Honors Algebra: Math 512 and Math 513

Professor Karen E. Smith
East Hall 3074

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:
1. Professsor Smith's notes on Representation Theory , for a course she gave for math and (mostly) physics students in Finland. (Note: this is possibly a book in progress, so please report all typos and unclear explanations if you want your name mentioned in it!)
2. Herstein, Topic in Algebra (a classic: the book I learned it from! focused more on finite groups as the main examples)
3. Dummit and Foote, Abstract Algebra (a book I seriously considered for Math 512/513; tell me what you think!)

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

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)