# 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, Room D)

**Course Webpage:**http://web.stanford.edu/~jchw/2017Math122

Grades will be made available through Canvas.

**Previous yearsâ€™ webpages:**

(2016) http://web.stanford.edu/~jchw/2016Math122

(2015) http://web.stanford.edu/~jchw/2015Math122

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

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

** Professor: ** Jenny Wilson

**Email:** jchw@stanford.edu

**Office Hours:** Wed 12pm–1:30pm and Thurs 3pm–4:30pm

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

**Course Assistant:** Bogdan Zavyalov

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

**Office Hours:** Tues 10am–12pm and Thurs 10am–11am (starting Week 3)

Week 2 will have a single office hours Thursday 13 April 10am–1pm

**Office:** Building 380 (Sloan Hall), Room 381-N (First Floor, Room N)

**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.

** Grading systems: ** I discourage students from taking Math 122 on a CR/NC basis. Please talk to me if you are considering this option.

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

### Homework

Homework 1 | Due: Friday 7 April 2017 |

and the (non-anonymous) midterm availability survey

Homework 2 | Due: Friday 14 April 2017 |

Homework 3 | Due: Friday 21 April 2017 |

Homework 4 | Due: Friday 28 April 2017 |

Homework 5 | Due: Friday 5 May 2017 |

Homework 6 | Due: Friday 12 May 2017 |

Homework 7 | Due: Friday 19 May 2017 |

Homework 8 | Due: Friday 26 May 2017 |

Homework 9 | Due: Monday 5 June 2017 |

### Exams

The course will have two closed-book midterm exams.

The exams are designed to take one hour, but you may take up to two hours to write them. No books, notes, calculators, cell phones, or other electronic aids are permitted.

** Midterm I: ** Tuesday 2 May, 7–9pm

**Location:** Building 380 (Math department), room 380-C (Basement room C)

**Alternate time (opt-in)** 6–8pm in room 380-Y (Basement room Y)

** Doors to the basement are locked at 5pm. ** Please enter the building through the first floor front doors after this time.

Midterm I will cover material up to and including Wednesday 26 April (Week 4). Review questions are available here:

Midterm I Review |

Midterm I and solutions are available here:

Midterm I Solutions |

** Midterm II: ** Tuesday 30 May, 7–9pm

**Location:** Building 380 (Math department), room 380-C (Basement room C)

**Alternate time (opt-in)** 6–8pm in room 380-Y (Basement room Y)

Midterm II will cover material up to and including Wednesday 24 May (Week 8). Review questions are available here:

Midterm II Review |

Midterm II and solutions are available here:

Midterm II Solutions |

### 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.