Math 174: Representation Theory

Spring 2019


The topics covered will include group rings, characters, orthogonality relations, induced representations, applications of representation theory, and other select topics from module theory.


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


This course will meet for lectures Monday and Wednesday, 1:15-2:30pm in Shanahan 2461.


We'll use The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, by Bruce Sagan.
It available online.


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


Princewill Okoroafor is our grader and tutor. He will hold tutoring hours Sunday 7-9pm in Shan 2444.


There will be two exams. Exam 1 will be distributed on Wednesday, March 6 and due Monday, March 11. Exam 2 will be distributed Wednesday, May 1, due Wednesday, May 15 at 5:00pm.


Written homework will be due each Wednesday at the beginning of class, and is posted below.

Homework consists of written problems graded for correctness. It is open book, but you are not to use other resources, aside from those of your previous courses.

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.

Critical Readings

In addition to the written homework, suggested readings will be posted on the homework page in conjunction with upcoming lectures. Class activities will depend on your study of this material in advance (which is a departure from most lower division courses). There will be comprehensive questions and warm up exercises in conjunction with the reading assignment. These are graded for completion as opposed to correctness. These are due on Monday at the beginning of class.

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.


Students interested in using LaTeX are encouraged to do so, but it is not required.


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 Brandon Ice, Coordinator for Student Disability Resources at , 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:
HMC: Brandon Ice -
CMC: Kari Rood - or
Pitzer: Gabriella Tempestoso -
Pomona: Disability Services -
Scripps: Bianca Vinci -

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
    CR 1. Due Mon Jan 28.
    Sections: 1.1-1.4, and Francis Su's Guidelines for Good Mathematical Writing

    Questions: 1. Is the sign representation a matrix representation? What is the regular representation of Z_2?
    HW 1. Due Wed Jan 30.
    Problems: (1.13) 1.
    HW 2. Due Wed Feb 6.
    Problems: 1.13.2, 1.13.5 (a), (d), and (e)
    CR 3. Due Mon Feb 11.
    Sections: 1.6
    Problems: (1.13) 8, 10
    HW 3. Due Wed Feb 13.
    Problems: (1.13) 7
    HW 4. Due Wed Feb 20.
    Problems: (1.13) 11.
    CR 5. Due Mon Feb 25.
    Sections: 1.8
    Problems: (1.13) 3, 5 (b).
    HW 5. Due Wed Feb 27
    Problems: 1.13 (6).
    CR 6. Due Mon Mar 4
    Sections: 1.9
    Problems: No problems due. Feel free to study using the practice exam in Sakai.
    HW 6. Due Wed Mar 6
    Problems: (1.13) 15
    Exam 1
    Out Wed Mar 6
    Due Mon Mar 11
    CR 7. Due Mon Mar 25
    Sections: 1.10 and 1.11
    HW 7. Due Wed Mar 27
    Problems: (1.13) 16
    CR 8. Due Mon Apr 1
    Sections: 1.12
    Problems: (1.13) 17 c,d.
    HW 8. Due Wed Apr 3
    Problems: (1.13) 18
    CR 9. Due Mon Apr 8
    Sections: 2.1, 2.2, 2.3.
    Problems: (2.12) 2, 3
    HW 9. Due Wed Apr 10
    Problems: (2.12) 1
    CR 10. Due Mon Apr 15
    Sections: 2.4
    Problems: (2.12) 5 (a), (d)
    HW 10. Due Wed Apr 17
    Problems: (2.12) 4
    HW 11. Due Wed Apr 24
    Problems: (2.12) 7.
    No class Wednesday (Turn in HW to Shan 3414)
    CR 12. Due Mon Apr 29
    Sections: Terry Tao's recent post on prismatic cohomology, and Western Mathematics, by Bishop.
    Problems: Write a one-page (not more than 500 words) reflection on self expression in mathematics. How do you express yourself in your mathematical work?
    HW 12. Due Wed May 1
    Problems: Describe the Specht modules in case n = 3. How many are there? What is their relationship?