FreeMathTexts.org

For people who want to learn or teach mathematics on the basis of reason …

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The texts on FreeMathTexts.org are reasonable in that they acknowledge facts, in particular that:

Math Anxiety invariably originates with bad textbooks:
- in the best cases because the textbooks leave so much to go "without saying" that reason has become invisible,
- in the worst cases because the textbooks have been gutted to "disconnected topics" so that no reason is left.
Reducing learning mathematics to memorizing does not work: With memorization at its core, "developmental education", which has now been in existence for at least thirty some years, has never shown any sign of progress.
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", i.e. 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 commercial textbooks, the texts to be found on FreeMathTexts.org

emphasize only a very few but very powerful ideas on the basis of which everything finds its natural place and can then be investigated as thorougly and as long as the student feels,
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.

A 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 these texts, namely that:

In order to be usable in developmental mathematics classes, the texts to be found here were designed as parts of "bundles" suitable for "turnkey" classroom use in that they include all that is needed, Homeworks, Quizzes, Reviews, 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.

As of this date, two titles have been completed and are freely available:

Reasonable Basic Algebra. It is complete but a significant modification will be made in the text soon. Also, the question bases and the control files for the ancillaries are being recast into the format newly developed for Reasonable Algebraic Functions.

Reasonable Algebraic Functions. The text is "done" and all individual chapters are available for download. The ancillaries which are in the newly developed unified format are undergoing preflight checking and will be uploaded during the next few weeks.

Also, the system for managing the ancillaries is freely available to anyone wanting to develop ancillaries for their own text.

At the request of some of the people who have downloaded Reasonable Basic Algebra, printed copies of the text can be purchased from Lulu for $8.40 plus shipping. I would like to acknowledge the fact that Lulu waived its own "fees" inasmuch as I do not collect any royalties. Printed copies of Reasonable Algebraic Functions should soon be also available from Lulu.

Last, but certainly not least, Dax Mickelson just started a forum. It seems to be the place where to go to tell the world all that is wrong with the stuff on this site---but it's also OK to point out what's nice---and/or to discuss the Notes From the Mathematical Underground.

There are of course other possible approaches to mathematical exposition. For instance, Santos' notes are free texts that follow the Edmund Landau style of presentation. More generally, there are several sites in which free mathematical texts can be found such as Textbooks, Lecture Notes and Tutorials in Mathematics, 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 any trouble with links or downloads, please let me know.