ABSTRACT
    At Morehouse College the first theoretical mathematics course the student takes in a mathematics major or minor is, The Principles of Mathematics, Math 180. The course is an introductory exposition to theoretical mathematics in which the student is introduced to logic, predicate calculus, axiomatics, basic sets, combinatorics, probability, statistics, and linear algebra. A central component of this course is the presentation of the many fields of mathematics through the lens of logic and proof. In this proposal, the author is applying for an ACS Teaching with Technology Fellowship for Spring of 2002 to support the development of a web-based text for the course.

PURPOSE
    The type of activity proposed is the writing of a textbook / workbook / web support for Mathematics 180, Principles of Mathematics. There is a great need for a text specific to the course due to the unique nature of the course. The course is an introductory exposition to theoretical mathematics in which the student is introduced to logic, predicate calculus, axiomatics, basic sets, combinatorics, probability, statistics, and linear algebra. It is preferable to have such a text web-based and interactive so that not only do students have a course specific text; but, are encouraged to use the web to research and expand on concepts presented, do interactive exercises, communicate outside of the traditional classroom with colleagues, and, become comfortable with the use of technology.
    No such text currently exists on the market that covers each of these topics in the depth appropriate to the level. Presently, books that cover the topics are written at too low a level, usually for non-science majors, giving an overview of the ideas of mathematics and not a rigorous introductory proof driven course appropriate for Mathematics majors. In addition, books at the appropriate level do not cover all of the material; hence the need for the course presently to require two books and supplementary materials. Further, none of the materials presently available from publishers combine classic texts with interactive web based exercises and support.

DESCRIPTION
    Development of said materials would be of great assistance to the department and to the mathematics programme so course appropriate materials would be available for use by our students. Further, the department is presently in the process of seeking approval from the College to enhance our major programme so as to better serve our students and meet Mathematical Association of America (MAA) and American Mathematics Society (AMS) standards for an undergraduate programme. Creation of a web text, workbook, and support appropriate for the course and for the level of entering mathematics students at Morehouse will better serve the community by bridging the gap that presently exists between the High School background many mathematics students bring to Morehouse and College level work.
    An integrated approach to introductory theoretical mathematics is envisioned. First, construction of a web text appropriate for the course such that it is readily available for students' use. The current "make piece" situation that exists requires the student to purchase two texts (total price approximately $170.00) and collect notes from the instructor teaching the course such that about three-quarters of one text is used, half of the second texts is used, and interspersed are notes. Second, construction of a web workbook that is interactive, integrates appropriate exercises, and further reading is envisioned so that concepts are reinforced and expansion of concepts can be executed. Currently, no such appropriate workbook accompanies the texts that are used (web or bound). Third, construction of web support for the course that aids the student in his work throughout the course is envisioned. Currently, one of the instructors (P. McLoughlin) maintains web support for his section of the course; however, management and enhancements of the site oft take a back seat to other more mundane tasks that all of the faculty find themselves having to do. It is envisioned that funding may allow for more work on web support: enhancing and expanding it.

TIMELINE
    A rough draft of the first chapter of a text appropriate for the course was written by the initiator in 1996, but abandoned due to teaching load and a return to graduate school. A basic web site for the course was begun by in 1997 and augmented over the years.
    Completion of the project is not anticipated until Fall, 2002. The author envisions that a draft of at least the first six chapters can be completed by June of 2002 (logic, predicate calculus, axiomatics, basic sets, combinatorics, and probability) for the web text, workbook, and web support. The author envisions that a draft of the last two chapters of the web book and the six sections of the workbook can be completed by August of 2002. The course materials would then be piloted during the Fall of 2002 so that final materials would be available for use starting in Spring of 2003.
    The timeline proposed is envisioned to be minimal; that is, more might be accomplished over each of the designated periods. It is feasible that it could be completed in less time, but it is felt by the author that careful consideration of each part of the project is called for and time should be allowed for faculty in the department to offer suggestions, revisions, additions, and deletions. Speed at the cost of quality is not desired by either the author or his colleagues; hence, the cautious timeline is warranted.

TECHNOLOGY
    The technology needed to compleat the project is available at Morehouse College.

OTHER SUPPORT
    No other support is anticipated to be necessary at present.

LEARNING OUTCOMES
    As previously stated, central to the course and this approach is the presentation of the many fields of mathematics through the lens of logic and proof. The learning outcomes for students should be as with any introduction to advanced mathematics course - - understanding and ease of use of the concepts expounded on during the course. Moreover, the learning outcomes for students should be understanding and ease of use of technology to enhance learning: use the web to research and expand on concepts presented, do interactive exercises, communicate outside of the traditional classroom with colleagues, etc.

CURRICULUM
    The course exists in the present curriculum. Such a project to enhance the course has been approved by the Mathematics faculty at Morehouse College.

ASSESSMENT
    The materials created in this project will be subjected to two forms of evaluation. First, as materials are created and before they are used they will be reviewed by the Curriculum Committee of the department. Second, after the project is implemented, the materials will be evaluated by both faculty and students at Morehouse. Student and faculty comments will be collected and compiled.
 

DISSEMINATION
    The materials created in this project will be available for use and downloading from the author's web site: http://facstaff.morehouse.edu/~pmclough. A link to the materials will be available from the department web site: http://www.math.morehouse.edu. In addition, the author will request that a link to the materials be included on the ACS technology resources web site. Finally, the author will directly e-mail all ACS Mathematics Departments to advise his colleagues of the availability of such materials and the opportunity to provide comments as to the utility of the materials.