For people who want to learn or teach mathematics on the basis of reason …
On August 18, 2008, this page read in part as follows:
Today, nearly two years later,
To the extent that things will work out as foreseen—they haven't always in
the past, the number of standalone bundles ought to reach four in a not
too distant future:
- By the end of Spring 2008, I hope to finish a
standalone package for a
PRECALCULUS I course, Reasonable
Algebraic Functions (RAF).
This is a redesign and a 3-hour reduction of the first part of Lagrange Differential Calculus,
that is an investigation of algebraic functions
via local polynomial approximations, without the study of
"derivatives" per se but with qualitative
discussions of slope and
concavity for each type of algebraic functions via localization.
Essential global graphs are then discussed as the simplest global
incorporates the results of the local investigations.
- By the end of Fall 2008, I hope to finish a standalone
package for an
ARITHMETIC course, Reasonable
Decimal Arithmetic (RDA).
This will consist of Part I of RBA
together with a discussion of the decimal numbers
in the context of the metric
system but with only the
strict minimum on fractions which we need only
consider as specifying a division.
So, Reasonable Algebraic Functions is really finished, text and ancillaries, and what I am about to start on now is:
- I have uploaded the 18 chapters of Reasonable Algebraic Functions and am running the last checks on its ancillaries with the hope to be done within a week or two. I will then bundle and upload the entire source.
- But I have also developed---and actually finished---a new, much needed, system for developing and managing ancillaries. Not only that, but M. Sharpe wrote ADM, a Graphic User Interface for the system that allows you to generate the homeworks, quizzes, reviews and exams exactly the way that you want without your having to even open a LaTeX file as ADM does that for you.
What makes me think that I should be able to finish this in a reasonable amount of time is that (a) I already have a lot of what I need fairly well developed, and (b) I now have a management system in which to put the Checkable Items as I write them.
- Carry out the significant modification I had planned for Reasonable Basic Algebra.
- Finish transfering the ancillaries of Reasonable Basic Algebra to the new system.
Develop Reasonable Decimal Arithmetic as described above, keeping a very stern eye on both Part II and Part III of RBA
so as to make it relatively easy to get Reasonable Arithmetic Algebra (RAA),
that is a standalone package suitable for a five-hour-semester solid alternative to the ARITHMETIC - BASIC
ALGEBRA two three-hour-semesters sequence usually offered in Developmental Programs.
Beyond that, as I already wrote at the time, things get a bit fuzzy.
- I need to write Reasonable Transcendental Functions (RTF),
a standalone package for a PRECALCULUS II course as a 3-hour reduction of the second part of Lagrange Differential Calculus,
that is an investigation of transcendental
functions via local polynomial approximations, again
without the study of
"derivatives" per se.
- But, a very important issue, probably the most important at this stage, is the question of exactly how much explanation is enough explanation and at what point enough explanation becomes too much explanation. And, in that regard, since I didn't want to take any chance, I have obviouly sinned by excess. And so it seems to me that there is a necessity for a terse edition of the already existing texts henceforth to be subtitled verbose edition. This should not involve too work inasmuch as the contents would remain unchanged so that the ancillaries could also remain as they are.
—Is this a personal project of yours or would it be possible to be part in it?
This project is a very large one whose development should certainly not be left to a single person, not even me. I can see at least four areas in which work could atart right now. In order of increasing difficulty:
Write terse editions for Reasonable Basic Algebra and Reasonable Algebraic Functions.
Complete and improve the ancillaries for the existing standalones.
Develop a verbose edition for Reasonable Transcendental Functions
Integrate the standalones into a three-semester sequence Arithmetic To Differential Calculus.
If you are interested in any of the above, you can of course contact me at Schremmer dot Alain at this site but that is by no means necessary since this project is under a GNU Free Documentation License so that anyone can modify the stuff whether I like it or not.