Table of Contents | |

1. Description | |

2. Class Notes | |

3. Schedule | |

4. Homework | |

5. Exams | |

6. Resources |

UNIVERSITY OF CALIFORNIA, LOS ANGELES - FALL 2021

MATH 110AH:1 - Algebra (Honors)

Instructor : Pablo S. Ocal

Office hours : M 2:00 pm-3:30 pm (no appointment necessary)

Table of Contents | |

1. Description | |

2. Class Notes | |

3. Schedule | |

4. Homework | |

5. Exams | |

6. Resources |

Description

The honors course on *Algebra* will treat, among others, groups and the three isomorphism theorems, group actions, and the three Sylow theorems. The prerequisites required for this course are covered in Math 115A.

The course will have weekly classes on

**Mondays, Wednesdays, and Fridays in MS, room 5148, from 1:00 to 1:50 pm.**

The book we will be following is *Lectures on Abstract Algebra* by Richard S. Elman. We will be covering material in Chapters 1, 2, 3, and 4. The recommended reference books are *Algebra* by Thomas W. Hungerford and *Algebra* by Larry C. Grove. You may find all the information you will need on the **Syllabus**.

Class Notes

The following notes are a formal outline of the material we will be covering. These notes are not comprehensive nor are intended to be a substitute for the textbook or the lectures. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

The following are additional materials closely related to the class notes.

- Problems for 18 October 2021.
- Doubts for 26 October 2021.
- Zoom lecture for 3 November 2021.
- Problems for 8 November 2021.
- Zoom lecture for 17 November 2021.
- Zoom lecture for 24 November 2021.
- Problems for 29 November 2021.
- Problems for 1 December 2021.
- Problems for 3 December 2021.
- Expository papers by
**Keith Conrad**. - The well-ordering principle by
**Quo-Shin Chi**. - The well ordering principle by
**MIT OpenCourseWare**.

Tentative Schedule

Sep 20-24 | Sections 2-4, Well-Ordering and Induction, the Greatest Integer Function, Division and the Greatest Common Divisor. |

Sep 27-Oct 1 | Sections 5, 6, Equivalence Relations, Modular Arithmetic. Office hours. |

Oct 4-8 | Sections 8, 9, Definition of Group, First Properties. Office hours. |

Oct 11-15 | Sections 10, 11, Cosets, Homomorphisms. Office hours. |

Oct 18-22 | Sections 12, 13, Review, Midterm 1, the First Isomorphism Theorem, the Correspondence Principle. Office hours. |

Oct 25-29 | Sections 14, 16, Finite Abelian Groups, Finitely Generated Groups. Office hours. |

Nov 1-5 | Section 19, The Orbit Decomposition Theorem. Office hours. |

Nov 8-12 | Section 21, Review, Midterm 2, Examples of Group Actions. Office hours. |

Nov 15-19 | Section 22, The Sylow Theorems. Office hours. |

Nov 22-26 | Section 24, The Symmetric and Alternating Groups. Office hours. |

Nov 29-Dec 3 | Sections 2-6, 8-14, 16, 19, 21-22, 24, Review. |

Dec 10 | Sections 2-6, 8-14, 16, 19, 21-22, 24, Final Exam. |

Homework

There will be typically weekly homework. The assignments will be posted before Tuesdays at 9:00 am. The assignments will be due the next week, at your discussion section. The assignments, deadlines, and solutions will be posted here.

Sep 21 | Homework 0. Deadline: Sep 30. |

Sep 28 | Homework 1. Deadline: Oct 7. |

Oct 11 | Homework 2. Deadline: Oct 18. |

Oct 15 | Homework 3. Deadline: Oct 22. |

Oct 19 | Homework 4. Deadline: Oct 28. |

Nov 1 | Homework 5. Deadline: Nov 8. |

Nov 4 | Homework 6. Deadline: Nov 12. |

Nov 9 | Homework 7. Deadline: Nov 18. |

Nov 12 | Homework 8. Deadline: Dec 8. |

Exams

Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams **here**.

Oct 20 | Midterm 1, MS 5148 from 1:00 to 1:50 pm. |

Nov 10 | Midterm 2, MS 5148 from 1:00 to 1:50 pm. |

Dec 10 | Final Exam, MS 5148 from 8:00 to 11:00 am. |

Resources

There are many resources available for a student at UCLA, I encourage you to use them and make the most out of them. Here are some materials specific to this course:

- The open office hours at the Student Math Center can be found
**here**. - The mathematics software Sage can be found
**here**. - Four standard tricks to show that a group is not simple can be found
**here**. This was made by**Tai-Danae Bradley**.

I also encourage you to form study groups with your classmates. However, please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions or copying others' work is absolutely useless.