# Math 366: Introduction to Abstract Algebra

## Colorado State University, Spring 2020

**UPDATE: This class is moving to online instruction after spring break.**Please see this webpage for my current thoughts on my plan for the class. I am certainly interested in your input and suggestions along these lines!

**Instructor:** Henry Adams
**Email:** henry dot adams at colostate dot edu
**Office:** Weber 120
**Office Hours:**
Wednesdays 1-2 in Weber 017, Thursdays 3-4 in Weber 017, or by appointment

**Lectures:** MWF 12:00-12:50pm in Weber 223
**Textbook:** *Contemporary Abstract Algebra* by Joseph Gallian. Any edition is fine.
The book has selected answers in the back, which is great! See this webpage for online resources associated with our book.

**Overview:** This course is a rigorous and proof-based introduction to abstract algebra. Topics covered include sets, integers, polynomials, real and complex numbers, groups, integral domains, and fields.

**Syllabus:** Here is the course syllabus prior to the move to online instruction, and the course syllabus after to the move to online instruction.

**Course notes:** Here are Henry's course notes.

## Homework

We will have weekly homework assignments. All homework is due in class at the beginning of class. Your homework should be well-organized, legible, stapled, and with no dangling paper tabs on it if you rip it out of a spiral bound notebook. You do not need to do your homework assigments in LaTeX; I include the LaTeX source files for your homework below only if it is convenient for you.

Homework 1 (LaTeX Source) is due Friday, January 31.Homework 2 (LaTeX source) is due Friday, February 7.

Homework 3 (LaTeX source) is due Friday, February 14.

Homework 4 (LaTeX source) is due Friday, February 21.

Homework 5 (LaTeX source) is due Friday, February 28.

Homework 6 (LaTeX source) is due Friday, March 27.

Homework 7 (LaTeX source) is due Friday, April 3.

Homework 8 (LaTeX source) is due Friday, April 10.

Homework 9 (LaTeX source) is due Friday, April 17.

## Exams

The exams will be in-class. You will only be able to use your brain and a pen or pencil - no notes, books, or electronic devices. The exams will be comprehensive. Here is Practice Midterm 1A.

Here is Practice Midterm 1B.

Here is Practice Midterm 2A.

Here is Practice Midterm 2B.

Here is Midterm 2.

Here is the Final Assignment.

## Schedule

Date |
Class Topic: Book Chapter, Notes Pages |
Remark |

Jan 22 | Course overview: Chp 1, Notes 1-3 | |

Jan 24 | Groups: Chp 1, Notes 3-5 | |

Jan 27 | Groups: Chp 2, Notes 5-7 | |

Jan 29 | Groups: Chp 2, Notes 8-10 | |

Jan 31 | Groups: Chp 2, Notes 11-14 | Homework due |

Feb 3 | Subgroups: Chp 3, Notes 15-16 | |

Feb 5 | Subgroups: Chp 3, Notes 17-19 | Last day to drop or change grading option |

Feb 7 | Subgroups: Chp 3 and Cyclic groups: Chp 4, Notes 19-20 | Homework due |

Feb 10 | Cyclic groups: Chp 4, Notes 21-23 | |

Feb 12 | Cyclic groups: Chp 4, Notes 24-26 | |

Feb 14 | Cyclic groups: Chp 4, Notes 26-28 | Homework due |

Feb 17 | Cyclic groups: Chp 4, Notes 29-31 | |

Feb 19 | Permutation groups: Chp 5, Notes 32-34 | |

Feb 21 | Permutation groups: Chp 5, Notes 35-36, list S_{4}
(Short Video) |
Homework due |

Feb 24 | Permutation groups: Chp 5, Notes 37-39 | |

Feb 26 | Permutation groups: Chp 5, Notes 39-41 | |

Feb 28 | Permutation groups: Chp 5, Notes 42-44 | Homework due |

Mar 2 | Notes 45, Isomorphisms: Chp 6, Notes 46-47 | |

Mar 4 | Isomorphisms: Chp 6, Notes 46-48 (Video 46-48) | |

Mar 6 | How to learn to write proofs | |

Mar 9 | Review | |

Mar 11 | Review | |

Mar 13 | Midterm 1 | Through Chapter 5 |

Spring Break, Mar 16-20 | ||

Mar 23 | Class cancelled | End of course withdrawal period |

Mar 25 | Isomorphisms: Chp 6, Notes 49-51 (Video 49-51) | |

Mar 27 | Isomorphisms: Chp 6, Notes 52-54 (Video 52-54) | Homework due |

Mar 30 | Isomorphisms: Chp 6, Notes 55-57 (Video 55-56), (Video 56-57) | |

Apr 1 | Cosets, Lagrange's Theorem: Chp 7, Notes 58-60 (Video 58), (Video 59-61) | |

Apr 3 | Cosets, Lagrange's Theorem: Chp 7, Notes 60-62 (Video 60-62) | Homework due |

Apr 6 | Cosets, Lagrange's Theorem: Chp 7, Notes 63-64 (Video 63-64) | |

Apr 8 | Cosets, Lagrange's Theorem: Chp 7, Notes 65-67 (Video 65-67) | |

Apr 10 | Class cancelled | Homework due |

Apr 13 | Cosets, Lagrange's Theorem: Chp 7, Notes 68-69 (Video 68-69) | |

Apr 15 | Normal subgroups, Quotient groups: Chp 9, Notes 70-72 (Video 70-72) | |

Apr 17 | Normal subgroups, Quotient groups: Chp 9, Notes 73-76 (Video 73-76) | Homework due |

Apr 20 | Homomorphisms: Chp 10, Notes 77-80 (Video 77-80) | |

Apr 22 | Homomorphisms: Chp 10, Notes 80-82 (Video 80-82) | |

Apr 24 | Homomorphisms: Chp 10, Notes 83-85 (Video 83-85) | |

Apr 27 | Direct products: Chp 8, Notes 86-89 (Video 86-89), Review | |

Apr 29 | Review | |

May 1 | Midterm 2 | Through Chapter 10 |

May 4 | Finite abelian groups: Chp 11 | |

May 6 | Rings: Chp 12 | |

May 8 | Integral domains: Chp 13 | |

Monday May 11, Final take-home assignment due |
||

11:50am-1:50pm in Weber 223 |