Department of Mathematics

Syllabus

**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.

**OBJECTIVES:**

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.

**CONTENT:**

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

**POSSIBLE TEXT(S):**

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.