Survey of Modern Algebra

There is no textbook. All lecture notes will be posted right here.
Item Date Information
Homework 1 Solutions Fri Jan 30 Course Notes
Algebra pre- and post-1930
al-Khwarizmi and his al-jabr
The Quadratic Formula
Rings and Fields
Descartes' Factor Theorem
Newton's Method
Homework 2 Solutions Fri Feb 13 Course Notes
Equality of Polynomials
The Depressed Cubic
Cardano's Formula
The Cubic Formula
Bombelli's Idea
Complex Numbers
De Moivre's Formula
Exam 1
Review Notes
Wed Feb 18 Total: 25 points
A = 21 and above
B = 17 and above
C = 10 and above
Homework 3 Solutions Fri Feb 27 Course Notes
Euler's Formula
Polar Form
Roots of Unity
Factoring x^n-1 over C and R
Homework 4 Solutions Fri Mar 20 Course Notes
Primitive Roots of Unity
Factoring x^n-1 over Z
Cyclotomic Polynomials
Compass and Straightedge
Constructible Numbers
Exam 2
Review Notes
Wed Mar 25 Total: 25 points
A = 23 and above
B = 21 and above
C = 8 and above
Homework 5 Solutions Fri Apr 10 Course Notes
Impossible Constructions
Euler's Totient Function
Fermat Primes
Gauss-Wantzel Theorem
Homework 6 Solutions Wed Apr 22 Course Notes
Solvability of Polynomials
Abel-Ruffini Theorem
Symmetric Functions
Lagrange's Method
Along Came Galois
Exam 3
Review Notes
Fri Apr 24 In Class