"Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect."
 Hermann Weyl, Symmetry
 Hermann Weyl, Symmetry
Textbook 
M.A. Armstrong, Groups and Symmetry, SpringerVerlag (1988)

Course Goals 
This course will develop the basic theory of groups. Although our perspective will be extremely abstract, we will devote considerable attention to group theory's myriad applications (for instance, to number theory and geometry). Of particular interest will be the manner in which group theory provides a powerful mathematical tool for studying symmetries.

Exams 
There will be two midterms during the semester. The first midterm will take place during class on Wednesday March 8. The second midterm will be a take home tentatively due on Wednesday April 19. There will also be an inclass final exam on Thursday May 11, 79pm. Please let me know as soon as possible if there is a problem with any of these dates.

Project 
Towards the end of the semester you will work with one or two other students on an independent project related to group theory. This project will have two components. You will make a brief presentation (~1520 minutes) in class and submit a written report (~5 pages). Additional information regarding the project will be forthcoming.

Grading 
Participation: 5%
Homework / Special project: 35% Midterms: 20% each Final exam: 20% 
Disabilities 
Any student with a documented disability is asked to notify their instructor and the Office of Disability Services (located in Peters G27/G28) so that accommodations may be made. For more information, see http://new.oberlin.edu/office/disabilityservices/index.dot.

Honor Code 
Oberlin requires that all students sign an Honor Code for all assignments. This pledge (which is to be written out on each assignment) states: “I affirm that I have adhered to the Honor Code in this assignment.” More information about the honor code can be found at the following website: http://new.oberlin.edu/office/deanofstudents/honor/students.dot
As an example of how this applies to this class, you should not search for solutions to problem sets or takehome midterms on the internet. Similarly, you may not copy any portion of the work of another student and submit it as your own. 
Outline 
Introduction and basic notions (chapters 18) 4 weeks
Products, quotients, homomorphisms (chapters 9–16) 4 weeks Group actions and enumeration (chapters 17–19) 2 weeks Sylow theorems, structure of abelian groups (chapters 20–22) 2 weeks Additional topics As time permits 