What kind of math topics exist?

Question

What kind of math topics exist?

The question says everything I want to know, but for more details: I enjoy studying mathematics but the problem is that I can't find any information with a summary of all math topics, collected together. I also googled this and took a look at other websites and searched this website but without success.

So if someone knows most of the topics, then please let me know them. The topics I am looking for are the ones from basics, to the university, and beyond university limit. Any comprehensive information you can provide would be useful.

Further thanks and have a nice day.

Answer 1

You might find the "Princeton Companion to Mathematics" helpful.

http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809

Answer 2

You might want to start at the Mathematical Atlas. It gives a visual map of domains of mathematics, and how they are inter-related: you can click on any "bubble" to learn more about each area. There is also a menu to the right-hand side: for example, see A Gentle Introduction to the Mathematics Subject Classification Scheme, also referred to as MSC.

The Mathematics Subject Classification was developed to help categorize publications and research in mathematics.

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See also the entry in Wikipedia: Lists of Mathematical Topics. This list includes topics which may sound more familiar to you, and groups them together in a sort of classification, each topic with its own link, so you can further explore any/all of them, at your leisure.

The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society....This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.