Abstract Algebra I
|
There is no required textbook. All lecture notes will be posted here. For further reading I recommend Michael Artin's Algebra and Charles C. Pinter's Book of Abstract Algebra.
Office Hours: Thurs, 3-5pm on Zoom. Also by appointment. Here is the syllabus. There is also an optional writing project. | ||
| Course Notes | ||
|---|---|---|
| Item | Date | Information |
|
Homework 1 Solutions |
Fri Sept 10 |
Cardano's Formula C as a ring and a field C as a vector space C as linear functions and matrices Roots of Unity |
|
Homework 2 Solutions |
Fri Sept 24 |
Rings of Polynomials Descartes' Factor Theorem Concept of a Splitting Field |
| Exam 1: Fri Oct 1, in class Solutions | ||
|
Homework 3 Solutions |
Fri Oct 21 |
Partial Fractions Euclidean Domains The Euclidean Algorithm Unique Prime Factorization |
|
Homework 4 Solutions in the notes |
Mon Nov 1 |
Equivalence Relations Modular Arithmetic The Group of Units (Z/nZ)^X The Euler-Fermat Theorem |
| Exam 2: Fri Nov 5, in class Solutions | ||
|
Homework 5 Solutions |
Fri Nov 19 |
Chinese Remainder Theorem Partial Fractions |
|
Homework 6 Solutions |
Fri Dec 3 |
Field of Fractions Statements of the FTA |
| Exam 3: Wed Dec 8, in class Solutions | ||