Here's a tentative Table of Contents. and a detailed discussion of the presentation of logic used in the text. Here's a set of student evaluations I got using this material. Here's my vita.
I'm seeking a publisher. For more information, write me at vlorbik@aol.com.
Numbers, Sets, and Logic by Owen Thomas is intended for a (one semester) ``liberal arts'' course in mathematics at the college level. There are no prerequisites other than basic reading and arithmetic skills. In particular, the text does not assume (or cover) the algebraic skills from the standard Algebra-Trigonometry-Calculus sequence.

A course based on this text would most likely be intended for students not majoring in mathematics or ``hard'' sciences. Most of the students in such a course will very likely be taking it to fill a distribution requirement. Probably more than a few will report ``math anxiety''.

The omission of algebra is apparently unusual in such a course and requires some comment. In fact, some of the texts in this area (for example, ITP's Mathematics: Its Power and Utility by Karl J. Smith or Freeman's Mathematics: A Human Endeavor by Harold R. Jacobs) are essentially algebra books. Others (like Harper Collins' Mathematical Ideas by Miller, Heeren, and Hornsby or McGraw Hill's A Mathematical Journey by Stanley Gudder) include algebraic topics like polynomial functions and graphing along with less mainstream topics like logic and number theory.

College students have generally had some prior exposure to the algebraic ideas, frequently in more than one course. As a result, the population of a liberal arts class varies widely in preparedness for these ideas. This fact makes it difficult (or impossible) to pace the presentation appropriately. The topics chosen for inclusion in Numbers, Sets, and Logic will be fairly new to almost all the students, so everyone can begin learning together. The symbol manipulations learned in studying Boolean algebra and the algebra of sets will be useful to students needing practice in ``ordinary'' real-number algebra (commutative and associative laws, for example); but, again, this course does not treat real-number algebra explicitly.

The pedagogical approach is based on very short readings each describing a particular technique and followed by exercises using that technique. I am strongly opposed to the use of photographs, ``sidebars'', and cartoons. Illustrations should be used only to clarify the mathematics. There is good evidence of a competitive advantage to this approach: consider study guides like McGraw-Hill's famous Schaum series. These books stay in print year after year and continue to sell even though they are seldom required texts.

The only ancillaries to accompany the text, if any, should be an instructor's manual and test item file. I have never found ancillary documents to be very useful and would much prefer to keep the cost of the book down by avoiding the production of such material.

The hard copy was prepared by me using the TeX typesetting program. I can modify the code to produce camera-ready copy of any specifications.

Most of this material has been classroom tested in one or more sections of Ohio Dominican College's "Mathematical Concepts" course and Capital University's "Quantitative Reasoning" course.

July 22, 1997