Survey of Modern Algebra

There is no textbook. Here are my lecture notes.

Here is the optional writing assignment. First deadline: Friday, March 20.

Here is the course syllabus.

My office hours are Wednesdays 2-3pm and Thursdays 12-1pm.
Item Date Information
Homework 1
Fri, Jan 31 The Quadratic Formula
Long Division of Polynomials
Descartes' Factor Theorem
Unique Factorization
Homework 2
Fri, Feb 14 Intermediate Value Theorem
Newton's Method
Cardano's Formula
Complex Numbers
Exam 1
Review Notes
Fri, Feb 21 Approximate Grade Ranges:
A = 20-24
B = 16-20
C = 13-16
Homework 3
Fri, Mar 6 Trigonometry
De Moivre's and Euler's Formulas
The Complex Plane
Roots of Unity
Coronavirus Happened Here
Homework 4
Fri, Apr 10 Preview of Gauss-Wantzel
Vector Spaces
Complex Numbers as Real Matrices
FTA and Partial Fractions
Euclidean Domains
Partial Fractions Theorem
Leibniz' Mistake, nth Roots of Any Number
HW4 Discussion
Homework 5
Fri, May 1 Euler's Attempt at the FTA
Equivalent Statements of FTA, Laplace's Proof
Symmetric Polynomials
Fundamental Theorem of Symmetric Polynomials
Conclusion of Laplace's Proof
Epilogue Modular Arithmetic in Z and F[x]
Kronecker's Theorem
Algebraic Translation of "Constructibility"
HW5 Discussion, Quadratic Field Extensions
Three Impossible Constructions
Gauss-Wantzel and Beyond
Who Was Evariste Galois?
Cheat Sheet for a Fictional Exam: Due Wed, May 6