Math 171: Abstract Algebra

Spring 2018

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 Karp
Office: 3414 Shan
Office hours: Tue/Wed/Thu 3-4pm, and open door.

Lectures

This course will meet for lectures Tuesday and Thursday, 1:15-2:30pm in Shanahan 3460.

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 by
AVG (A,B,C,D)

Homework

Written homework will be due each Thursday 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

Adam Busis, Haoxing Du, Joe Nunez and Jeffrey Rutledge are our graders and tutors. They will hold tutoring hours Sunday and Wednesday, 7-9pm in Shan B445.

Exams

There will be two exams, both of which are take-home. Exam 1 will be distributed 2/20 and due 2/27. Exam 2 will be distributed 4/26, due 5/8.

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) 607-3148 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 Collins-Eaglin (jan.collins-eaglin@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.
Homework and Readings
    HW 2. Due Thu Feb 1
    Reading: Chapter 4
    Problems (3.4) 40, 41, 42, 43, 45, 50.
    HW 3. Due Thu Feb 8
    Reading: Chapter 5
    Problems:(4.4) 4, 5, 36. (5.3) 1, 2, 6.
    Rewrite: HW 1
    HW 4. Due Thu Feb 15
    Reading: Chapter 6
    Problems:(6.4) 5 a-d, 11, 12.
    Rewrite: HW 2
    Exam 1
    Distributed: Tue Feb 20
    Due: Tue Feb 27 (start of class)
    No homework due Thursday, Feb 22.
    HW 5. Due Thu Mar 1
    Reading: Chapter 10 and 11
    Problems: (10.3) 5, 6, 14. (11.3) 4, 11, 19.
    Rewrite: HW 3
    HW 6. Due Thu Mar 8
    Reading: Chapter 9
    Problems: (9.3) 4, 7, 23, 26, 48, 50.
    Rewrite: HW 4
    HW 7. Due Thu Mar 22
    Reading: Chapter 16
    Problems: (16.6) 2, 5, 7, 9, 20, 21.
    HW 8. Due Thu Mar 29
    Reading: Chapter 17
    Problems: (16.6) 34, 35, 37. (17.4) 1, 5, 7.
    Rewrite: HW 5.
    HW 9. Due Thu Apr 5
    Reading: Chapter 18.1
    Problems: (16.6) 4, 6, 29, 33, 38. (17.4) 26.
    Rewrite: HW 6.
    HW 10. Due Thu Apr 12
    Reading: Chapter 18.2
    Problems: (18.3) 1, 11 (a) and (b), 14, 15. (17.4) 9, 10.
    Rewrite: HW 7.
    HW 11. Due Thu Apr 19
    Reading: Section 1.1 of Category Theory in Context by Emily Riehl.
    Problems: (18.3) 2, 5, 12, 13, 16, 19.
    Rewrite: HW 8.
    Final Project. Applications of Algebra.
    Research a particular application of abstract algebra in another field of mathematics (e.g., topology) or another discipline (e.g., chemistry).

    Due Tue Apr 24: 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 Tue, Apr 24.

    Thu Apr 26: Written exposition. Write a 1-2 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.