# Math 122

Modules and Group Representations

### Course Information

**Lecture:**Monday, Wednesday, Friday 11:00am–11:50am

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

**Course Webpage:**http://web.stanford.edu/~jchw/2015Math110

Grades will be made available through Coursework.

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

** Professor: ** Jenny Wilson

**Email:** jchw@stanford.edu

**Office Hours:** Monday 12–1:30pm and Wednesdays 6:45–8pm, starting in Week 1

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

**Course Assistant:** Caitlin Stanton

** Email:** ckstanton (at stanford.edu)

**Office Hours:** Wednesdays 2pm–3:30pm and Thursdays 4:15–5:45pm , starting in Week 2

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

**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 | 45% |

Midterm | 20% |

Final | 35% |

**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 3 April 2015 |

Homework 2 | Due: Friday 10 April 2015 | |

Homework 3 | Due: Friday 17 April 2015 | |

Homework 4 | Due: Friday 24 April 2015 | |

Homework 5 | Due: Friday 1 May 2015 | |

Homework 6 | (Not to hand in) | |

Homework 7 | Due: Friday 15 May 2015 | |

Homework 8 | Due: Friday 22 May 2015 | |

Homework 9 | Due: Friday 27 May 2015 |

### Exams

The course will have one closed-book ** midterm exam, in class on Wednesday 6 May. **

The midterm will cover material up to (and including) Wednesday 29 April.

Midterm Review Problems

Midterm & Solutions

Your take-home exams have been distributed. They are due **Friday 5 June at 8:30am**, at the time of our final in-class exam.

Final Review Problems

The in-class ** final exam ** has been scheduled by the registrar for **Friday 5 June at 8:30am in 381-U **(our usual classroom).

The exam is 3 hours long, closed-book, and will cover material from the whole course.

### 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.