1 
W 1/10 
Introduction, representing numbers, signvalue systems, Roman numerals 
2 
F 1/12 
Positional number systems, decimal number system, binary number system, and other bases 

M 1/15 
NO CLASS 
3 
W 1/17 
Mayan and Babylonian number systems 

4 
F 1/19 
Sets, elements, ∈, ∉, ellipses, union, ∪, intersection, ∩, subsets, ⊆, natural numbers, integers 
5 
M 1/22 
Sets, complements, setbuilder notation 
6 
W 1/24 
Definitions, size of a set, cardinality, 1to1 matchings between sets, Cantor's definition of cardinality 
7 
F 1/26 
Cardinality, countable sets, integers and rationals are countable, the Grand Hilbert Hotel 
8 
M 1/29 
Uncountable sets, proof by contradiction, √ 2 is not rational, real numbers are uncountable 

9 
W 1/31 
√ 13 is not rational, introduction to number theory 
10 
F 2/2 
There are infinitely many primes, finding primes, Fermat primes, Mersenne primes 
11 
M 2/5 
Sieve of Erathosthenes, Fundamental Theorem of Arithmetic, divisibility, Euclid's Lemma 
12 
W 2/7 
Existence of prime factorizations, uniqueness of prime factorizations 
13 
F 2/9 
Review of number systems, sets, cardinality, and prime numbers; FAQ 
14 
M 2/12 
FIRST MIDTERM EXAM 

15 
W 2/14 
Gauss' formula, proof by induction 
16 
F 2/16 
Introduction to graph theory, graphs, vertex degrees 
17 
M 2/19 
Degree Sum Formula, connected graphs, regular graphs, complete graphs, bipartite graphs, graph isomorphism 
18 
W 2/21 
Examples of isomorphic and nonisomorphic graphs, planar graphs and faces 
19 
F 2/23 
Euler's formula for planar graphs 
20 
M 2/26 
Nonplanarity of the complete graph on 5 vertices; polyhedral graphs 
21 
W 2/28 
Platonic solids 
22 
F 3/2 
Dual polyhedra, from map colorings to graph colorings 


SPRING BREAK 
23 
M 3/12 
Greedy coloring algorithm, Every planar graph contains a vertex of degree <6 
24 
W 3/14 
Planar graphs are 6colorable, Euler paths and Euler cycles 
25 
F 3/16 
Review of graph theory; FAQ 
26 
M 3/19 
SECOND MIDTERM EXAM 

27 
W 3/21 
SNOW DAY 
28 
F 3/23 
Euler paths, Hamiltonian cycles and paths, introduction to secure communication 
29 
M 3/26 
Introduction to secure key exchange, modular arithmetic: addition 
30 
W 3/28 
Modular arithmetic: multiplication, remainders, standard representation 
31 
F 3/30 
Divisibility by 9, modular exponentiation, Fermat's Little Theorem 
32 
M 4/2 
examples of modular exponentiation, DiffieHelmann key exchange 
33 
W 4/4 
DiffieHelmann key exchange, public key cryptosystems, digital signature 
34 
F 4/6 
Random numbers, linear congruential generators 

35 
M 4/9 
The birthday paradoxon, Fibonacci numbers 
36 
W 4/11 
Recurrence relations, closed form, characteristic equation 
37 
F 4/13 
Closed form of recurrence relations, golden ratio, amortized loans, rotational symmetry and mirror symmetry 
38 
M 4/16 
Binary operators, identity elements, inverses, groups 
39 
W 4/18 
Uniqueness of identity elements, examples of groups, applications of group theory 
40 
F 4/20 
Review FAQ 

41 
M 4/23 
THIRD MIDTERM EXAM 
42 
W 4/27 
* Special Guest Lecture * 