Survey of Modern Algebra
There is no official textbook. Here are the typed course notes from a previous semester. I will update them as needed as we go along. For a second opinion, I recommend the following textbooks:
Here is the syllabus. There is also an optional writing credit. | ||
| Assignment | Due Date | Topics |
|---|---|---|
|
Homework 1 Solutions |
Thurs, Feb 2 |
The Quadratic Formula Division with Remainder Descartes' Factor Theorem Rings, Fields, Polynomials |
|
Homework 2 Solutions |
Thurs, Feb 16 |
Euclidean Domains Bezout's Identity The Euclidean Algorithm Unique Prime Factorization |
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Exam 1: Thurs, Feb 23 Solutions | ||
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Homework 3 Solutions |
Thurs, Mar 9 |
Cardano's Formula Complex Numbers Euler's Formula Roots of Unity |
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Homework 4 Solutions |
Thurs, Mar 30 |
Fundamental Theorem of Algebra Complex Conjugation Laplace's Proof of FTA |
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Exam 2: Tues, Apr 4 Solutions | ||
| Ran out of time :( |
Modular Arithmetic The Group of Units Mod n The Euler-Fermat Theorem Intro to Finite Fields |
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Homework 5 Solutions |
Tues, Apr 25 |
The Minimal Polynomial Adjoining an Element to a Field Quadratic Field Extensions Impossible Constructions |
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Exam 3: Thurs, Apr 27 Solutions | ||