Time and Place: 8:008:50am MWF, CB 347 Instructor: Alberto Corso, POT 969, 2573167, corso@ms.uky.edu, www.ms.uky.edu/~corso. Office Hours: MWF 10:0010:50am or by appointment. Textbooks:
An approximate distribution of the weights of each of the above assignments is: quizzes (40%); inclass 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); nonEuclidean geometry (Chapter 7); polyhedra (Chapter 8); etc. Bibliography: Other relevant references are listed below:
