V63.0246: Abstract Algebra
| Term: | Spring 2011 |
| Lectures: | TThu 2:00pm-3:15pm in WWH 201 |
| Recitations: | Fr 8:00am-9:15am in WWH |
| Instructor: | Prof. Harold Edwards |
| Office: | 611 WWH |
| Office hours: | and by appointment |
| Phone: | 212-998-3168 |
| Email: | edwards@cims.nyu.edu |
Prerequisites
V63.0122 Calculus II and V63.0140 Linear Algebra with a grade of C or better. Course not open to math majors and/or students who have taken Algebra I V63.0343
Description of the course
An introduction to the main concepts, constructs, and applications of modern algebra. Groups, transformation groups, Sylow theorems and structure theory; rings, polynomial rings and unique factorization; introduction to fields and Galois theory.
Course Details
The first half of the course will
deal with the solution of algebraic equations,
developing the method of Galois for solving equations of degree three and greater.
This method leads naturally to a study of permutation groups, the basic aspects
of which will occupy the second half of the course.
No textbook will be used. Instead, extensive notes will be made available via
Blackboard.
developing the method of Galois for solving equations of degree three and greater.
This method leads naturally to a study of permutation groups, the basic aspects
of which will occupy the second half of the course.
No textbook will be used. Instead, extensive notes will be made available via
Blackboard.
Exams
Final exam Tuesday, May 17th from 2:00pm-3:50pm. [Classroom TBD.]
1. What It Means to "Solve" a Polynomial Equation 2. Fields 3. Solutions of Cubics 4. The Euclidean Algorithm for Polynomials 5. Simple Field Extensions 6. Galois's Method 7. The Galois Group of a Cubic 8. Permutation Groups 9. Normal Subgroups 10. Quotient Groups 11. Solutions of Equations of Degree Four 12. The Group of the Dodecahedron 13. Unsolvability of the Quintic
Calendar
| Week | Topic |
|---|---|
| 1 | What It Means to "Solve" a Polynomial Equation |
| 2 | Fields |
| 3 | Solutions of Cubics |
| 4 | The Euclidean Algorithm for Polynomials |
| 5 | Simple Field Extensions |
| 6 | Galois's Method |
| 7 | The Galois Group of a Cubic |
| 8 | Permutation Groups |
| 9 | Normal Subgroups |
| 10 | Quotient Groups |
| 11 | Solutions of Equations of Degree Four |
| 12 | The Group of the Dodecahedron |
| 13 | Unsolvability of the Quintic |
| 14 | Review |