Perspectives
in Algebra, Math 250
Tuesdays & Thursdays, 5:30-6:45
PM, Room S2 307.
Office hours: MW from 9:05 to 11:35 AM, or by
appointment.
IMPORTANT:
If you want to learn your grades so far, and how
your scores are compared with the rest of the class please log into
Blackboard here.
Syllabus
Lecture notes
Chapters 1-5 (corrected).
Updated 11/13.
Material covered in class:
08-25: Solving ax=b yields the idea of a group. Examples. Conditions for a set of functions to be a group under composition.
08-27: Permutations, cyclic groups.
09-01: Left multiplication map, multiplication tables, magic squares. Basic properties of Z.
09-03: Basic properties of divisibility in Z. Divisibility by n criteria for 1< n < 13.
09-08: gcd, Euclidean algorithm, Bezout's theorem.
09-10: Linear Diophantine equations.
09-15: Polynomial equations with coefficients in Z with non-integral solutions. Z_n.
09-17: Pythagorean triples. Equations over Z_n.
09-22: Linear congruences/equations. The equation (a+1)x+b =x+c.
09-24: Rings, ideals and vector spaces.
09-29: Vector spaces as solutions of homogeneous systems of linear equations.
10-01: How to write solutions of systems of linear equations. Introduction to polynomials.
10-06: Polynomials. The fundamental theorem of algebra. The factor theorem.
10-08: The division algorithm, the remainder theorem.
10-13: Lemma of Gauss. Rational root theorem.
10-22: Eisenstein's criterion and similar results.
10-27: Review.
10-29: Exam 1
11-03: Field extensions.
11-05: Presentations (Kristi & Cher ). NEW!!!
Updated 11/18
11-10: Algebraic and transcendental elements.
11-12: Minimal polynomials, conjugate elements, quotient rings.
11-12: Kaplanski's theorem, how quotient rings that are fields can be presented in an easier way.
11-19: Presentations
Assignments, Solutions,
Handouts, etc. (pdf files)
Homework
Updated 11/13
Presentations Updated 10/02
Homework Solutions Updated 11/13
Exam 1 Info
Exam 1 Solutions
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