Math 531 History of Mathematics --CRN# 11473
11:00 AM - 12:15 PM Tuesday and Thursday
||Instructor:||Professor William H. Richardson|
||Class Time:||11:00-12:15 TR, August 21 - December 14||
||Office:||322 Jabara Hall|
||Office hours:||9:30-10:20 TR, 2:00-3:00 MW and by appointment|
||Text:||A History of Mathematics, Brief Edition, by Victor Katz.|
|This course is designed to show what mathematics
is, how mathematics
has developed from man's
efforts to understand the world around him, what the mathematical
approach to real problems
can accomplish, and the extent to which mathematics has molded our
civilization and culture.
The extent to which civilization and culture have affected mathematical
development will also
be investigated. Although the course is about mathematics, the intimate
mathematics to science, philosophy, religion, music, painting, and
other arts, cannot be
overlooked. For here lie many of the motivations for mathematical
studies. Since mathematics
is what mathematicians do, a look into the lives of mathematicians will
integral part of the course.
On occasion, you will be asked to solve some mathematical problems related to the historical period or person being discussed.
A collection of short papers will be required. The topics are listed below. In addition, a semester project will be required. The semester project will be a paper or project appropriate to the course.
The course can be basically separated into eight parts (not equal in length), as given below. Basically the coverage will be chronological; however, certain topics will be covered out of order. For example, Part II, Numbers and Number Systems, will cover the evolution of numbers and number systems from ancient times to the present. This is done so that the students have a general idea of the problems mathematicians faced with inadequate numbers and number systems at various times in the history of mathematics.
|What is mathematics? A look at the difficulties
arising from an effort
define the term "mathematics."
What is a mathematician? A look at the wide spectrum covered by mathematics from philosophy to technology. When does a philosopher become a mathematician? When does a mathematician become a technician?
A chronological listing of events in mathematics and history. Quite often dates important in mathematics have no meaning to a student without reference to familiar historical events. This will be an overview of the time period covered by the course for later reference.
|Part II.||NUMBER AND NUMBER SYSTEMS|
|Counting and the history of number.
Numbers systems. An investigation of number systems from antiquity to the present. Number systems in various bases will be seen, as well as the effectiveness of each system.
Idiot Savants. - Human calculators. Here we look at the interesting phenomenon of people who can calculate difficult numerical problems with machine speed and how their views of numbers and number systems aided their mental computations.
|Part III.||ANCIENT MATHEMATICS|
| Babylonian and Egyptian mathematics. The
development of arithmetic
and geometry for use in commerce and agriculture. No interest in pure
Greek mathematics. The arrival of mathematics as a pure discipline.
Pythagoras. The life of an ancient mathematician and his school. How his mysticism and worship of the whole number influenced and held back further discoveries in mathematics.
Euclid. The man who is credited with formalizing the study of mathematics. The axiom, definition, theorem development of mathematical topics presented in his Elements produced the foundation of "Modern Mathematics."
During this period we will meet a variety of mathematicians who did remarkable work with elementary mathematics--one of the most remarkable was Archimedes.
India, the Middle East and China. Was mathematical knowledge isolated or did it spread geographically? Who did what first?
|Part IV.||THE DARK YEARS|
| The decline of mathematics and the sciences. In
the first ten centuries or so C.E.,
advances in mathematics and the sciences seemed to come to a halt.
Mathematics and religion. An investigation of the effects of religious thoughts on the development of mathematics. To quote St. Augustine (circa 400 C.E.)
"The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell."The rebirth of mathematical thought. This is a lead-in to the "golden age" of mathematics - how the use of mathematics in art rekindled interest in mathematics.
|Part V.||THE "GOLDEN AGE" OF MATHEMATICS|
| A chronological look at the "golden age" of
mathematics. The period of the 14th
through 19th centuries were very rich in mathematical development. Many
mathematical as well as historical importance occurred here, so it is
valuable to once
again have reference points.
Mathematics and the arts. The contribution of mathematics to the arts and architecture will be discussed throughout the course; however, in this period the topic deserves special attention.
Mathematics and society. Mathematics was widely studied in this period for general educational purposes. Educated persons took great pride in their knowledge of mathematics and new developments in mathematics. Mathematics enjoyed its greatest popularity during this period. It was not uncommon for newspapers and general periodicals to publish mathematical papers.
|Part VI.||BIOGRAPHICAL SKETCHES OF MALE MATHEMATICIANS FROM THE "GOLDEN AGE" OF MATHEMATICS|
|A partial list of some of the male mathematicians
whose lives we may
discuss in class. Not
all can be discussed in the time available; however, there are some who
must be discussed.
Descartes. (1596-1650) French.
The list of mathematicians was chosen from a list of many. The choice is the instructor's. Other people teaching this course may choose a different collection. These were chosen because of the interesting aspects of their lives. Of course, Newton, Euler and Gauss have made such prominent contributions their names would probably appear on everyone's list.
|Part VII.||BIOGRAPHICAL SKETCHES OF FEMALE MATHEMATICIANS|
|A partial list of some of the female
mathematicians whose lives we may
discuss in class. Not
all can be discussed in the time available; however, there are some who
must be discussed. For
many years female mathematicians were ignored in the history of
Hypatia (370-415) Greek
The list of female mathematicians was chosen from a list of many. The choice is the instructor's. Other people teaching this course may choose a different collection. These were chosen because of the interesting aspects of their lives. As well as for their contributions to mathematics.
|Part VIII.||THE 20th CENTURY|
|A brief history of the development of the
The computer as a tool. These two sections will cover the development of the computer and its value in science, mathematics and society. Very few people have a good understanding of what computers really do as a tool.
Mathematics and modern society. Have the giant strides of advancements in mathematics in the 19th and 20th centuries left the average person floundering in its wake? What effects have the educational processes of the "new math" of the 1960 had on modern education? What are the new standards for K-12 mathematics education?
Where do we go now? Here we will discuss what may be in store
for the mathematician in
the future. Might the mathematician, in the classical sense of the
word, disappear with future advances in computer technology? Or, will
there always be a need for people who dream mathematical thoughts?
|The student is responsible for attending class
and for all reading
materials and assignments.
Take care not to postpone doing work until the last minute. Assignments
will consist of written assignments and a term
project. All written assignments must contain a
bibliography. Not all references should be from the internet (no Wikipedia references please) and
no encyclopedias (Brittanica, Compton, etc.) should be used. Get
to know your library! Cutting and pasting from web sites is NOT
permitted--the punishment will be harsh.
The written assignments will be contained in a notebook (loose-leaf binder) as well as submitted to me electronically as PDF files. The building of this notebook starts with the beginning of the semester. It will contain all written assignments, as well as any other material you feel is interesting or important to you. I will collect these periodically during the semester.
The contents of the notebook should be arranged in sections for ease of locating material. An example might be:
Final Examination will be Tuesday, Dec. 11, from 10:00 AM to 11:50 AM. Brief oral presentations of your term papers will be given at this time. Attendance is required.
|Final grades will be determined by the contents of your notebook. All written assignments will be graded.
The following scale gives an idea of the worst grade you would receive.
100 - 94 A
Please be aware of the Statement of Academic Honesty
A standard of honesty, fairly applied to all students, is essential to a learning environment. Students abridging a standard of honesty must accept the consequences; penalties are assessed by the appropriate classroom instructors or other designated people. Serious cases may result in discipline at the college or University level and may result in suspension or dismissal. Dismissal from a college for academic dishonesty constitutes dismissal from the University.
(WSU Student Code of Conduct)
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