MATH 304 A History of Mathematics Fall 2003

Professor: George L. Ashline

Office: 261 Jeanmarie Hall, Phone: 654-2434

Office Hours: M,W from 1:30 to 2:30 PM and T,Th from 1:30 to 3:00 PM; also, feel free to set up appointments with me for other times.

Class Meets: T and Th from 10 to 11:15 AM in Jeanmarie 380

Course Goals:

A. To enrich your knowledge of mathematics

B. To describe some important developments in mathematics

C. To enable you to read and interpret mathematical literature from a variety of sources

D. To enhance your technical writing skills

E. To encourage your use of library and internet research tools

Textbook: A History of Mathematics (second edition) by Carl B. Boyer and revised by Uta C. Merzbach, John Wiley & Sons, 1991. You are expected to read the text carefully during the semester. Many of the homework problems will be based on ideas described in the text.

Homework: There will be problems assigned on a regular basis. Your text doesn't contain any explicit exercises. In lieu of this, some problems will be assigned that will require a careful reading of the text. Other problems will arise from class discussions.

Exams: There will be a midterm exam tentatively scheduled for Thursday, October 16 and a cumulative final for Thursday, December 18 from 9 to 11:30 AM. More information on these will be forthcoming.

Library Projects: During the first month of the semester, two projects will be assigned. The first assignment is due Thursday, September 18 and the second is due Thursday, October 2. These are designed to familiarize you with the resources available at the library. These include periodicals/journals, encyclopedias, databases, and indexes. A list of some of these will be handed out separately.

In the first project you will be given a mathematician's name and then need to gather certain information about that person. A separate handout concerning this project will be provided. You will be asked to write a short two page biography about your mathematician. In this paper, you should include important background information about the individual and describe some specific, significant ways in which the person contributed to the mathematical community. Be sure to supply complete references for your sources. You may find The Dictionary of Scientific Biography in the library very useful for this project. You are expected to use other sources besides this Dictionary. Finally, you will be our class expert on your mathematician and will be expected to provide some commentary in class about the person at the appropriate time.

In the second project you are to use available databases and periodicals to complete short summaries of at least three articles on topics of your own choosing in the history of mathematics. You can find articles simply by browsing through one of our library's math journals or using one of our databases to search for a particular topic (see handouts for listings of periodicals and databases). For each paper you are to include complete bibliographical data, including name of author, title of article, journal, volume, year, and pages. You should also write up a synopsis describing the content of the paper and how useful/appealing it was to you. You should use your research in this project as an opportunity to explore possible paper topics. An example of a summary is given below:

Grabiner, Judith, "Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions", The American Mathematical Monthly, 104 (1987), pp. 393-410. A useful description of Maclaurin's influence on mathematics and how his Treatise helped to transmit an improved, expanded form of Newtonian calculus to the Continent. A very readable account providing much background and many references (over 90).

Paper: You are to write a paper on a topic of your own choosing. The only restriction on your choice is that it can't be the mathematician that you considered in your first library project. You should explore possible choices while doing your initial library work. Once you have an idea for a paper, let me know and can discuss its feasibility. By Thursday, October 23, each of you should give me your final paper topic. There are a few things to keep in mind when writing your paper:

A. Your paper should focus on a topic in the history of mathematics and should neither be all history nor all mathematics. It should contain enough background material to be self-contained. A good way to check this is to have a classmate critically read it over.

B. Be sure to use various research sources and reference all the materials you use with a bibliography and footnotes as needed. The technical details of your paper, such as length, format, etc., are to be decided by you. Keep in mind that a paper should include sufficient background and details and consequently has a natural length. You are to turn in two copies of your paper since I will keep one of them.

C. Your paper will be graded according to a number of criteria, including mathematical and historical context, significancy and accuracy of material, citation of resources, and overall form and style.

You are to turn in an outline/preliminary report for your paper on Thursday, November 6. In this report, you should specify your topic, your intentions for the paper, an outline, an initial bibliography of sources you have found, and any questions you may have concerning it. The final version of your paper is due Tuesday, November 25.

Grading: Your grade will be based on homework, library work, paper, and exams according to the following distribution:

Homework 120 points

Two library projects 80 points total

Paper outline 20 points

Paper 130 points

Midterm exam 100 points

Final exam 150 points

Thus, your final grade will be based on a total of 600 points.

Summary of Important Dates:

Library project 1 due Th September 18

Library project 2 due Th October 2

Midterm exam Th October 16

Paper topic due Th October 23

Paper outline due Th November 6

Paper due T November 25

Final exam Th December 18, 9-11:30 AM

If you are aware of a conflict with any of these dates, let me know of this as soon as possible before the actual due date or exam date.

LEARNING DISABILITIES: Any student having a documented learning disability that may affect the learning of mathematics is invited to consult privately with me during the first week of the semester so that appropriate arrangements can be made.

ACADEMIC INTEGRITY:  You are reminded of the academic integrity policy of St. Michael's College.  Simply stated, academic integrity requires that the work you complete for this class is your own.  Some examples of offenses against academic integrity include plagiarism, unauthorized assistance, interference, and interference using information technology.  Details about academic integrity offenses and the possbile sanctions resulting from them have been distributed a the beginning of the academic year and also can be found in the Associate Dean's office.

CLASS ATTENDANCE:  The following is taken from pp. 48-49 of the St. Michael's College 2003-2005 Catalogue:

       "Students should understand that the main reason for attending college is to be guided in their learning activities by their professors.  This guidance takes place primarily in the classroom and the laboratory.

        The following policies have been established:

1. Members of the teaching faculty and students are expected to meet all scheduled classes unless prevented from doing so by illness or other emergencies.

2. The instructor of a course may allow absences equal to the number of class meetings per week.  Additional absences will be considered excessive.

3. The instructor may report excessive absences to the Associate Dean of the College, who may warn the student.

4. If absences continue, the Associate Dean of the College may remove the student from class with a failing grade."


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