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EXD 350-1 The History of Mathematics

3 Hours Social Sciences, Humanities, or Mathematics
Instructor: Dr. Joseph Neggers-Professor
Box 870350
Department of Mathematics
University of Alabama
Tuscaloosa, AL 35487
(205) 348-5304
jneggers@gp.as.ua.edu

*Prerequisites: Successful completion of several mathematics courses and approval from advisor.
*Contract to be completed 9 months from enrollment date.

Important Contract Policies

Purpose

The overall purpose of this contract is to assist the student in increasing awareness of the historical roots of the subject and its universal application in a variety of cultural settings. Thus, the perspective, so gained, will be useful in recognizing how mathematics, in a variety of disciplines, has played a critical role in the evolution of cultures both over time and over space. Students will be encouraged to explore viewpoints of personal importance wherever and whenever possible.

Learning Objectives

NOTE TO STUDENT: The basic outline and requirements of the course are laid out in this contract; however, the contract is individualized for each student at the beginning of the study, i.e., each student's contract will be different depending on the topics of interest chosen.

A great deal of steady and consistent interaction and communication between the student and Dr. Neggers will be necessary in order to achieve the learning goals established. Good time management skills will be a plus, so please do not enroll for the contract if you are not a self-starter and cannot set and meet the goals of the contract in the required 9 mos. completion time.

After receiving the "go ahead" letter from the External Degree office after enrollment, call, write or email Dr. Neggers for discussion. You may need to "talk" several times. As you choose the topics for your papers, write them in on your copy of the contract (and any other pertinent information that will further refine or show the specifics of your contract). Dr. Neggers will do the same on his copy of your contract. This will serve as a reference and starting point for both of you and enable you to "sing off the same sheet of music."

While students should have a math background of 2-3 courses, it is not required if the student has the interest and capacity of independent investigation and reflective/analytical thinking.

The basic text/reference is Boyer's A History of Mathematics, which should be used as a source of information as well as a starting point for independent research on the topic. The student should note that The Encyclopedia Britannica is also an excellent resource along with the volumes of the "Syntopicon" (Great Books) generally available in college, high school, or public libraries.

The student will write 3 smaller and 1 larger papers. The papers will come from distinct areas, i.e., no 2 papers may come from the same area of inquiry.

Areas that are divided by period:
  1. Chapters I-XI: "Classical Mathematics"
  2. Chapters XII-XVI: "Middle Ages and Renaissance"
  3. Chapters XVII-XXI: "The Beginning of Modern Times"
  4. Chapters XXII-XXVII: "Modern Times (continued)"
Areas that are divided by field:
  1. Foundations and logic
  2. Arithmetic and algebra
  3. Geometry and topology
  4. Analysis
  5. Discrete mathematics
  6. Probability and statistics
  7. Computer science
  8. Applications:

      a) Physical Sciences
      b) Social Sciences
      c) Biological Sciences
      d) Art and Architecture
      e) Engineering
Areas that are divided by geography:
  1. Middle East/Iran
  2. Greece
  3. Europe/Americas
  4. Ancient Americas
  5. Africa
  6. China/Korea/Japan
  7. India
Areas that are divided by some other criterion:
  1. Great mathematicians
  2. Women mathematicians
  3. Indian mathematicians
  4. Great theorems
  5. Your own
Methodology
  1. Obtain the textbook.
  2. Submit to the contract director a selection of 5 choices for smaller papers and provide a beginning list of references to be used for each of these papers.
  3. The contract director will suggest 3 short papers to be taken from this choice of 5. He will suggest material in Boyer to be read as well as other materials (if necessary). The order in which the papers are to be handed in is not crucial. What is crucial, however, is that the second paper not be sent in before the first one has been corrected, so that any matters of style, etc., can be adjusted--similarly for the third short paper.
  4. A short paper should be 8-12 typewritten pgs., not including the bibliography or the title page. The emphasis should be on historical perspectives, as this is a course on the history of mathematics, but mathematical facts should not be shied away from even so.
  5. After the short papers have been done, it is time for the larger paper, minimum 20 pgs., but no upper number here.
  6. The way to proceed is to prepare a prospectus/outline including: reasons for selecting the topic; approach of the author to the topic; suggested table of contents; bibliography (probably incomplete).
  7. This prospectus will be critiqued and, on that basis, the paper will be written in its final form after notification and go-ahead from the contract director.
Resources
  1. The textbook: Boyer, Carl B. A History of Mathematics. Princeton: Princeton University Press,Princeton, NJ .
  2. Access to an Encyclopedia Britannica.
Elements of this contract may be found as an online course reserve. Go to http://www.lib.ua.edu, click on "course reserves" and select "Joseph Neggers." Note: the document is in pdf format. You will need to download Adobe's free reader at http://www.adobe.com. If you need help, please call us at (205)348-6000.

Evaluation
  1. The papers will weighed as follows:

    Short papers (3 x 15%) = 45%
    Prospectus = 10%
    Long paper = 45%
    Total = 100%

  2. The papers will be judged on:

    Content = 60%
    Style/Writing = 30%
    Presentation = 10%
    Total = 100%

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