Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Do you feel that lectures and textbooks are incomprehensible?

This is just a variation on the theme of being lost.

But here's another point about reading textbooks (or any other mathematical literature). Suppose you just bought that 1,000 page textbook and after getting past all the introductory stuff you spend a day working through the first real mathematical page. You figure it will take you 999 days to get through the rest of the book, but the semester is only some 90 working days long, and anyway, you don't have all day every day to work on this particular course.

Well, it's not really like that. First of all, not all pages of the book are equally difficult, and probably a large number of them aren't important. But the main effect is that as you work through one page or piece of text you gain experience in this particular area of mathematics, and subsequent work in the same area will be easier! That process feeds upon itself, and once you've incorporated the subject of the book into your understanding of mathematics the once formidable book will be much less intimidating.

Much of the text in contemporary beginning math textbooks is what I consider embellishment and clutter. For example, to handle logarithms, all you really need to understand is exponentials, and the definition of a logarithm. Everything flows from there and the rest of what the book is trying to tell you you can just as easily figure out yourself. Doing it that way may even be easier because you do not have to put up with the idiosyncrasies of the book's authors!

Fine print, your comments, more links, Peter Alfeld, PA1UM