Math 420 B
Special Topics in Mathematics
Spring 2011: History of Mathematics
Please note: This is an offering of a
course under consideration for inclusion in the course offerings in the
Department of Mathematics at the University of Puget Sound. Accordingly, I
expect that this page, and particularly the topic list and bibliography, will
undergo substantial changes over the course of the semester.
This page last revised 1/6/2011
Introduction
- Catalog Description: The course will tell the story of
Mathematics with emphasis on the modern era beginning with the development of the calculus and proceeding to
the present time. Prerequisite: Math 180 or permission of
the instructor.
- Objectives: It is important for students of mathematics,
and particularly prospective teachers of mathematics, to have an
understanding of how mathematics came to be. To that end, the course
will provide a quick survey of ancient and medieval mathematics up to the
time of Fibonacci, with a slower and more detailed survey of mathematics
from the development of the calculus on. The development of the
principle ideas will be developed along with biography and an appreciation
for the cultural / historical context of the development of those ideas.
- Prerequisites: Math 180 or permission of the
instructor.
Poster copy
Much of the way in which we learn mathematics has little to do with how it
came about. This course will start to tell that story, together with
stories about the people (some of whom are very interesting characters indeed!)
who developed the ideas and techniques we study in our other mathematics
courses.
The topic is much too large to cover in one course. In this course,
then, we will look primarily at the history of modern mathematics. We will
begin with a quick survey of the mathematics before the development of the
calculus and move more deliberately through the mathematics of the seventeenth
century on to the present time.
It will be useful for the interested student to have a basic understanding of
the differential and integral calculus, such as is gained in the first year of
calculus. This will form the background to the discussion. This is
not intended as a firm prerequisite however, and interested students who have
not yet taken a year of calculus should talk with the instructor.
Topics
This section is still in development, and will undergo changes throughout the
semester.
- Mathematics before the 17th century (briefly)
- The reasons for the development of mathematics in ancient cultures
- A survey of ancient mathematics (with some comments on the mathematics
of China and India)
- Greek and Arabic Mathematics: The rise of formalism.
- The great sleep: Medieval mathematics and mathematics through the "dark ages"
- The re-awakening of European Mathematics
.
- The plan is that these first topics will be moved through quickly,
mostly by reading with lecture and some problem assignments.
- The rise of analysis
- The development of the calculus
in the 17th century
- The development of the theory of probability
- Non-Euclidian Geometry, the rise of formalism, and the first
foundational crisis.
- Analysis during the 18th and 19th
centuries.
- Set theory and more foundational confusion.
- The rise of modern mathematics
- Algebra
- Combinatorics
- Topology (Personal comment: This is my area of mathematics, and it
was through the study of the history of this topic that I became interested
in the history of mathematics generally).
- Computer Science
- The International Congress of Mathematicians and the
internationalization of Mathematics (see the books by Olli Lehto and Constance Reid
in the bibliography)
- Foundations and the loss of certainty (which is also a title of a
book by Morris Kline - see the bibliography).
Formalism, Intuitionism, and Logicism (Please see also The Three Crises in Mathematics: Logicism,
Intuitionism and Formalism Mathematics Magazine, Vol. 52, No. 4. (Sep.,
1979), pp. 207-216.
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Bibliography