(If you are not a native English speaker, like Japanese, Indian, French, etc., you could recommend some good website or books to Alex. And I’ll try my best to understand these good stuff!)
♦ Math History
MacTutor is created and maintained by Edmund Robertson, and John O’Connor, of the School of Mathematics and Statistics at the University of St Andrews. When it comes to the website about math history, I think MacTutor is the best. In addition to some historical figures, there are various history topics such as the four-color theorem, the history of topology, non-Euclidean geometry, and so on. Due to the large amount of pages, there are some search methods for these articles. Among them, I like the way of searching by map. When you zoom in the map, the name of these places would be showed in the local language. There is also a spot in Taiwan. This spot is for a graph theory mathematician, Fan Chung. I’ll introduce this person in the future.
♦ Math Application
It’s is a household application, isn’t it? I always see it in some math forums or communities. I think it should be regarded as a “mathematical calculation engine” (it’s similar to the concept of the search engine). So the way you use WolframAlpha is the same as the way you use goole search. Just throw something you want to know, and it can give you the result of anything about the question. WolframAlpha is based on Mathematica, a powerful and widely used math software. So you can understand why WolframAlpha can be so well known.
This application is also mentioned in the article [Some great math websites in other countries]. (You may find that the introduction in both sides are the same. XDD)
Have you heard about GeoGebra before? Actually until I wrote this introduction I found that there is an online version for GeoGebra. I used to use it as an software by downloading to the computer. GeoGebra provides a user-friendly interface. The only thing you need is basic math concepts, and then learn how to use GeoGebra and do some practice.
Unlike teachers has to draw the graph on the black board in the past, GeoGebra has high interactivity. The graph on the black board cannot be changed easily, and some are drawn uglily by teachers. The same graph drawn by GeoGebra can be changed as you want, and much prettier and more precise. No matter who you are, GeoGebra can be the best application.
I suggest that you can use (or just play) this kind of application whenever you have any idea. In the past day, we need to draw all of graph by ourselves. Now, we can spend less time doing the trivial stuff and get more time to focus on your own idea.
♦ Math Learning
You can easily see that the categories of math are classified according to grade. It’s interesting that math is divided into various small topics, and each topic attaches some question. You can find exactly what you want, and check if you understand the part you choose.There are some other topics like science and social studies.
♦ Comprehensive Math Website
The design of the wesite is really old-fashion that can be found in Taiwan. XD There are quite a lot of categories about math, such as recent conferences, competitions, development in recent year, etc. But some links are really old. MMA is much more like a math website museum for me. You can find something old but valuable. You can know the trends of math, or what new mathematical tools is used nowadays. It’s important to open up the horizons of math for yourself so that you won’t work behind the closed door.