Math 366: Introduction to Abstract Algebra
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Colorado State University, Spring 2019
Instructor: Henry Adams
Email: henry dot adams at colostate dot edu
Office: Weber 125
Office Hours: Wednesdays 11-12 in Weber 17, Thursdays 1-2 in Weber 17, or by appointment
Lectures: MWF 10:00-10:50am 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.
Course notes: Here are Henry's course notes.
Homework
Homework 1 (LaTeX Source) is due Friday, February 1.Homework 2 (LaTeX source) is due Friday, February 8.
Homework 3 (LaTeX source) is due Friday, February 15.
Homework 4 (LaTeX source) is due Friday, February 22.
Homework 5 (LaTeX source) is due Friday, March 1.
Homework 6 (LaTeX source) is due Friday, March 29.
Homework 7 (LaTeX source) is due Friday, April 5.
Homework 8 (LaTeX source) is due Friday, April 12.
Homework 9 (LaTeX source) is due Friday, April 19.
Homework 10 (LaTeX source) is due Friday, April 26.
We will have weekly homework assignments. All homework is due in class at the beginning of class. Your homework should be legible and stapled.
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 1.
Here is Midterm 1.
Here is Practice Midterm 2.
Here is the Final Exam.
Schedule
| Date | Class Topic: Book Chapter, Notes Pages | Remark |
| Jan 23 | Course overview: Chp 1, Notes 1-3 | |
| Jan 25 | Groups: Chp 1, Notes 3-5 | |
| Jan 28 | Groups: Chp 2, Notes 5-7 | |
| Jan 30 | Groups: Chp 2, Notes 8-10 | |
| Feb 1 | Groups: Chp 2, Notes 11-14 | Homework due |
| Feb 4 | Subgroups: Chp 3, Notes 15-16 | |
| Feb 6 | Subgroups: Chp 3, Notes 17-19 | Last day to drop or change grading option |
| Feb 8 | Subgroups: Chp 3 and Cyclic groups: Chp 4, Notes 19-21 | Homework due |
| Feb 11 | Cyclic groups: Chp 4, Notes 22-24 | |
| Feb 13 | Cyclic groups: Chp 4, HW 2 review, Notes 25-26 | |
| Feb 15 | Cyclic groups: Chp 4, Notes 25-26 | Homework due |
| Feb 18 | Cyclic groups: Chp 4, Notes 26-28 | |
| Feb 20 | Class cancelled; Henry sick | |
| Feb 22 | Cyclic groups: Chp 4, Notes 29-31 | Homework due |
| Feb 25 | Permutation groups: Chp 5, Notes 32-34 | |
| Feb 27 | Permutation groups: Chp 5, Notes 35-36, listed S4 | |
| Mar 1 | Permutation groups: Chp 5, Notes 37-39 | Homework due |
| Mar 4 | Permutation groups: Chp 5, Notes 39-41 | |
| Mar 6 | Permutation groups: Chp 5, Notes 42-43 | |
| Mar 8 | Permutation groups: Chp 5, Notes 44-45 | |
| Mar 11 | Review | |
| Mar 13 | Class cancelled; Snow day | |
| Mar 15 | Midterm 1 | |
Spring Break, Mar 18-22 | ||
| Mar 25 | Isomorphisms: Chp 6, Notes 46-48 | End of course withdrawal period |
| Mar 27 | Isomorphisms: Chp 6, Notes 49-50, automorphism preview! | |
| Mar 29 | Isomorphisms: Chp 6, Notes 52-53 | Homework due |
| Apr 1 | Isomorphisms: Chp 6, Notes 52-54, cardinality of infinite sets | |
| Apr 3 | Isomorphisms: Chp 6, Notes 55-57 | |
| Apr 5 | Cosets, Lagrange's Theorem: Chp 7, Notes 58-60 | Homework due |
| Apr 8 | Cosets, Lagrange's Theorem: Chp 7, Notes 60-62 | |
| Apr 10 | Cosets, Lagrange's Theorem: Chp 7, Notes 63-64, number theory | |
| Apr 12 | Cosets, Lagrange's Theorem: Chp 7, Notes 65-67 | Homework due |
| Apr 15 | Cosets, Lagrange's Theorem: Chp 7, Notes 68-69 | |
| Apr 17 | Normal subgroups, Quotient groups: Chp 9, Notes 70-72 | |
| Apr 19 | Normal subgroups, Quotient groups: Chp 9, Notes 73-76 | Homework due |
| Apr 22 | Homomorphisms: Chp 10, Notes 77-80 | |
| Apr 24 | Class cancelled | |
| Apr 26 | Homomorphisms: Chp 10, Notes 80-83 | Homework due |
| Apr 29 | Homomorphisms: Chp 10, Notes 82-84 | |
| May 1 | Review | |
| May 3 | Midterm 2 | |
| May 6 | Direct products: Chp 8; Finite abelian groups: Chp 11 | Class picture |
| May 8 | Rings: Chp 12 | |
| May 10 | Integral domains: Chp 13 | |
Thursday May 16, Final take-home assignment due |
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