Fall Term 2015

Lior Silberman
- Office: MATX 1112, 604-827-3031
- Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
- Office hours (Winter 2022): by appointment or
Time Location Zoom Meeting ID Zoom Password MF 11:30-12:30 My office and Zoom 691 7826 7667 761818 Wed 21:30-22:30 Zoom only 682 2985 1665 155350

- Classes: TTh, 14:00-15:30, LSK 460.
- Syllabus.
- (Rough) lecture notes.

This is the introductory course in algebra, intended for honours students. Students who wish to buy a single abstract algebra book should buy the book [1], which will serve you for both 322 and 323 this year, and also covers the material of 422 and 423. The gentler and less-terse alternative is the book [2]. If you want a group-theory specific textbook, the best book in my opinion is Rotman's (reference [3] below). You can download a copy by following the link while on the UBC network. That said, any book titled "Group Theory" (topic-specific) or "algebra" or "abstract algebra" (wide-coverage) is fine.

- Dummit and Foote, Abstract Algebra
- Gallian, Contemporary Abstract Algebra
- Rotman, An Introduction to the Theory of Groups, also available from SpringerLink.

During the course, we will study three classical theorems by Sylow. They are, of course, discussed in detail in the textbooks. Sylow's original paper from 1872 (written in French) is available online from the GĂ¶ttingen University Library.

- The final exam will take place on Tuesday, December 8th between 15:30-18:00 at the IK Barber learning centre, room 182.
- Examinable material includes everything covered in the lectures and the problem sets (except the proof of the structure theorems for finite and finitely genreated abelian groups).
- There will be a
*review session*on Monday, December 7 between 10:00-12:00 at MATH 225. In this session the instructor will answer questions from the audience -- please prepare some! - Here is last year's exam. There are also past exams posted on the department website. Note that pre-2012 exams reflect a previous version of the course; only the group theory questions on those exams are relevant.

- The midterm exam will take place during class on Tuesday, October 20th. The midterm will include calculational and abstract problems, and also one problem asking for the statement of a definition from class.
- Examinable material includes everything up to the isomorphism theorems and the simplicity of A_n, and all problem sets up to PS5.
- Here are last year's midterm and its grade statistics.
- Here are this year's midterm and its solutions.

- Solutions (only) are stored on a secure website; registered students can access them after first logging on to Connect.
- Problem set grade statistics.
- Here are Computational problems with solutions for your use.

- Problem Set 1, due 17/9/2015 (hint to 2b fixed). Solutions.
- Problem Set 2, due 24/9/2015. Solutions.
- Problem Set 3, due 1/10/2015. Solutions.
- Problem Set 4, due 8/10/2015. Solutions.
- Problem Set 5, due 15/10/2015. Solutions.
- Problem Set 6, due 27/10/2015,
**Problem 6 postponed to PS7**. Solutions. - Problem Set 7, due 5/11/2015. Solutions.
- Problem Set 8, due 12/11/2015. Solutions.
- Problem Set 9, due 19/11/2015. Solutions.
- Problem Set 10, due 26/11/2015. Solutions.
- Problem Set 11, not for submission. Solutions.

Readings are generally from Dummit and Foote (sections marked "N" are in the lecture notes). Those reading Rotman can find the material there

Week | Date | Material | Reading | Notes |
---|---|---|---|---|

1 | Th 10/9 | Introduction The Integers |
§0.2 |
Putnam Sessions |

T 15/9 | Modular arithmetic | §§0.3,0.1 | Relations | |

Th 17/9 | (continued) | PS1 due | ||

2 | T 22/9 | Permutations | §1.3 | |

Th 24/9 | (continued) | PS2 due | ||

3 | T 29/9 | Groups and subgroups | §§1.1,1.2,1.5,2.1 | Concepts to review |

Th 1/10 | Homomorphisms, Cyclic groups | PS3 due | ||

4 | T 6/10 | Cosets and Lagrange's Theorem Normal Subgroups |
§3.2 | |

Th 8/10 | Quotient groups | §3.3 | PS4 due | |

5 | T 13/10 |
Isomorphism Theorems Simplicity of A_n |
§3.3 §4.6 |
Feedback form |

6 | Th 15/10 | Group actions | §1.7, §§4.1-4.2 | PS5 due |

T 20/10 | Midterm Exam | Midterm | Midterm | |

7 | Th 22/10 | Conjugation | §4.3 | Zagier's Trick |

T 27/10 | Orbits, stabilizers | Examples PS6 due |
||

8 | Th 29/10 | p-groups | N4.1 | Groups of order p^3 |

T 3/11 | pq-groups | N4.2 | ||

9 | Th 5/11 | (continued) | N4.2 | PS7 due |

T 10/11 | Sylow's Theorems | §4.5 | ||

10 | Th 12/11 | Applications | PS8 due | |

T 17/11 | Groups of medium order | §6.2 | ||

Th 19/11 | Finite Abelian groups | §6.1 | PS9 due | |

11 | T 24/11 | Finitely generated abelian groups | §5.2 | |

Th 26/11 | Nilpotent groups | §6.1 | PS10 due | |

12 | T 1/12 | Solvable groups | §6.1 | |

Th 3/12 | Last lecture | §6.1 | ||

M 7/12 | Review: 10:00-12:00 at MATH 225 | |||

T 8/12 | Final exam: 15:30-18:00 at IBLC 182 |

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