University of Connecticut

Course Info


MATH 5020: Topics in Algebra

Description: Advanced topics chosen from group theory, ring theory, number theory, Lie theory, combinatorics, commutative algebra, algebraic geometry, homological algebra, and representation theory. With change of content, this course may be repeated to a maximum of twelve credits.

Prerequisites: MATH 5211.

Credits: 3


MATH 5020 - Section 1: Class Field Theory

Description: Class field theory is the study of the abelian extensions of arbitrary global or local fields. It is prerequisite for most any kind of research in algebraic number theory. In the course, facility with Galois theory will be assumed.

Offered: Fall

Credits: 3


MATH 5020 - Section 2: Introduction to Algebraic Geometry

Description: Algebraic geometry is an area of mathematics with deep connections to other areas: number theory, commutative algebra, complex and differential geometry, combinatorics, physics, statistics and engineering. Hence some working knowledge of algebraic geometry is useful in many different contexts. We will introduce basic concepts in algebraic geometry, such as affine and projective varieties, the Zariski tangent space, the Hilbert polynomial, rational maps, divisors, line bundles and maps to projective spaces. We will finish with the Riemann-Roch theorem for curves. Concepts will be illustrated with many examples, such as projective spaces, Grassmannians, the Segre and Veronese embeddings, and blow-ups.

Offered: Fall

Credits: 3



Sections: Fall 2009 on Storrs Campus

PSCourseID Course Sec Comp Time Room Instructor
08023 5020 001 Lecture MWF 1:00-1:50 MSB307 Lee, Kyu-Hwan
14013 5020 002 Lecture TuTh 12:30-1:45 MSB117 Milena Hering