MA484 HISTORY OF MATHEMATICAL THOUGHT (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 312 (Abstract Algebra with Applications) or MA 331 (Geometry I).

Offered:  Fall

Course Description
An historical view of mathematics. Studies in discovery, rigorization, and generalization through abstraction.

Goal Purpose
The study of the history of mathematics is as vast and diverse as the study of mathematics.  The purpose of this course is to introduce students to the history relating to the mathematics which they have in their background, including topics in systems of numeration, number concepts, arithmetic and algebra, geometry, number theory, probability, and calculus.

Objectives
Students are expected to:

1. do historical research and report their findings.
2. develop understandings of the contributions to mathematics by different civilizations.
3. gain an appreciation of the effects of cultural backgrounds of individuals on their contributions to mathematics.
4. develop understanding of the controversies in the development of mathematics.
5. become familiar with the resources relating to mathematics.

Course Content Outline

1. Ancient Developments of Systems of Numeration and Number Systems
   1. Primitive communication and counting
   2. Babylonian, Egyptian, Roman, Chinese-Japanese, Mayan, and possibly other cultural contributions to numeration
   3. Hindu-Arabic systems
   4. Pythagoreans
   5. Computations and algorithms from various cultures
2. Geometry
   1. Pre-Hellenic
   2. Early Greek geometry (deductive rather than empirical)
   3. Euclid, Archimedes, and Appolonius
   4. Non-Euclidean
   5. Projective Geometry
   6. Analytic Geometry
3. Algebra and Number Theory
   1. Equations
   2. Theorems in algebra
   3. Primes, Pythagorean triples, Fibonacci numbers
   4. Complex numbers
4. Calculus
   1. Evolution of the limit concept, method of exhaustion, Zeno's paradox, infinitesimals
   2. Middle of the 16th century to the middle of the 17th century - a century of anticipation
   3. Newton and Leibnitz
   4. Integration and measure; Cantor, Dedikind, C. Jordan, Borel, Cauchy, Riemann, and others
5. Topics in the Foundations of Mathematics
   1. Axiomatics
   2. Intuitionism, logicism, and formalism