Mathematica is like the Band in a box of mathematics. Band in a box is a musical sequencer that includes musical styles based from many different musicians. Mathematica is an information system and it contains many functions that have been designed by other mathematicians. I own about 20 Mathematica books and NKS. Mathamtica is usually taught as a broad discussion that covers many different kinds of maths. The problem is that no one is familiar with the University math stars like rock stars and so people don't ordinarily understand how to discuss families of algorithms or math facts. Because Eric's site exists that is very helpful. I think history and math function and facts work together. I would translate what you want to do from regular programming books and ask questions when you get stuck. You could subscribe to like Safari Books online (wait till they offer it for $200 a year and you have access to 9 mathematica books and any language or anything that has to do with computers. Or you could just hunt up mathematica books on Amazon used and pick them up for real cheap. I have a large enough vocabulary to get through most math books so I can't give myself and excuse why I can't pass algebra 2. But I have been trying to put how the Mathematica world operates but this software introduces you to a world and so little of math is understood by most people. I am more interested in the historical pursuts rather than the functionality because my disability has limited me in the past because my vocabulary was so poor but now I have a better idea of what is happening.

You can find the table of contents and index for all of Wellin's books on his website. Here's the link to this for the current textbook: http://www.programmingmathematica.com/front-and-back-matter1.html

From the Help menu open Wolfram Documentation. At the bottom you will see an Introductory Book link. Click it to get a pretty good introductory book by Stephen Wolfram.

Then try flying solo by doing mathematics from a simple non-Mathematica book, such as a college calculus book.