I. Number and title of course

Mathematics 696 History of Mathematics

A. A student who is working toward an advanced degree in mathematics is not worthy of the degree if he has learned nothing about the history of mathematics.

B. Studying the lives, works and methods of the great mathematicians can inspire gifted students to greatness.

C. Secondary and elementary school teachers taking the course will find it courses they useful as a source of background and enrichment material for may be teaching.

D. It is a standard course in every college or university that offers the Master's degree.

A. To study the contributions to mathematics of past and present civilizations.

B. To familiarize the student with the lives, works and methods of the great mathematicians of the past.

C. To give the student a better understanding of the nature of mathematics by singling out the ideas and discoveries that have had a great impact on the scope and development of mathematics.

D. To acquaint the student with the development of techniques for solving certain mathematical problems. In particular, to have the student solve some of these problems by both modern methods and methods used in the past.

E. To help the student develop a philosophy of mathematics.

A. Egyptian and Babylonian Mathematics

B. Greek Mathematics

1. The birth of demonstrative mathematics

2. Pythagoras and the Pythagoreans

3. The discovery of irrational numbers

4. Endoxus' definition of proportion

5. Geometric solutions of quadratic equations

6. The three famous problems of antiquity

7. The Elements of Euclid

8. Archimedes

9. Apollonius and the Conic Sections

10. Heron, Diophantus and Pappus

C. The period 500 to 1500 A.D.

1. Contributions of the Hindus and Arabs

2. Omar Khayyam's geometric solution of cubic equations

3. Fibonacci and the Fibonacci sequence

4. The gradual acceptance of the Hindu-Arabic Numerals

D. The Renaissance

1. The algebraic solution of the cubic and quarter equation

2. Viete and the beginning of symbolic algebra

E. The Seventeenth Century

1. The invention of logarithms

2. Galileo and Kepler

3. The invention of analytic geometry

4. The development of projective geometry

5. The invention of the calculus

6. The beginnings of mathematical probability

7. Contributions of Fermat, Descartes, Desargues, Pascal, Newton and  Leibniz

F. Mathematics after 1700 but prior to the Twentieth Century

1. Euler and Lagrange

2. Gauss

3. The discovery of non-Euclidean geometry

4. The arithmetization of analysis

5. The rise of abstract algebra

6. Other mathematicians and their contributions

Bell, E.T. Development of Mathematics. New York. McGraw-Hill, 1940.

Bell, E.T. Men of Mathematics. New York. Simon and Schuster, 1937.

Boyer, C.B. A History of Mathematics. New York. John Wiley and Sons, 1968.

Cajori, F. A History of Mathematical Notations, 2 Vols. Chicago: Open Court 1928-1929.

Coolidge, J. L. The Mathematics of Great Amateurs. New York. Oxford Univ. Press, 1949.

Dantzig, T. Number, The Language of Science. New York. Macmillan, 1954.

Eves, H. An Introduction to the History of Mathematics. New York. Halt, Rinehart and Winston, 1964.

Ginsburg, J. and D.E. Smith. A History of Mathematics in America before 1900. LaSalle, Ill. Open Court, 1930.

Heath, T.L. A Manual of Greek Mathematics' New York. Dover, 1963.

Heath, T.L. Apollonius of Perga, Treatise on Conic Sections. New York. Barnes and Noble, 1961.

Heath, T.L. The Thirteen Books of Euclid's Elements, 3 Vols. New York. Dover, 1956.

Heath, T.L. The Works of Archimedes. New York. Dover, 1963.

Kline, M. Mathematics in Western Cultures New York. Oxford University Press, 1953.

Newman, J. The World of Mathematics. 4 Vols. Schuster, 1955.

Ore, O. Niels Henrik Abel, Mathematician Extraordinary. Minneapolis. University of Minnesota Press, 1957.

Sanford, V. A Short History of Mathematics. New York. Houghton Mifflin, 1930

Smith, D.E. A Source Book in Mathematics. New York. McGraw-Hill, 1929.

New York. D. E. A Sourse Book in Mathemtics. NewYork. McGrawHill,1929.

A. Presentation will be mainly by lectures of the instructor. The student may be required to do some teaching by giving an oral report on some outside reading or showing the class how to do a problem assigned only to him.

B. Evaluation will be based on tests, homework assignments that are handed in, written book reports, and any oral presentations required of the student.

12 semester hours of mathematics beyond the calculus.

3 semester hours

This course proposal was examined in accord with recommended procedures and was approved by the Graduate Faculty of Mathematics.

Math. 696 - History OF MATHEMATICS- Chronological study of the development of elementary mathematics; contributions of nations, ages or periods; selected biographies; appraisals and critiques, problem studies.

Classification: Elective for M.S. and M.A. mathematics students.

Prerequisite: 24 semester hours of mathematics beyond the calculus.

Credit. 3 semester hours.

Cherkauer, R. J. Ed. D. State University of NY at Buffalo 1948-69
Torchinelli, G. M.S. University of Illinois 64 hrs. beyond Masters 1954-69