Syllabus for Ma 330-001 - History of Mathematics

Time and Place: 8:00-8:50am  MWF, CB 347

Instructor: Alberto Corso, POT 969, 257-3167, corso@ms.uky.edu, www.ms.uky.edu/~corso.

Office Hours: MWF 10:00-10:50am or by appointment.

Textbooks:

  • A Coincise History of Mathematics, by D.J. Struik, Dover Publications, ISBN 0486602559.
  • Geometry: Euclid and Beyond, by R. Hartshorne, Undergraduate Texts in Mathematics, Springer, 2000, ISBN 0-387-98650-2.
Assignments and Grade: You'll take several quizzes (based on the material presented in class) during the semester. There will also be two assignments that will help improve your oral and written communication skills in a technical situation. Namely, you'll give an in-class group presentation on a topic that the instructor will assign you well ahead of time; you will also be given a major source from which to elaborate your presentation. The instructor will give some in-class presentations (using PowerPoint or a similar software package) so that you'll have an idea of what you are expected to do. Finally, you will write a 7/8 page paper on a topic of your choice. Your topic will be (1) a particular mathematical work or part of a work, or (2) a topic in mathematics during a suitably narrowed period of time, or (3) the contributions of a particular mathematician. Keep your topic fairly narrow otherwise your paper won't get any depth. This paper will be due at the end of the semester; however, by the end of March you'll have to submit a one-page outline describing the main topics that you'll address in your paper. This assignment will also help you learn how to use the Math Library as well as the Internet for Mathematics.
An approximate distribution of the weights of each of the above assignments is: quizzes (40%); in-class presentation (30%); topic paper (30%).

Course Description: We will explore some major themes in mathematics and their historical development in various civilizations, ranging from the antiquity (Babilonia and Egypt) through classical Greece, the Middle and Far East, and on to modern Europe.
The basic text for the course is A Coincise History of Mathematics, by D.J. Struik. However we will supplement the textbook using additional sources. These supplements will have a major mathematical content (such as proofs of original results which deeply influenced the development of Mathematics). Later in the course, these supplements will be delivered to the class in the form of formal presentations by groups of students (but still with the help of the instructor!). Among the topics that we will analyze in greater detail we list: Hippocrates' quadrature of the lune; Euclid's proof of the Pythagorean Theorem; Euclid and the Infinitude of primes;Archimedes' determination of circular areas; Heron's formula for triangular area; Cardano and the solution of the cubic; Newton's approximation of pi; the Bernoullis and the harmonic series; the extraordinary sums of Leonard Euler; a sampler of Euler's number theory. Time permitting, other topics will be added to the previous list.
Although the course will probably stop approximatively in the middle of the 18th century, Mathematics didn't die there. It is just that the Mathematics gets more advanced and more abstract, and we don't have time to look at it in just one semester. The further developments of mathematics are likely to be good choices for the topic paper that students are required to write.
The book Geometry: Euclid and Beyond, by R. Hartshorne, will be used to gain a deeper understanding of Euclid's Elements. This rather challenging book can also be used as a starting point for some interesting topic papers: Hilbert's axioms (Chapter 2); Construction with ruler and compass (Chapter 6); non-Euclidean geometry (Chapter 7); polyhedra (Chapter 8); etc.

Bibliography: Other relevant references are listed below:
  • C.B. Boyer, A History of Mathematics, New York, 1968.
  • W. Dunham, Journey through Genius, New York, 1990.
  • J.H. Eves, An Introduction to the History of Mathematics, 1990.
  • V.J. Katz, A History of Mathematics: an Introduction, New York, 1998.