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I am an undergraduate non-math major. I just finished my university's engineering calculus series, looking forward to linear algebra in the coming semester. To be frank, I always despised math because I couldn't help but find it tedious. I have recently had a change in heart, however, due to advice and encouragement from my favorite professor and some experience with proving logic statements (which I mysteriously find ridiculously fun...). Starting to read math review journals sounds like a great way to begin as an amateur mathematician.

So where can one find (free, online) mathematical articles with a fighting chance to be understood by high school students and undergraduates?

(The "free, online" part of the question is nonmandatory. I have access to academic journals through my university.)

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"Starting to read math review journals sounds like a great way to begin as an amateur mathematician." I don't actually think that it is, unless I'm misunderstanding what you mean by "amateur mathematician. Are you trying to learn some "recreational math", more on the fun side of things? Have you tried any of the books my Martin Gardner? You may want to look at the College Mathematics Journal, too, although this may or may not be what you're after - it's a bit hard to say. – Alon Amit Aug 25 '11 at 3:14
Most stuff in math journals are at a level that most high school students don't have a fighting chance of understanding, though there are definitely some articles that fit the bill. I don't think there is really any categorization of research according to whether students could understand them or not. Your best bet would be to focus in on some specific topics and become familiar with the basics. – anon Aug 25 '11 at 3:18
Did you know that "MIT OpenCourseWare" have lots of free undergraduate maths video lectures, notes, etc.? 18.06 looks like a nice linear algebra course. As a computer scientist you might already know the stuff, but course 18.410J has a nice introduction to algorithms. Unfortunately there's no logic stuff. – Billy Aug 25 '11 at 3:22
"undergraduates" - Most of the articles in The College Mathematics Journal should be easily accessible. You could try taking a stab at Mathematics Magazine; the exposition-y articles are a delight to read... – J. M. Aug 25 '11 at 3:22
@Alon Amit - Sorry, that was a bit vague. Yes, I meant "more on the fun side of things." But not like recreational math (though that is something I will look into, thanks). I meant like classic examples of math research papers that are written in an accessible style, require comparatively less math knowledge to understand on a reading comprehension level, etc. – sionydus Aug 25 '11 at 4:56 describes itself as "an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics." It's very well written. The level of the maths varies, but I think you'll find some content that's at the right level for you.

And to echo @Alon Amit's comment - Martin Gardner was a very lucid and entertaining maths writer, and several of his books and magazine columns are knocking around on the web in one form or another.

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I highly recommend material available on the Mathematics Association of America web site. Under Publications, Electronic Resources, they have freely available a full archive of the many articles in MAA publications that have won awards. The material is often demanding. But there are many articles, on many interesting topics, and some or all of each article is accessible to an undergraduate.

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Here in Western Canada we have a magazine intended for high school students. Maybe you will find something you like:

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I really like "Math Horizons" (see here). MAA desctibes it as

...a vibrant and accessible forum for practitioners, students, educators, and enthusiasts of mathematics, dedicated to exploring the folklore, characters, and current happenings in mathematical culture.

And I have to agree; the articles are quite interesting and most of them can be understood by undergraduates.

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