# Abstract Algebra I - 1st semester - 2015

The lectures of the abstract algebra course will be based on a book by the same title, written by Dummit and Foote (Los Andes biblioteca # 512.02 D855 2004). We will cover the first 9 chapters. In the process, we might skip some sections or add topics from external resources. The lectures will be mostly in English but students also are welcome to ask quesions, have discussions with their peers or give presentations in Spanish.Download the coures outline here.

## Evaluation policy

- 5 Homework (3% each)
- 2 Quizzes (5% each)
- 2 Midterms (20%)
- Presentation (5%)
- Final exam (30%)

## Office hours

Martes 11:30-1:30 y Jueves 8-10H 007

## Projects

Group theory in cryptography | Juan Camilo Chavez and Andres Camilo Paz
link |

Lattices, Minkowski's theorem and the sum of four squares theorem | David Stiles, Juan Camilo Azuero, Juan Pablo Lievano and Ivan Felipe Herrara
link |

Group rings and Maschke's theorem | Daniel Rodriguez, Juan Felipe Ceron and Gloria Buritica
link |

Burnside's theorem and Escher's patterns | Juan Esteban Perez and Santiago Villegas
link 1 y link 2 |

Symbolic computations with GAP | Christian Poveda and German David Cardozo
link Presentation file |

PGL and PSL and their simplicity | Nicolas Cuero, Paula Rodriguez, Juan Felipe Uribe and Daniel Tamayo
link 1 y link 2 |

Topological Groups | Juan Sebastian Aguirre, Daniel Bermudez, Diego Alejandro Murillo and Juan Felipe Ariza
link |

## Homeworks, Quizzes and Midterms

HW #1, Friday Jan 30 - Tuesday Feb 3Solutions here

Quiz #1 on Friday Feb 13

Solutions here

Parcial #1 on Sat Feb 21

HW #2, Friday Feb 27 - Tuesday Mar 3

Solutions here

Quiz #2 on Friday Mar 13

Solutions here

Parcial #2 on Fri Mar 20

HW #3, Friday Mar 27 - Tuesday Apr 7

HW #3 Solutions

HW #4, Friday Apr 17 - Friday Apr 24

HW #4 Solutions

HW #5, Para Viernes, 8 Mayo

HW #5 Solutions

Final Exam

Final Exam Solutions

## Practice Homework

These are some suggested homework questions to get you started.1.1 | 1, 7, 12, 19, 22, 24, 30, 31, 36 |

1.2 | 1, 4, 9, 14, 17 |

1.3 | 2, 5, 10, 14, 20 |

1.4 | 2, 3, 8, 10, 11 |

1.5 | 1, 2, 3 |

1.6 | 4, 7, 9, 17, 19, 20, 26 |

1.7 | 3, 4, 5, 8, 12, 15, 16, 21 |

2.1 | 3, 9, 12, 15, 17 |

2.2 | 2, 4, 6, 7, 13 |

2.3 | 2, 6, 9, 10, 21, 23 |

2.4 | 2, 6, 7, 9, 14, 19 |

2.5 | 2, 8, 9, 11, 16, 18 |

3.1 | 1, 3, 6, 12, 19, 22, 28, 34, 41 |

3.2 | 2, 4, 5, 10, 11, 17, 20, 22 |

3.3 | 1, 3, 7, 8 |

3.4 | 1, 3, 7, 8 |

3.5 | 3, 6, 10, 17 |

4.1 | 1, 2, 4, 6, 10 |

4.2 | 2, 3, 4, 8, 13 |

4.3 | 3, 4, 6, 8, 9, 17, 20, 25 |

4.4 | 1, 2, 5, 6, 8, 11 |

4.5 | 1, 2, 3, 4, 5, 13, 19, 26, 29 |

4.6 | 1, 2, 5 |

5.2 | 1, 2, 7, 14 |

5.5 | 1, 2, 3, 5, 9, 11 |

6.1 | 3, 7, 8, 9, 10, 12, 13, 16 |

7.1 | 7, 11, 13, 21, 22, 26, 27 |

7.2 | 3, 5, 10, 12 |

7.3 | 2, 6, 8, 10, 13, 14, 15, 16, 22, 29, 34 |

## Miscellaneous

Mathematics on a distant planetWho wanted to make the Heisenberg group abelian?

Fun with F_{un}

or just let Allan Connes tell you about it