Catalog Description:

1701.498 Mathematics Seminar                                                                                                                         3 s.h.

(Prerequisites:  Senior standing and successful completion of two of the following courses: College Geometry,
Modern Algebra I, Ordinary Differential Equations, Introduction to Real Analysis or permission of the instructor)

This course is designed to integrate students' knowledge of mathematics and to further developing their problem solving abilities.  The course content includes problem-solving techniques, a review of the literature of mathematics, solving problems drawn from a variety of current resources, and study of techniques of proof and issues in the philosophy of mathematics and its foundations.  Additionally, each student is required to write and to present orally a research report on a mathematical topic.

Prerequisite Comments:

Senior standing and permission of the instructor, or the Department chairperson if the seminar is unstaffed at the time of enrollment.  Normally, such permission will be based on the successful completion of two of the following:  Geometry I, Modern (Abstract) Algebra, Differential Equations, Real Analysis I, Numerical Analysis, Applications of Mathematics or Complex Analysis I.

Objectives:

At the end of the seminar, students will be able to:

 1. Demonstrate various problem solving techniques as applied to advanced mathematical problems.

 2. Demonstrate various methods of proof.

 3. Cite the literature, implications, and applications of a topic from mathematics.

 4. Cite or demonstrate the developing relationship between computers and problem solving in mathematics.

 5. Write mathematical prose and explain orally undergraduate mathematics to others.

Topics:
 1. Introduction to Problem Solving

  Patterns and algorithms.
  Discovery, invention, and generalization.
  Heuristic strategies.
  Logic and proof.
  Types of problems.
  Historic and current unsolved problems.
  Recently solved problems.

 2. Solving Problems from Various Areas

  Algebra
  Analysis
  Foundations
  Geometry
  Emerging areas

 3. The Literature of Mathematics

  Journals, reviews, and abstracts.
  Developing a mathematical prose.
  Writing mathematical prose.
  Exposition of mathematical topics.
 

TEXTS:
None specified but certain Resource materials will be used such as:
 Journals:
  Journal for Recreational Mathematics
  The Mathematics Magazine
  The College Mathematics Journal
  The Mathematics Teacher
  The Arithmetic Teacher
  School Science and Mathematics
  Scientific American
  The Mathematics Association of American Monthly
  The Mathematics Intelligencer

 Books:

 * Davis, Hersh, Marchisotto, The Mathematical Experience-Study Edition, Birkhauser, Boston, 1999.

  *Young, Robert M., Excursions in Calculus-An Interplay of the Continuous and the Discrete, The Math Association
  of America, 1992.

* Usiskin, Peressini, Marchisotto, Stanley, MATH FOR HIGH SCHOOL TEACHERS--aN ADVANCE PERSPECTIVE, Prentice Hall, 2002

  Krantz, Steven G., A Primer of Mathematical Writing, American Mathematical Society, 1997.

  Krantz, Steven G., Techniques of Problem Solving, American Mathematical Society, 1997.

  Agrawal, O.P., GRE Mathematics Test, Research and Education Assoc., Piscataway, NJ