Solutions and grades of Quizzes 

Quiz 1 
Results 
Quiz 2 
Results 
Quiz 3  Results 
Detailed
Syllabus * 

Date 
Material 
Assignment 
Misc. 
September
35 
Sets, Methods of Proof. Functions 

September
812 
Functions. On the notion of
cardinality. Complex
numbers. Polynomials and the
fundamental thm
of Algebra. Rings and Fields
(definition only). 
Assignment
1 Solutions 

September
1519 
Divisibility, gcd, Euclidean algorithm for integers. 2^(1/2) is irrational. Infinity of primes. Primes and the sieve of Eratosthenes. The Fundamental Thm of Arithmetic.  Assignment
2 Solutions 

September
22  26 
The Fundamental Thm of Arithmetic, cont'd. (Quiz 1) Equivalence relations. Congruences.  Assignment
3 Solutions 

September 29 October 3  Congruences  cont'd. Fermat's little theorem, computing and solving equations in Z_{n}. Public Key crypto and RSA.  Assignment
4 Solutions 
Quiz
1, October 1. 19:00  20:30 in STBIO S1/4. Please be sitted at 18:50. 
October
610 
The ring of polynomials over a field F. Degree. Division with residue. GCD's. The Euclidean algorithm for polynomials. Irreducible polynomials.  Assignment
5 Solutions 

October
1517 
Unique factorization. Roots of polynomials. Roots of rational and real polynomials.  No class October 13 (Thanksgiving) 

October
2024 
Roots of polynomials over Z_p. (Quiz 2) Rings (recall). Ideals. Z and F[x] are
principal ideal rings. 
Assignment
6 Solutions 

October
2731 
Homomorphisms and kernels. Quotient rings. First isomorphism theorem. F[x]/(f(x)).  Assignment
7 Solutions In question 11, it should say "Prove that d is not a square of a rational number" and "Prove that Q[\sqrt{d}] = .... is a subring of C and is in fact a field" 
Quiz
2, October 29. 16:3517:55
STBIO S1/4.

November
37 
Constructing finite fields. Roots in extension fields. Chinese remainder theorem. Applications of CRT.  Assignment
8 Solutions 
Deadline
to submit assignment 7 is extended to Wednesday November 5. 
November
1014 
Applications of CRT. (Quiz 3). Groups: the basic definition and examples. The symmetric group.  Assignment
9 Solutions 

November
1721 
The dihedral group. Cosets and Lagrange's theorem. Homomorphisms and isomorphisms. Group actions on sets: first definitions and properties.  Assignment
10 Solutions 
Quiz 3,
November 19. 16:3517:55
STBIO S1/4 
November
2428 
Group actions on
sets:
Examples. CauchyFrobenius
formula. Applications to Combinatorics. 

December
12 
Homomorphisms, normal subgroups,
quotient groups and the first isomorphism theorem. Examples. 
Day 
Time 
Monday (Eyal) 
14:00  15:00 
Tuesday (Mike) 
09:00  10:30 Cancelled
due to last minute emergency 
Thursday 
Victoria 09:00  11:00 Vicotria 16:00  18:00 
Friday 
Eyal 10:00  12:00 Mike13:00  15:00 