Math 4510.001/5700.002 -- Exploratory Galois Theory

Lectures:   MWF 9:00-9:50 a.m. in BLB 050.

Instructor: William Cherry

Office Location: General Academic Building (GAB) 405.


Math 3510 or an undergraduate course in abstract algebra. Students are expected to be familiar with groups and be comfortable with algebraic formalism and abstraction.

Course Description

A set of numbers with addition, subtraction, multiplication, and division is called a field. Familiar examples are the rational numbers Q, the real numbers R, and the complex number C. A less familiar example is, say, the Gaussian rational numbers Q[i]={a+bi : a,b are in Q}. A field, such as this last example, which is also a finite-dimensional Q-vector space is called a number field. The automorphisms of a number field form a group, and there is a beautiful connection between the structure of this group and the algebraic and arithmetic properties of the number field. This is what is known as Galois Theory, after its inventor, Evariste Galois. This course will be a concrete hands-and exploration of this so-called Galois correspondence, and we will make extensive use of computer explorations. This course serves as a bridge between an undergraduate first-course in abstract algebra and a graduate-level modern algebra course.


John Swallow, Exploratory Galois Theory, Cambridge University Press, 2004

Course Requirements

In Class Midterm15%
Take Home Midterms25% (12.5% each)
In Class Final Exam25%


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