Math 558:  Introduction to modern algebra
Fall 2017
TR 2:30-3:45 SNOW 302

Terry Soo, Snow 610
Office hours: Tuesdays 4-5. Wednesdays 2.30-3.50.

Course description
This course serves as a basic introduction to abstract algebra--groups, rings, and fields.   We will also give a brief introduction to writing mathematical proofs.  Proof are an important part of this course.  Highlights of the course may include: the fundamental theorems of arithmetic and algebra, the RSA encryption method, counting the number of different ways to color the faces of a cube with a fixed number of colors, the classical angle trisection problem, and John Stillwell's recent proof of Abel's theorem. If you ever wondered why you never learned a formula like the quadratic formula for higher degree polynomials, I think you will enjoy this course.

Prerequisites.
Linear algebra.  Math 290 or Math 291.  This course can be one of the more difficult undergraduate courses.  Experience with proofs is an asset. 

Grading
Subject to revision

Homework:   20%
Midterm 1:    20% Septemeber 14. M1-with solutions
Midterm 2:    20% November 2. M2-with solutions
Final Examination: 40% December 13. 1.30-4PM. Official Registrar Final exam schedule
Final

Textbook and lecture notes.
No textbook is required.  I will post lecture notes online.

Suitable references are:

Introduction to applied algebraic systems.  Reilly
Undergraduate algebra.  Lang
Groups and symmetry. Armstrong
A concrete introduction to higher algebra.  Childs
A course in Galois theory.  Garling
Number theory.  Andrews


Papers, you may need to be at KU to access these.

The original RSA paper
Korner's proof of the fundamenetal theorem of algebra
John Stillwell's proof of Abel's theorem
Notes:
Sets, relations, and functions
Introduction to proofs
Induction
Number theory basics
Gcd computations
Modular Arithmetic
Chinese remainder theorem
Euler's totient function
Complex numbers
Fundamental theorem of algebra
Groups
Subgroups





Homework:
HW1: Due Tuesday September 5 HW1sol
HW2: Due Tuesday September 12 HW2sol
HW3: Due Thursday September 28
HW4: Due Thursday October 5 HW4sol
HW5: Due Thursday October 12 HW5sol
HW6: Due Thursday October 26 HW6sol
HW7: Not for submisson.
HW8: Due Tuesday December 5 HW8sol

Other:
In class worksheet
In class worksheet II
In class worksheet III