Department of Mathematics

Math 01.180 - Introduction to the Foundations of Mathematics


Math 01.180 Introduction to the Foundations of Mathematics                                                                         3 s.h.
(prerequisites: registration by invitation only)

This is a lower-level general education honors course which provides the student with a working
knowledge of the foundations of mathematics; basic concepts and principles in the philosophy of
mathematics and mathematical logic, including set theory, the concept of infinity and proof. The
course requirement includes a major essay.


This course is designed to provide students with the opportunity to explore the foundations of mathematics. Students will be expected to:

-- develop an understanding of the interrelationships within mathematics and an appreciation of its unity.

-- explore the connections that exist between mathematics and other disciplines.

-- develop their own processes, concepts, and techniques for solving problems.

-- exercise mathematical reasoning through recognizing patterns, making and refining conjectures and definitions, and constructing logical arguments, both formal and heuristic, to justify results.

-- develop skills in both written and oral communication of mathematical concepts and technical information.

-- understand and appreciate the power of mathematical language and symbolism in the development of mathematical concepts.

-- develop and use alternate strategies for solving problems.

-- explore the dynamic nature of mathematics and its increasingly significant role in social, cultural, and economic development.


Topics will be selected from the following, according to student and faculty interests:

I. Problem solving process

II. Philosophy of mathematics (conceptions of the nature of mathematics)

II. Number

     A. Number bases and logarithms
     B. Sequences and series
     C. Number theory
     D. Concept of an algorithm

III. Space

     A. Tilings
     B. Algebraic curves
     C. Fractals

IV. Logic

     A. Laws of logic
     B. Syllogisms
     C. Godel's Theorem
     D. Turing Machines
     E. Set theory and Boolean algebra
     F. Axiomatic systems

V. Infinity

     A. Cardinality
     B. Infinitesimals

VI. Information

     A. Algorithmic complexity
     B. Inconceivability
     C. Runtime


This course is particularly suitable for the use of multiple texts. Some which might be used include the following:

Davis, Philip J. & Hersh, Reuben. The Mathematical Experience.  Boston: Houghton-Mifflin, 1981.

Jacobs, Konrad. Invitation to Mathematics. Princeton: Princeton University Press, 1992.

Maor, Eli. To Infinity and Beyond: A Cultural History of the Infinite. Boston: Birkhauser, 1986.

Stevenson, Frederick. Exploratory Problems in Mathematics.  Reston, VA: National Council of Teachers of Mathematics, 1992.

Seteky, Gallo. Fundamentals of Mathematics. 8th edition, Prentice Hall, 1999.

Gurant, Robbins, and Stewart. What is Mathematics?, Oxford University Press, 1996.

Stewart. From Here To Infinity, Oxford University Press, 1996.

Devlin. Mathematics: The Science of Patterns: The Search for Order in Life, Mind, and The Universe, W.H. Freeman, 1997.