The Internet continues to amaze me, as it is a wealth of hidden resources. If you happen to do the right search or click the right link, you might find some of the gems. So, I try random stuff, and see what emerges.
The Mathematical Atlas
is an example that often energes. The current version can be traced back to an informal collection of mathematical links first posted Dave Rusin, a mathematics professor at Northern Illinois University.
Offered as a "Gateway to Modern Mathematics," the web site starts with a collection of short articles that introduce the areas of modern mathematics, describes fundamental results, and then provides links/pointers to further information..."as well as answers to some common (or not!) questions."
The design of the Atlas is interesting, though Rusin claims it has been "designed with the visitor in mind who wants to know something about a topic in mathematics -- why it's interesting, how it fits in with the rest of mathematics, and how it may be useful for solving some problem in or out of mathematics." Regardless, you have some exploring to do...with many options (e.g. click on the "About this Site" link at the bottom of the opening page.
To understand the meaning of the "balls with numbers," start with the section "Layman's Guide to Math Subject Areas." It gives an overview of the Mathematics Subject Classification (MSC) scheme, and a good overview of mathematics as a broad discipline.
Though I have done some partial explorations in the areas of number theory, geometry, calculus, probability, and statistics, I must admit my usual turf involves the sections classified under the category "Other." These sections are:
When you are in the "Other" subsection of the "Other" section, you do know you are facing the interesting but uncategorical ideas, or what Rusin calls "None of the Above."
- History and Biography (01)
- Mathematics Education (97)
- Other (00)
The level of website equates to undergraduate mathematics, so as you browse, pick content carefully. Also, a good place to start are the overviews and "the Selected Topics at this site" (bottom of overview pages).