A First Course in Abstract Algebra

Instructor:  Prof. Ilya Kapovich

Spring 2002 ;  MATH 317 Section B1

MWF, 9am;   Henry 149

WWW:     http://www.math.uiuc.edu/~kapovich/317-02/317-02.html
 
 

COURSE SYLLABUS


Chapter 1:   NUMBER THEORY
 
 
Sections Class Hours
1.1: Introduction and 1.2: Binomial Coefficients 2
1.3: Greatest Common Divisors 2
1.4: Fundamental Theorem of Arithmetic 1
1.5: Congruences 2

Chapter 2:  GROUPS
 
 
Sections Class Hours
2.1: Functions (Review) 1
2.2: Permutations 3
2.3: Groups 2
2.4: Lagrage's Theorem   2
2.5 Homomorphisms 2
2.6: Quotient Groups 4
2.7: Group Actions 1

 

Chapter 3: COMMUTATIVE RINGS
 
 
Sections Class Hours
3.1: Definitions and Basic Properties 1
3.2: Fields 2
3.3: Polynomials 1
3.4: Homomorphisms 2
3.5: Greatest Common Divisors 2
3.6: Unique Factorization 1
3.7: Irreducibility 3
3.8: Quotient Rings and Finite Fields 3

 
 

NOTES ON THE SYLLABUS:

This is approximate plan for the course: it can be changed slightly along the way.  Some topics contained in the above chapters will be excluded.
I will explicitly mention these topics when we do get to the appropriate chapters. However, the general rule is that (unless I tell you otherwise) all the material of the above sections is a part of the course. Some of the theorems, propositions and lemmas from the book will not be explicitly stated during the lectures because of time constraints, but you should read these statements anyway. 
Also, be aware that this course places a substantial emphasis on proofs and you should pay special attantion to this aspect.
 
 
 


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