**Honors Algebra: Math 512 and Math 513 **

Professor
Karen E. Smith

East Hall 3074

3-5048

Math 512/513 is a year long sequence intended to introduce honors math students to the art and practice of abstract modern algebra.

Prerequisites:
Math 296.

The course is also appropriate for
some senior math majors with A+'s in both 412 and 217, as well as at least one further proof-oriented math course.

The lectures for the course are MWF at 2 pm in 1372 East.

Office hours immediately after class on mondays and 12 noon on Thursdays; also by appointment.

Assistant: Alex Carney, senior honors math major. Discussion Session will be Tuesdays at 3 pm in Room 3088 EH, with office hours immediately following.

** Text: ** Artin, Algebra, first edition, 1991. Here are electronic copies of the
first chapter and appendix, as well the second chapter , if you are still waiting for yout texbook.

** Supplementary Reading:
**

Syllabus for Math 512/513: essentially the table of contents of the textbook. In 512, we will cover groups and their actions on vector spaces and other sets, essentially the first nine chapters of Artin's book (lightly reviewing of 1-4 and much of 7, which were covered in 296). In 513, we will ocover rings, modules, fields and Galois theory (chapters 10-14).

Details about course organization on the Math 512 Course Information Sheet

Resources for Latex and more helpful Commutative Diagram tips for Tex

The Daily Update, a summary of what was discussed in class each day, including assignments and quiz announcements.

** Class Exercises: **

on the symmetry group of a square;

the quaternion group

the isometry group of Euclidean space

The Automorphism group of the quaternion group (assigned as part of Homework Set 5)

the dihedral groups

Orbits and Counting

Cayley Graphs

Representations of S4

** Exams: **

Exam 1 Results and the
Actual Exam

Exam 2

Exam 2 Results

The Final: The In-Class Part and the
Take-Home Part

Quizzes: Quiz 1 , Quiz 2 with solutions , Quiz 3 with solutions , Quiz 4 with solutions , Quiz 5 , Quiz 6 , Quiz 7 ,

Problem Sets: Set 1 , Set 2 , Set 3 , Set 4 , Problems for Exam 1 , Set 5 , Set 6 , Set 7 , Set 8 , Exam 2 Problems , Set 9 , Set 10 , Final Exam , (Take-home exam; basically a problem set)