|"These difficulties can be easily disposed of if we apply some simple logic and elementary tensor analysis."|
Since the University of Hawaii has chosen to screw up its main (Hawaii.Edu) email system, I am now using the Math Department system, www.math.hawaii.edu as my main address. The old address firstname.lastname@example.org no longer functions correctly.
[ Calculus | Linear Algebra | Discrete Mathematics | Elementary Arithmetic ]
[ Abstract Algebra | Homological Algebra | Miscellaneous ]
[ Do Numbers Really Exist? | Celsius to Farenheit ]
[ Torsion Free Modules over Dedekind Domains ]
In any formal or semi-formal teaching, there are always two conflicting paradigms being carried out simultaneously. The first one is a capitalist paradigm, where the teacher functions as a boss who assigns work, for which the students earn credit. I am convinced, in fact, that the main reason many employers look for employees with college degrees is that college is a fairly good simulation of the workplace, and it is fairly reasonable to hope that someone who has functioned reasonably well in meeting the requirements in school will also function satisfactorily in meeting the requirements at work.
The other paradigm is that of teaching as a "helping" profession. In this model, the student comes to a teacher because he has a desire to learn something, and the teacher works cooperatively with the student as a guide to help him achieve his goal.
I think that both these paradigms are always at work to some extent, but in my experience, the capitalist paradigm is always by far the domininant one in our system of formal education, whereas the cooperative model is much stronger in the many classes I have experienced outside the academic system.
Several of the files below are simply hand-outs made up for various classes I was teaching. Some of these are fairly readable, others (such as the differential geometry notes) are pretty unintelligible unless you happen to be taking a course in the subject using the same text I was using.
Some of the other articles here are more self-contained and longer -- a lot longer, in some cases. For the most part, these represent a particular approach I have developed over the course of years for my classroom presentation of a particular subject.
None of these notes are intended as a replacement for a textbook. Rather than giving a concise presentation of some topic, my aim has been to present a number of ideas that I hope will increase the student's interest and motivate him/her to want to learn more. Several of the longer articles illustrate very well my tendancy, which some students complain about, to "not be very focused" or "go off on a tangent." In my own opinion, these "tangents" are the most valuable part of my articles and lectures. It's fine if I manage to be successful in teaching students to insert Tab A into Slot B, but it's even better when I can get a student to say, "That seems strangely interesting. I'd like to find out more about that."A lot of the files listed below are in PDF (Adobe Acrobat) format. Alternate versions are in DVI format (produced by TeX; see see here for a DVI viewer provided by John P. Costella) and postscript format (viewable with ghostscript.) Some systems may have some problem with certain of the documents in dvi format, because they use a few German letters from a font that may not be available on some systems. (Three alternate sites for DVI viewers, via FTP, are CTAN, Duke, and Dante, in Germany.)
(Being an unfinished book in twelve chapters)
See my NLP archive (formerly available by FTP) at <Http://www2.Hawaii.Edu/~lady/archive/>