- Classes start Mon Aug 28th, 9:00--9:50.
- Location: Math 110

- Office Hours: Mon, Wed, Fri; 11:00--12:00.
- Homework: Set periodically and posted
to this website.

- Exams:
- The first midterm exam will be on
Friday the 13th of October.

- Syllabus:
- Textbook:
*Algebra Pure and Applied.*By Papantonopoulou.

- Outline: The course will cover some basic topics from an area of abstract algebra known as Group Theory. Group Theory provides a way to encode the symmetry of mathematical objects. The topics from the book that I intend to cover are:
- 0.3 Properties of the integers
- 1.1 Examples and Basic Concepts
- 1.2 Subgroups
- 1.3 Cyclic Groups
- 1.4 Permutations
- 2.1 Cosets and Lagrange's Theorem
- 2.2 Homomorphisms
- 2.3 Normal Subgroups
- 2.4 Quotient Groups
- 2.5 Automorphisms
- 3.1 Examples and Definitions
- 3.2 Computing Orders
- 3.3 Direct Sums
- 3.4 Fundamental Theorem of Finite Abelian Groups
- 4.1 Group Actions and Cayley's Theorem
- 4.2 Stabilizers and Orbits in a Group Action
- 4.3 Burnside's Theorem and Applications
- 4.4 Conjugacy Classes and the Class Equation
- 4.5 Conjugacy in the Symmetric Groups and Simplicity of the Alternating Groups.
- Note: This syllabus may be
subject to modest alterations in content as the semester
progresses.

- Assessment:
- Homework assignments will contribute to 10% of your grade. It is important that you hand them in on time.
- There will be two midterm exams, worth 25% each.

- There will be a final exam, which will be worth 40%.

Homework |
Date due |

Sec 0.3: Q2, 3, 4. |
Fri 8th September. |

Sec 0.3: Q16, 17, 18, 23. |
Fri 15th September. |

Sec 0.3: Q24, 29, 32, 35. |
Fri 22nd September. |

Sec 1.1: Q1, 11, 14, 16, 18, 25, 26. |
Fri 29th September. |

Sec 1.2: Q2, 6, 11, 20, 22, 25. |
Fri 6th October. |