Overview
Topics in group theory include groups, subgroups, quotient groups, Lagrange's theorem, symmetry groups, and the isomorphism theorems. Topics in Ring theory include Euclidean domains, PIDs, UFDs, fields, polynomial rings, ideal theory, and the isomorphism theorems. In recent years, additional topics have included the Sylow theorems, group actions, modules, representations, and introductory category theory.Instructor
Dagan KarpOffice: 3414 Shan
Office hours: Tue 34pm, and open door.
Lectures
This course will meet for lectures Monday and Wednesday, 1:152:30pm in Shanahan 3421.Textbook
We'll use Abstract Algebra: Theory and Applications, by Tom Judson.It is freely available online, in both html and pdf.
Grading
There will be two exams and weekly homework. Let A be your homework average, B your score on Exam 1, C = Exam 2, D = Max (A,B,C) and Then your grade will be determined byHomework
Written homework will be due each Wednesday at the beginning of class, and is posted below.You are encouraged to discuss the homework with other members of the class, and it is appropriate to acknowledge the assistance of others. You will, however, be expected to write up your solutions on your own. The instructor will reserve the right to refuse to accept late homework for any reason. Graded homework, however, may (in most cases) be rewritten and submitted at a later date. Please consult the HMC mathematics homework format guidelines for helpful tips on homework submission and formatting.
Rewrites
Like other writing, good math writing is a process that includes revision. In Math 171 this is reflected in the rewrite policy. You will have the opportunity to turn in a rewritten copy of every homework assignment.For details, see the Math 171 Rewrite Policy.
Grutors
Feiyand Lin and Princewill Okoroafor are our graders and tutors. They will hold tutoring hours Sunday and Tuesday, 79pm in Shan 2444.Exams
There will be two exams, both of which are takehome. Exam 1 will be distributed Wednesday, 10/3 and due 10/10. Exam 2 will be distributed Wednesday, 12/12, due Tuesday 12/18.Critical Readings
In addition to the written homework, suggested readings will be posted on the homework page in conjunction with upcoming lectures. Before each lecture, read the corresponding material. Class activities will depend on your study of this material in advance (which is a departure from most lower division courses).The goals of the critical reading exercises are manifold: to better the student's independent intake of mathematical exposition, to train in independent learning, to increase the interactive nature of the course (by allowing the instructor to respond to questions and comments), and to make the course more tailored to the specific curiosities of the class as a whole.
LaTeX
Students interested in using LaTeX are encouraged to do so, but it is not required.Disabilities
It is the policy of The Claremont Colleges to accommodate students with temporary or permanent disabilities. Any student with a documented disability who requires reasonable accommodations should contact Deborah Kahn, Coordinator for Student Disability Resources at (909) 6073148 or dkahn@hmc.edu, as soon as possible. Students from the other Claremont Colleges should contact their home college's disability officer. Counterparts at the other campuses are as follows: CMC: Julia Easley (julia.easley@cmc.edu) CGU: Chris Bass (chris.bass@cgu.edu) HMC: Deborah Kahn (dkahn@hmc.edu) Pitzer: Gabriella Tempestoso (gabriella_tempestoso@pitzer.edu) Pomona: Jan CollinsEaglin (jan.collinseaglin@pomona.edu) Scripps: Leslie Schnyder (lschnyde@scrippscollege.edu)Math is for all
My goal is to welcome everyone to mathematics, and to broaden participation in the mathematical sciences. Our classroom should be an inclusive space, where ideas, questions, and misconceptions can be discussed with respect. There is usually more than one way to see and solve a problem and we will all be richer if we can be open to multiple paths to knowledge. I look forward to getting to know you all, as individuals and as a learning community.Lecture Notes
Here are (old) course notes. Introduction to groups: symmetry and permutation
 Formal definition of group, first examples and properties
 Subgroups
 Cyclic Groups
 Symmetric and Dihedral Groups
 Cosets and Lagrange's Theorem
 Group Homomorphisms
 Normal Subgroups
 Isomorphism Theorems
 The Fundamental Theorem of Finitely Generated Abelian Groups
 Definition of Ring, first examples and properties
 Ring homomorphisms, subrings, and quotient rings
 Polynomial rings, matrix rings and group rings
 Ideals
 Maximal and Prime Ideals
 Euclidean Domains
 Principal Ideal Domains
 Unique Factorization Domains
 Polynomial Rings Revisited
 Introduction to Category Theory: Objects and Morphisms
 Functors
Homework and Readings

Reading: Chapter 3, and Francis Su's Guidelines for Good Mathematical Writing Problems: (3.4) 2, 5, 10, 33, 48, 54. 
Reading: Chapter 4 Problems (3.4) 40, 41, 42, 43, 45, 50. 
Reading: Chapter 5 Problems:(4.4) 4, 5, 36. (5.3) 1, 2, 6. Rewrite: HW 1 
Reading: Chapter 6 Problems:(6.4) 5 ad, 11, 12. Rewrite: HW 2 
Distributed: Tue Wed Oct 3 Due: Wed Oct 10 (start of class) No homework due Wed, Feb 10. 
Reading: Chapter 10 and 11 Problems: (10.3) 5, 6, 14. (11.3) 4, 11, 19. Rewrite: HW 3 

Reading: Chapter 9 Problems: (9.3) 23, 28, 49. Rewrite: HW 4 
Reading: Chapter 16 Problems: (16.6) 1 (ad), 1 (eh), 2, 3a, 3e, 4. Rewrite: HW 5 
Reading: Chapter 17 Problems: (16.6) 6, 7, 29, 34, 35, 37, 38. Rewrite: HW 6. 
Reading: Chapter 18.1 Problems: (17.4) 1, 7, 10, 12, 26, 27. Rewrite: HW 7. 
Reading: Chapter 18.2 Problems: (18.3) 11 (a) and (b), 14, 15. Rewrite: HW 8. 

Reading: Section 1.1 of Category Theory in Context by Emily Riehl. Problems: (18.3) 2, 5, 12, 13, 16, 19. Rewrite: HW 9. 
Research a particular application of abstract algebra in another field of mathematics (e.g., topology) or another discipline (e.g., chemistry). Due Mon Dec 10: Oral Presentation. Give a 3 minute oral presentation on your chosen application of algebra. Your talk should use roughly 3 slides. Submit your slides to your dropbox in Sakai by 10am on Monday, December 10. Due Wed Dec 12: Written exposition. Write a 12 page paper describing an application of algebra. Your piece should be written as though it could be included seamlessly in a future edition of our text book, and you must use at least one outside source (aside from wikipedia). Your paper must be typset in latex. 
The second and final exam will be distributed on Wednesday, December 12 and due Tuesday, December 18 by 5pm. 