Instructor: Prof. Ilya Kapovich
Spring 2005 ; MATH 417 Section C13
MWF, 9am; Altgeld Hall 145
WWW:
http://www.math.uiuc.edu/~kapovich/417-05/417-05.html
APPROXIMATE COURSE SYLLABUS
Chapter 1: NUMBER THEORY
| Sections | Class Hours |
| 1.1: Induction and 1.2: Binomial Coefficients | 2 |
| 1.3: Greatest Common Divisors | 2 |
| 1.4: Fundamental Theorem of Arithmetic | 1 |
| 1.5: Congruences and applications to cryptography |
2 |
Chapter 2: GROUPS
and GROUP ACTIONS
| Sections | Class Hours |
| 2.1: Functions (Review) | 1 |
| 2.2: Permutations | 3 |
| 2.3: Groups | 2 |
| 2.4: Lagrange's Theorem | 2 |
| 2.5 Homomorphisms | 2 |
| 2.6: Quotient Groups | 4 |
| 2.7: Group Actions | 2 |
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 |