# Math 122

Modules and Group Representations

### Course Information

**Lecture:**Monday, Wednesday, Friday 10:30am–11:20am

Building 380 (Sloan Hall), Room 380-D (Basement Floor)

**Course Webpage:**http://web.stanford.edu/~jchw/2016Math122

Grades will be made available through Coursework.

**2015 Course Webpage:**http://web.stanford.edu/~jchw/2015Math122

**Textbook:**Dummit–Foote, Abstract Algebra

**Suggested Reading:**Fulton–Harris, Representation Theory (pdf at SpringerLink)

** Professor: ** Jenny Wilson

**Email:** jchw@stanford.edu

**Office Hours:** Wednesdays 12–1:30pm & Thursdays 2:30–4pm

Building 380 (Sloan Hall), Room 382-H (Second Floor, Room H)

**Course Assistant:** Adva Wolf

** Email:** advaw "at" stanford.edu

**Office Hours:** Wednesdays 5–6:30pm & Thursdays 5–6:30pm

Building 380 (Sloan Hall), Room 381-J (First Floor, Room J)

**Course Description:** Modules over PID. Tensor algebra. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite: Math 120. Also recommended: 113.

**Syllabus:** We will follow Dummit & Foote Chapters 10, 12, 18, and parts of 19 as time permits.

Grading Scheme: | |

Homework | 50% |

Midterm I | 15% |

Midterm II | 15% |

Final | 20% |

**Students with documented disabilities:** Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (723-1066, http://studentaffairs.stanford.edu/oae).

** Homework policy: ** Homework assignments will be posted to the course webpage. Homework is due Fridays, and collected at the beginning of lecture. Late homework is generally not accepted except under extenuating circumstances. Your homework solutions should be * neat, legible, and stapled *. You may work in groups and discuss homework problems with other students, but your solutions must be written up *independently and in your own words*.

Each student's lowest homework score will be dropped.

You are welcome to use other texts and online resources to review the mathematical theory and computational techniques we cover. You may not, however, seek out solutions to specific homework problems. Outside sources should be used to improve your understanding of the material, not as a shortcut to finish assignments with an incomplete understanding. Use your discretion.

You are encouraged to discuss the homework with classmates and work on difficult problems in groups. * You must, however, write your own homework solutions, and you are responsible for understanding what you've written. * The homework is your foremost resource for practice with the course material, and for feedback on your work. Doing the homework thoughtfully is essential to your success in this class.

** Honour Code: ** The Stanford Honour Code is available through Stanford's Office of Community Standards.

### Homework

Homework 1 | Due: Friday 1 April 2016 |

Homework 2 | Due: Friday 8 April 2016 |

Homework 3 | Due: Friday 15 April 2016 |

Homework 4 | Due: Friday 22 April 2016 |

Homework 5 | Due: Friday 29 April 2016 |

Homework 6 | Due: Friday 6 May 2016 |

Homework 7 | Due: Friday 13 May 2016 |

Homework 8 | Due: Friday 20 May 2016 |

Homework 9 | Due: Friday 27 May 2016 |

Homework 10 | Due: Wednesday 1 June 2016 (by 5pm) |

### Exams

The course will have two closed-book ** midterm exams, in class on Wednesday 27 April (Week 5) and Wednesday 25 May (Week 9). **

These exams will take place in our usual classroom at the usual class time. You will have 50 minutes. No books, notes, calculators, cell phones, or other electronic aids are permitted.

Midterm I will cover material up to the end of Week 4. Review questions are available here:

Midterm I Review |

The midterm and solutions are available here:

Midterm I Solutions |

Midterm II will cover material up to the end of Week 8. Review questions are available here:

Midterm II Review |

The midterm and solutions are available here:

Midterm II Solutions |

Your take-home final exams have now been distributed. The exams are due at 5pm on Wednesday 8 June. Submission instructions are printed at the end of the exam.

### Outside Reading

The following reading is strictly optional: it is not related to the course material and will not be discussed in the course. These are articles on math education and learning psychology which may be of interest to math students.