HISTORY OF MATH

MA 410

Catalogue Description

This course is a historical narrative of the development of major mathematical ideas and concepts over the centuries. It is a historical narrative. Students concentrate on related problems and their applications, which provide them with valuable information in business, science, education, and research. Knowledge of the rudiments of mathematics through calculus is desirable for the course.

3 credits. Prerequisite: MATH 191 Calculus II or equivalent.

Goals

A. To review the topics of mathematics that are usually covered in K-12, both of mathematical and historical content.

B. To present applications of the content that can be used in the College course, especially for teachers of mathematics in Elementary and Secondary schools.

C. To see the development of topics that began in early years to the present.

D. To introduce students to research presenting a topic both oral and written.

Procedures

A. Lecture/Discussion

B. Readings and Assigned Problems

C. Research Project

Course Content

A. History of Numbers and Numerals

1. Early Mathematics

1. Babylonian

2. Egyptian

3. Roman

4. Greek

5. Chinese - Japanese

6. Mayan

2. Primes and Composites

3. Pythagorean Triplets

4. Eratosthenes

5. Al-Khowarizmi

6. Fibonacci Numbers

7. Magic Squares

B. History of Computation

1. The Pythagorean Theorem

2. History-ellipse, Hyperbola

3. Duplication of the Cube Trisection Problem

Quadrature of the Circle

4. The Golden Section

5. Non Euclidean Geometry

C. History of Algebra

1. Early Greek Algebra

2. Hindu Algebra

3. Arabic Algebra

4. Descartes' Rule of Signs

5. Discriminant

6. Complex Numbers

D. History of Trigonometry

1. Early Trigonometry

2. Ptolemy's Works

3. Right Angles and Angular Measure

E. History of Calculus

1. Archimedes and His Calculus

2. Johann Keplar

1. Contributions

1. Fermat

2. Newton

3. Barrow

4. Archimedes and the "Method of Exhaustion"

F. The Development of Modern Mathematics

Evaluation Methods

1. To present summaries at the end of each chapter with a test to discover the needs of the students.

2. To work with students on a paper in Mathematics-Research, outline, class presentation, written paper, evaluation, and conference with class.

3. Applications of historical topics for the students in modern days.

4. To see mathematics as:

1. An Art-Euclidean Geometry; Non-Euclidean Geometry.

2. Science

a. Applications in Physics and in Chemistry

b. Astronomy

c. Engineering Courses

d. Economics

Bibliography

Required Text: Eves, Howard, An Introduction to the History of Mathematics, 6th Ed., Saunders Publishing Co., 1990.

Boyer, Carl B., A History of Mathematics, John Wiley & Sons, New York, N.Y., 1968.

Calinger, Ronald, Classics of Mathematics, Moore Publishing Co., Oak Park, Illinois, 1982.

Chace, Arnold Buffum, The Rhind Mathematical Papyrus, translated, National Council of Teachers of Math, Reston, Va., 1979.

Crowder, Norman A., The Arithmetic of Computers, (An Introduction to Binary and Octal Mathematics), Doubleday & Co., Garden City, 1960.

Historical Topics for the Classroom, National Council of Teachers of Mathematics, 31st Yearbook, 1967.

Newman, James, The World of Mathematics, Vol. I, Simon & Schuster, New York, N.Y., 1956.

O'Daffer, Phares G & Clemens, Stanley R., Geometry: An Investigative Approach, Addison-Wesley Publishing, Reading, Mass., 1977.

Smith, David Eugene, History of Mathematics, Vol. I & II, Ginn & Co., Boston, Mass, 1925.

Struik, Dirk J., A Concise History of Mathematics, 3rd Rev. Ed., Dover Publishing Co., New York, N.Y., 1967.

Van Der Waerden, B.L., Science Awakening, Oxford University Press, New York, N.Y., 1961.