There are many types of history courses that you can design. Here are some standard types:
· Survey
· Theme
· Topics
· Sources
· Readings
· Seminar
In typical mathematical fashion, we begin with definitions.
A survey course is one that discusses a broad range of the history of mathematics including a variety of topics over many consecutive time periods. Here are some possible survey textbooks and examples of such courses:
History of mathematics for prospective elementary teachers.
Mathematical ideas leading to the calculus.
A theme course selects one mathematical topic to concentrate on for the entire term. Some examples:
The History of the Calculus.
Women in Mathematics.
Non-Euclidean geometry.
The mathematics of Isaac Newton.
A topics course chooses several mathematical topic to discuss and bases the whole course of ideas related to these topic. Here are a few examples:
Great Theorems of Mathematics.
Hilbert’s problems.
Some people ask the difference between a topics and a theme course. In a theme course one mathematical topic is chosen and concentrated on throughout the term. For example, if you theme is algebra, then you might well want to discuss the Mesopotamian solutions of quadratics, the work of Cardano and his "friends", Abel and Galois, and the rise of abstract groups. All of these topics are related mathematically. But in a topics course, one just moves from topic to topic and they need not be related mathematically. For example, a course on the topic of Hilbert's problems has a common theme, but that theme is the that the problems were made famous by Hilbert in his 1900 speech; they are not connected mathematically. Now this distinction is probably not important, so if you don't buy into it, that is OK.
A sources course bases a large part of the course on the readings of original sources, usually in English translation. Here are some possible sources textbooks. Examples:
Euclid in Latin.
A readings course is organized around reading a variety of types of material. Examples:
Mathematics in Russia.
Seminal papers in and about topology.
Important recent papers in the history of mathematics.
A seminar course is organized so that there is more discussion than lecture and so that several individuals take the lead in developing the individual topics chosen.
We have begun with definitions, but you will note that these are not as clear as a mathematician might wish and they are certainly not exclusive. For example, several people have used Journey through Genius by Bill Dunham as a textbook. This combines some of the idea of a topics course with a sources course.
Return to the minicourse home page.
If you have comments, send email to V. Frederick Rickey at
fred-rickey@usma.edu .
Posted 11 January 2003. Revised July 2005.