August 25: Upgraded Schremmer_RDA-v4.1, Schremmer_RBA-v4,0, and Schremmer_CARW-v1.0 so that they now all typeset under the same preamble. As a result, one can now copy any piece from any text and paste it in any other text. One must of course also copy, possibly renumber, and paste in the relevant folders both the graphic.intaglio and the figure.pdf that are involved in the piece being copy-pasted. (Else, LaTeX won't find them.)
The texts on FreeMathTexts.org are reasonable in that they acknowledge a number of facts namely:
Math Anxiety invariably originates with the standard textbooks:
in the best cases because the standard textbooks leave so much "going without saying" that reason has become invisible,
in the worst cases because the standard textbooks have been gutted down to disconnected "facts and skills" so that no reason remains.
For more about standard textbooks, see, for instance, Hung-Hsi Wu in the response of the Notices of the American Mathematical Society to Why Do Americans Stink at Math?, Elizabeth Green's New York Times article, in which he writes
If Americans do "stink" at math, clearly it is because they find the math in school to be unlearnable. [...] For the past four decades or so the mathematics contained in standard textbooks has played havoc with the teaching and learning of school mathematics.
Reducing learning mathematics to memorizing "facts and skills" does not work as witnessed by the fact that "developmental mathematics", with memorization at its core, has now been in existence for some fifty years without having ever shown any sign of success---as measured by what happens to the students in subsequent courses. (That there is about no "longitudinal study" may thus not be an accident and, in fact, the only one I know of is here.)
Contrary to what most people believe, students and teachers alike, there is nothing inherently difficult in mathematics up to and including the "mathematics of change", also known as Differential Calculus, which everybody should be able to learn.
The truth or falsehood of mathematical statements does not originate in textbooks, or in teachers saying so, but because the real world makes them necessarily so.
So, in contrast with the currently available standard textbooks, the texts to be found on FreeMathTexts.org
emphasize a very few, very powerful ideas on the basis of which everything finds its natural place and can then be questioned as thoroughly as the student feels without hitting a dead end,
appeal only to common sense and make no assumption of any kind about the students,
are focussed on helping the students convince themselves that statements need to be justified and their truth supported with arguments,
pay pedantic attention to matters of language wich often impede understanding.
A further discussion of these facts, and of how the texts on FreeMathTexts.org attempt to take them into consideration, can be found in Chapter Thirteen.
Two more facts govern the development of the texts on FreeMathTexts.org, namely that:
In order to be usable in mathematics classes, the texts to be found here were designed as parts of "bundles" suitable for "turnkey" classroom use in that they include the ancillaries, that is all that is needed, Homework, Classwork, Quizzes, Reviews, Review Discussions, Exams, in a form that makes it easy for the instructor to follow and assess their students' progress as well as adjust the materials to their own situation.
Mathematical exposition is no one's "intellectual property". All the materials on FreeMathTexts.org can thus be freely downloaded, used, copied, distributed and modified under the terms of the GNU Free Documentation License.
Another one of the very few authors of texts off the beaten path and to be taken most seriously is Herb Gross and his texts and videos are to be found
here. I should disclose the fact that Gross' treatment of Arithmetic and mine in Reasonable Decimal Arithmetic are very reminescent of each other and that, upon my discovery of his work, I wrote to him which resulted in a very pleasant exchange.
More generally, there are several sites in which free mathematical texts can be found such as Online Mathematics Textbooks, Online Science and Math Textbooks, etc. And then there is iBerry, with Open CourseWare and Higher Education Resources, which describes itself as the first academic porthole", that is as "a small but cheerful window in the side of the Higher Education ship for purposes of illumination and enlightenment.
If you are having trouble with links, downloads, ... or contents, please let me know at .