Math 558: Introduction to modern algebra
TR 2:30-3:45 SNOW 302
Terry Soo, Snow 610
Office hours: Tuesdays 4-5. Wednesdays 2.30-3.50.
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.
Linear algebra. Math 290 or Math 291. This course can
be one of the more difficult undergraduate courses.
Experience with proofs is an asset.
Subject to revision
Midterm 1: 20% Septemeber 14.
Midterm 2: 20% November 2.
Final Examination: 40% December 13. 1.30-4PM.
Official Registrar Final exam schedule
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
Sets, relations, and functions
Introduction to proofs
Number theory basics
Chinese remainder theorem
Euler's totient function
Fundamental theorem of algebra
HW1: Due Tuesday September 5
HW2: Due Tuesday September 12
HW3: Due Thursday September 28
HW4: Due Thursday October 5
HW5: Due Thursday October 12
HW6: Due Thursday October 26
HW7: Not for submisson.
HW8: Due Tuesday December 5
In class worksheet
In class worksheet II
In class worksheet III