MAT 300-02L

Spring 2004

 

 

Paper #3  250-400 words.   

Due no later than May 4, 2004.

 

Write a proposal for Paper #4.  Discuss what you plan to do in Paper #4, and give a preliminary bibliography.  You do not need to have read all of the references in the preliminary bibliography at the time that you submit this paper.  Do not just hand in an outline.  If this paper is not submitted before you turn in Paper #4, you will be penalized a full letter grade on Paper #4.

 

Paper #4.    At least 1600 words.  Diagrams and derivations do not directly count as words
Due May 13, 2004.

 

Write a report on one of the topics below.  You should use at least five sources, including at least one primary source and at least one journal article related to your topic.  The information from the primary source and the journal article should be integrated into the organization of the paper, not just added in to satisfy the requirements of the assignment. You may not use our text as one of your sources nor should you use web articles as sources for your paper unless you have my prior approval.   If the paper involves things we have done in class, it should not just be a restatement of what we have done in class.   The paper should follow the general outline that you established  in Paper #3.  If you need to vary from that significantly, then discuss it with me first.  Address the paper either to another  student in the class or to another student at your own level of mathematical sophistication. 

 

A.        The historical development of any concept or field in  mathematics, other than non-Euclidean geometry.  The paper   should concentrate on the period from 1400 C.E. to 1950 C.E., but you may discuss its origins in the classical and medieval periods and its further development after 1950.

 

B.         The work of a mathematician from the period 1500 C.E. to 1950 C.E.  If you choose someone that we have discussed in class, your report should not just duplicate that discussion.  You should concentrate on the person's work, although some biographical material should be given.  You should discuss the nature and unifying themes in the work; your paper should not be just a listing of his/her works.  You should discuss how that   person's work fit into the development of mathematics, what led up to it, and what later developed from it.

 

C.        Any aspect of mathematics in America prior to 1950.   This might be a specific mathematician or the specific development of some field in America.  Another possibility  might be the teaching of mathematics in America, but you should be sure that your paper is addressing mathematical  issues, not just educational ones.

 

D.        Any aspect of mathematics in a non-European country or region prior to 1950, except Egypt and Mesopotamia. This might be a specific mathematician or the specific development of some field.   Since we will be discussing some aspects of Arab and Indian mathematics in class, you may only use one of these areas with special permission.  Discuss with me what you want to do before proceeding too far.

 

E.         Wild card topics.  I am willing to listen to any reasonable   proposal as long as the history of mathematics is involved, but I reserve the right to reject any topic.

 

Possible topics for your major paper

 

 

Discuss the development of one of the following areas/topics:

Trigonometry (Discuss with me first.)

Probability

Mechanics  from a mathematical point of view

Number theory  from 1400 onward

Derivatives (Discuss with me first.)

Integration (Discuss with me first.)

Integration techniques

Series  infinite series, power series

Analytic geometry (Discuss with me first.)

Projective geometry

Geometric perspective and its relation to art

Mathematical education

Abstract algebra  groups, rings, fields

Logarithms

Statistics

Differential equations

Graph theory

Topology

Non-Euclidean geometry (Discuss with me first.)

Concept of a function

Geography and map projections

Mathematical logic

Calculating machines

Vector analysis (the history of vectors)

Matrices/linear algebra

Women in mathematics

African-Americans in mathematics (or any other significant minority)

Calculus texts

Mathematics texts

Art and mathematics

 

Discuss some aspect of the works/contributions of one of the following:

Francois Viete

Simon Stevin

John Napier

Johannes Kepler

Galileo Galilei

Girard Desargues

Rene Descartes (Discuss with me first.)

Pierre de Fermat (Discuss with me first.)

Blaise Pascal

Isaac Newton (Discuss with me first.)

Gottfried Wilhelm Leibniz (Discuss with me first.)

Johann Bernoulli

Jakob Bernoulli

Leonhard Euler (Discuss with me first.)

Joseph Lagrange

Pierre Laplace

Adrien Legendre

Charles Babbage

Carl Friedrich Gauss (Discuss with me first.)

Augustin-Louis Cauchy

Evariste Galois

George Boole

Karl Weierstrass

George Bernhard Riemann

Georg Cantor

Henri Poincare

John von Neumann