Topics in Mathematics
Listed in: Mathematics and Statistics, as MATH-37
Robert L. Benedetto (Section 01)
The topics may vary from year to year. The topic for fall 2007 is Galois Theory, which is the systematic study of the roots of polynomials. The key idea, first glimpsed by Lagrange and later brought to fruition by Galois, is that there is a deep relation between group theory and the structure of the set of roots of a given polynomial. One of the most famous results of the theory is that there is no analogue of the quadratic formula for polynomials of degree five and higher; another is the impossibility of trisecting an angle with straightedge and compass. This course will develop Galois Theory from the basics of groups and fields. Four class hours per week. Offered in alternate years. Requisite: Mathematics 26. First semester. Professor Benedetto.