Modern Algebra and Geometry I
MATH 4000/6000
University of Georgia, Fall 2008

Professor Clint McCrory
Office: 402 Boyd Graduate Studies Research Center, 706-542-2576
Home: 390 Franklin St., Athens 30606, 706-353-6517
Email: clint at math dot uga dot edu

Class meetings
Tuesday and Thursday 9:30-10:45
303 Boyd Graduate Studies Research Center

Office hours
Monday - Friday 12:30-2:00
or by appointment.
Exam week office hours: Monday, December 15, 1:00 - 3:00 pm

Prerequisites
(1) Linear algebra: MATH 3000 or MATH 3500 or MATH 3500H
(2) Introduction to proofs: MATH 3200
These prerequisites are essential for success in this course!

Syllabus
The textbook is Abstract Algebra: A Geometric Approach, by T. Shifrin. We will cover chapters 1-5: The integers, From the integers to the complex numbers, Polynomials, Homomorphisms and quotient rings, Field extensions.

Exams, homework, and grading
There will be three in-class exams and a final exam. Homework will be assigned almost every class. Your grade will be based on the exams, homework, and class participation. The three exams will count 20% each, homework will count 20%, and the final exam will count 20%. Class participation will be considered in borderline cases.

Problem set 1
Problem set 2
Problem set 3
Problem set 4

Problem set 5
Problem set 6
Problem set 7
Problem set 8 (don't hand in)

Problem set 9
Problem set 10
Problem set 11 (don't hand in)

Linear algebra review (don't hand in)
Problem set 12

Exam 1: Thursday, September 18. Solutions
Exam 2: Thursday, October 23. Solutions
Exam 3: Thursday, November 20. Solutions
Review session: Wednesday, December 10, 10:00-11:30 am, Boyd 303
Final Exam: Tuesday, December 16, 8:00-11:00 am

Notes from class
Roots of cubics
Quotients of the ring of Gaussian integers
Ruler and compass constructions

Useful links and references
Construction of the real numbers: Calculus, by Michael Spivak (third edition), chapters 29 and 30 (pages 578-596).
Proof of unique factorization in Z[x]: Algebra, by Michael Artin, chapter 11, section 3 (pages 398-401).
An inspiring book about applications of algebra: In Code, by Sarah Flannery
Compass and straightedge constructions - Wikipedia
Famous Problems of Geometry and How to Solve Them, by Benjamin Bold - Dover Publications
Euclid’s Elements, web version by David Joyce of Clark University

All academic work must meet the standards contained in the document A Culture of Honesty. Students are responsible for informing themselves about those standards before performing any academic work.

This page was created on August 1, 2008. It was last revised on December 17, 2008.