Solutions and grades of Quizzes 

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

Date 
Material 
Assignment 
Misc. 
September
57 
Sets, Methods of Proof. 

September
1014 
Methods of Proof. Functions, On the notion of
cardinality, 
Assignment
1 Solutions 
In question 1, all
the sets [n, n] and (n, n+2) and so on stand for intervals of real
numbers. In the definition of the A_n you may assume n is a positive
integer. 
September
1721 
Complex numbers, Polynomials and the fundamental thm of Algebra. Rings and Fields.  Assignment
2 Solutions 

September
2428 
Divisibility, gcd, Euclidean algorithm for integers. 2^(1/2) is irrational. Primes and the sieve of Eratosthenes. The Fundamental Thm of Arithmetic.  Assignment
3 Solutions 

October
15 
Infinity of primes (Quiz 1). Equivalence relations. Congruences.  Assignment
4 Solutions 
Quiz
1, Wednesday October 3, 16:30  18:00 in

October
1012 
Fermat's little
theorem, computing and solving equations in Z_{n}.
Public Key crypto and RSA.The ring of polynomials
over a field F. Degree.
Division with residue. 
Assignment
5 Solutions 
No
class October 8 (Thanksgiving). Tuesday
follows Monday's schedule. A correction was made in question 4 
October
1519 
GCD's. The Euclidean algorithm for polynomials. Irreducible polynomials. Unique factorization. Roots of polynomials. Roots of rational and real polynomials. Roots of polynomials over Z_p.  Assignment
6 Solutions 
Note
that you have 2
weeks to submit this (somewhat long) assignment. 
October
2226 
Rings (recall). Ideals. Z and F[x] are principal ideal rings. (Quiz 2). Homomorphisms and kernels. 


October
29  November 2 
Quotient
rings. F[x]/(f(x)) and
constructing finite fields. Roots in extension fields. 
Assignment
7 Solutions 

November
59 
First isomorphism theorem. Chinese remainder theorem. Applications of CRT. Groups: the basic definition and examples. The symmetric group. (Quiz 3).  Assignment
8 Solutions 

November
1216 
The symmetric group  cont'd. (Quiz 3).The dihedral group. Cosets and Lagrange's theorem.  Assignment
9 Solutions 

November
1923 
Homomorphisms
and isomorphisms; Cayley's
theorem. Group actions on
sets: first definitions and properties.
Examples. 
Assignment
10 Solutions 
This
is the last assignment!! Question 5 is
optional. 
November
2630 
CauchyFrobenius
formula. Applications to Combinatorics. Homomorphisms, normal subgroups,
quotient groups and the first isomorphism theorem. Examples. 

December
3 
Groups of low order. 
Day (all in the week Dec. 3 7). No office hours Mon. Dec. 10 
Time 
Monday 
1:302:30 (Eyal), 3:00  4:00
(Telyn) 
Tuesday 
1:00  2:00 (Gabriel), 2:00 
3:00 (Eyal) 
Wednesday 
1:00  2:00 (Telyn) 
Thursday 
9:00  10:00 (Eyal), 1:00  2:00
(Telyn) 
Friday 
11:00  12:00 (Gabriel), 1:00 
2:00 (Gabriel) 