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