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Internet Resources for the Mathematics Student

Overview (and some warnings) re Math on the Web

 There is a large and rapidly growing body of material on the Web that may be of use to the mathematics student. But not all of the material is equally valuable and it can be tricky to "separate the wheat from the chaff". Here are some tips that we hope you will find useful:

One useful class of web-based services consists of freely available tools for performing calculations and graphing (which can substitute for a graphing calculator or even a full fledged computer algebra system) as well as tables of values and formulas which can be useful for reference (some of these may be no more useful than the tables in the front cover of your calculus book, but others may be enhanced by hyperlinks and other interactive features). There are also people who offer tutoring services or even just to do your homework for you, but the value of such services can be questionable, and some may have up-front and/or hidden costs.

If you want to see an alternative presentation of your course material, there may be several on-line versions of the complete course available. Some of these are freely accessible and include features such as animation and response to your input etc that you could not get from a book; but others are of no more use than a second text, and/or the interesting features may be available only to registered fee-paying students.

There are also many examples of clever and compelling illustrations of individual concepts. These can be fun to look at and may improve your understanding, but may or may not address an issue on which you actually need more enlightenment.

If you want to just explore or get a general overview of what's "out there" there are several (in fact many) big resource collections which provide a natural starting point, but many of these collections refer to one another and so it is easy to find yourself going around in circles. If you are the kind who likes to poke into every corner and follow all the interesting looking links, then it might be wise to (a) limit yourself a bit at least when you have a particular topic that you are researching, and (b) keep some notes of where you have been, including both what you liked and what looked enticing but turned out to be a dud.

Also the quality of the material is quite variable and often does not correspond to the level of sophistication with which it is presented. Even "award winning" sites can contain mathematical errors, or less obvious (but thereby perhaps more dangerous) misleading emphases on unimportant aspects of the material. It is often hard to distinguish a good but perhaps naive student project from a professionally authored site, and even the latter often have not been subject to the same level of editing and review as would be required for a published text. This allows novel approaches to get some market exposure (which is a good thing) but also means that you may be reading an idiosyncratic or even discredited view of the material. What seems like a time-saving shortcut method might turn out not to be generally applicable and/or may divert your attention from an understanding of the underlying principles that you are being expected to learn for later application in other areas. It is always a good idea to check with your instructor before taking too seriously the information that you may come across.

If you use a search engine with keywords referring to a particular topic, your results will include a lot of sites that are tables of contents for on-line courses or even just course outlines or calendar descriptions of face-to-face courses which may include the topic of interest but for which the relevant material may not itself actually be available on the web. With experience you may become better able to pick out the real "direct hits" by looking carefully at the information presented by your search engine (eg if the page title looks like a course number, or if the keyword list includes other topics besides your target, then you may have to dig quite a bit to find the useful information, or it may not even actually be there at all).

Some of the big indexes do break down the material by subject area (eg Algebra, Calculus, etc) but at present (Spring of '98) not by detailed topic. And the various online courses may be well indexed, but each only gives you its own view of each topic.

Our site is intended to direct you to a selection of decent alternative presentations (to the extent that we have been able to find them) for each such detailed sub-topic. (One other site which takes the same approach is at the Chinese International School in Hong Kong. For the first year or so of this project that was the only other one we have seen, but since then a couple of others have been started and doubtless there will soon be many more)

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