Are there math journals that are aimed for undergraduates? I don't mean here journals where students can publish their papers, but journals that publish introductory articles that an undergraduate can read without too much sweating, preferably when he gets bored or tired from his assignments and wants to read something different. What journals do you recommend to undergrads to read on a regular basis?

4$\begingroup$ See also mathoverflow.net/questions/7329/…, mathoverflow.net/questions/4807/whichmagazinesshouldiread $\endgroup$ – Victor Protsak Aug 27 '10 at 8:43

$\begingroup$ The trouble is that you can't read them unless you have an account... $\endgroup$ – muad Sep 18 '10 at 9:41

5$\begingroup$ You CAN read them if you walk to the library... $\endgroup$ – Gerald Edgar Jan 29 '13 at 15:31

$\begingroup$ Related: Journals for undergraduates $\endgroup$ – Martin Sleziak Nov 27 '16 at 10:23

4$\begingroup$ ...and, in alternate months, Mathematics Magazine. As far as "age of audience" is concerned, the three MAA jounals can be ordered: CMJ < MM < AMM . $\endgroup$ – Gerald Edgar Aug 27 '10 at 13:15

4$\begingroup$ I wouldn't say the Monthly is aimed at undergraduates. $\endgroup$ – Thierry Zell Aug 27 '10 at 11:56

4$\begingroup$ I would say it is also aimed at undergraduates. $\endgroup$ – Gjergji Zaimi Aug 27 '10 at 12:08
The journal "Morfismos" published by CINVESTAV, Mexico, is aimed at undergraduate and graduate students. Although some articles are in Spanish, they publish fairly good expository articles in English. For example, there is a survey on the recent solution of the Kervaire invariant one problem in this issue.
Speaking of nonEnglish language publications, Сборник Математическое Просвещение and Kvant are terrific (and often overlooked) Russian journal, aimed primarily at undergraduates.
If you read German, you can also try Elemente der Mathematik, which also have some articles in english.
There are two such journals published in India:
Mathematics Newsletter published by the Ramanujan Mathematical Society.
Resonance (journal of science education) published by the Indian Academy of Sciences, which is a general science journal, but usually has a maths article in each issue.
The Harvard College Mathematics Review was another interesting venture, but it seems to be discontinued as of now.

1$\begingroup$ I believe it's just on haitus; I'm still on the mailing list, and have been receiving emails lately. $\endgroup$ – Daniel Litt Nov 16 '10 at 4:53

The MAA quarterly Math Horizons is explicitly aimed at undergraduates interested in mathematics.
``Plus" an onlineonly British journal (similar to Math Horizons):
http://plus.maths.org/content/
From their home page: ``Plus provides articles and podcasts on any aspect of mathematics, covering topics as diverse as art, medicine, cosmology and sport, a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers, reviews of popular maths books, and puzzles for you to sharpen your wits. We have a regular interview with someone in a mathsrelated career, showing the wide range of uses maths gets put to in the real world."
The intended audience is not limited to math undergraduates; science undergrads would find something interesting there, too. Some articles can be accessible even to highschool students.
And for those who read Polish, there is ``Delta" (which I used to read regularly in the paper version as an undergrad):
The 01/2013 issue contains e.g. an article on William Thurston and geometrization conjecture (by Zdzislaw Pogoda).
A journal similar to the American Mathematical Monthly, but in french, shall be launched by the SMF (french mathematical society) but I do not know when exactly nor what will be the title.


$\begingroup$ @Olga: no, unfortunately the project seems to have been abandoned. $\endgroup$ – Benoît Kloeckner Jun 3 '14 at 16:22

$\begingroup$ @ Benoît Kloeckner This is sad, maybe the good idea will come back in some years. People should be more motivated! $\endgroup$ – Olga Jun 4 '14 at 9:37
In the applied field there is SIAM Undergraduate Research Online. Although it is mainly for for research papers written by undergraduates they write that
"Outstanding expository papers written for the undergraduate audience by a faculty member or researcher featuring a survey topic or a subject of historical interest will also be considered."
An example is the paper "Moving Forward by Traveling in Circles" from the first volume.
If you understand french, "Quadrature" is also a good magazine which for instance contains sections about counter examples and history of mathematics. Recently a special issue about Poincaré has been published.
If you can read Japanese, 数学セミナー is quite good. I knew the work of Thurston, the history of galoia and new trend of mathematic world by this journal.
If you read French, you should certainly look at this site : http://images.math.cnrs.fr/?lang=fr This was first aimed at teachers and large audience interested in maths but on practice this is read by mathematicians themselves and graduate/undergraduate students. Lots of beautiful math in there!