## Math 5286H: Fundamental Structures of Algebra II (Spring 2012)

**Lectures:**MWF 10:10-11:00 in Vincent Hall 213.

**Instructor:**Gregg Musiker (musiker "at" math.umn.edu)

**Office Hours:**M 1:25-2:25, WF 11:00-12:05 in Vincent 251; also by appointment.

## Course Description:

This is the second semester of a course in the basic algebra of groups, rings, fields, and vector spaces. Roughly speaking, the Fall and Spring semesters should divide the topics as follows:Fall) Vector spaces, linear algebra, group theory, symmetry, and the Sylow Theorems

Spring) Rings, fields, modules, and Galois theory

**Prerequisites:**Some previous exposure to linear algebra (vectors, matrices, determinants) (such as from 2243, 2373, or 2573) would help. Also, one should either have the ability to write and read mathematical proofs (such as from 2283, 2574, or 3283), or have the desire and drive to learn how.

**Required text:**

*Algera*, by Michael Artin, (2nd edition 2011, Prentice Hall).

Fall: some (but not all) of Chapters 1-7;

Spring: some (but not all) of Chapters 11-16

Note that I will be following the brand new second edition in this course, and encourage you to do the same. If you have the first edition, your text will more or less contain the same topics (although with occasional exceptions and sometimes in a different order), but the references to section numbers and exercises will not match the ones I announce in class and on the website. If you are in this situation, please find a classmate with the new edition or come talk to me early on.

Title | Author(s) | Year |
---|---|---|

Introduction to abstract algebra | W. Keith Nicholson | 2007 |

Contemporary abstract algebra | Joseph A. Gallian | 1994 |

Algebra | Thomas Hungerford | 1980 |

Abstract Algebra | Dummit and Foote | 2004 |

Abstract algebra: theory and applications | Thomas Judson | 1994 |

## Grading:

**Homework (50%):**There will be 5 homework assignments due approximately every other week (tentatively) on Fridays in class. The first homework assignment is due on February 3rd.

I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates their collaborators. Late homework will not be accepted. Early homework is fine, and can be left in my mailbox in the School of Math mailroom in Vincent Hall 107. Homework solutions should be well-explained; the grader is told not to give credit for an unsupported answer. Complaints about the grading should be brought to me.

**Exams (15% each):**There will be 2 take-home exams, handed out on February 17th (due February 24th) and March 30th (due April 6th). Each will be open book, open notes, and with calculators allowed. However, for these exams, you are not allowed to consult other electronic sources, such as the internet, and you are not allowed to collaborate or consult with other students or other human sources. These exams are to be collected in class.

**Final Exam (20%):**The final exam will be take-home as well, under the same policies as above, handed out on April 27th, to be turned in during class on May 4th.

## Class Participation:

Participation in class is encouraged. Please feel free to stop me and ask questions during lecture. Otherwise, I might stop and ask you questions instead.## Course Syllabus and Tentative Lecture Schedule

David Perkinson's Webpage on Sandpiles

Assignment or Exam | Due date | Problems from Artin text, unless otherwise specified |
---|---|---|

Homework 1 | Friday 2/3 |
Chapter 11: 1.1, 1.3, 1.6 (a), 1.8, 1.9, 3.2, 3.3, 3.8, 3.9, 3.12, 3.13, 4.1, 4.2, 4.3, 5.1, 5.4 |

Homework 2 | Friday 2/17 |
Chapter 11: 6.2, 6.3, 6.4, 6.5, 6.7, 6.8, 7.1, 7.2, 7.3, 8.2, 8.3, Chapter 12: 1.4, 2.1, 2.3, 2.6, 3.1, 3.2 |

Exam 1 | Friday 2/24 | Download Here |

Homework 3 | Friday 3/9 |
Mostly computational this homework; more theoretical problems next set. Chapter 13: 1.1, 3.2 (a-b), 4.1, 5.1, 5.2 (Main Lemma is Lemma 13.4.8), 6.1, 6.3, 7.1, 7.4, Chapter 15: 2.1, 2.2, 3.2, 3.3, 3.7, 4.2 (a, b, d) |

Homework 4 | Wednesday 4/4 |
Chapter 15: 5.1, 6.3, 7.4, 7.5, 7.7, 7.8, 8.1 Chapter 16: 1.3, 2.2, 3.1, 3.2 (b-c), 4.1, 6.2, 6.3 |

Exam 2 | Friday 4/13 |
Download Here |

Homework 5 | Friday 4/27 |
Chapter 16: 9.3, 9.6, 9.8, 9.11, 10.3, 12.1, 12.3, 12.5, 12.7, (Bonus): M.12 Chapter 14: 1.3, 1.4, 2.2 |

Final Exam | Friday 5/4 | Download Here |