2010 or so) for their detailed and elementary treatment of various topics. Here's one I cited in stachexchange: Methods to prove axiom independence – Dave L. Renfro Dec 15 '16 at 15:03

You can take a look at this: The Mathematics Student