01/04 
M 
1 
Overview. Propositional Logic 
1.1, 1.2 
Leibniz –
On Computers
Mechanical Calculators


01/06 
W 
2 
Propositional Logic; Predicate Logic 
1.3, 1.4 
Sir Belvedere's Logic 

01/08 
F 
3 
Quantifiers; Inference rules 
1.5, 1.6 
Gödel's Proof –
Outline
Book


01/11 
M 
4 
Inference rules; Proofs 

Riemann Hypothesis
ζ Function –
Clay

Homework One
Proof Methods

01/13 
W 
5 
Proofs 2 
1.7, 2.1

Euclid's Postulates – Parallel Postulate
Spherical Easel – NonEuclid


01/15 
F 
6 
Set Theory 
8.1, 2.2

BanachTarski Paradox


01/18 
M 

MLK Holiday &ndash No Class 


Homework One Due
Homework Two

01/20 
W 
7 
Relations; Functions

2.3, 2.4

Russell's Paradox (Also)


01/21 
Θ 
8 
MLK xhour – Bijections; Sequences & Series 
4.1, 4.2

Hilbert's Grand Hotel
Salon cartoon – Souvenirs!


01/22 
F 
9 
Geometric series; Induction

5.1

Cantor's Diagonalization
Continuum Hypothesis


01/25 
M 
10 
Strong induction; Counting: Sum, Product, InclusionExclusion

5.2, 5.3

Cantor Set –
Cantor Egg

Homework Two Due
Homework Three

01/27 
W 
11 
Permutations; Combinations; Double Counting

5.4, 7.5

Gauss &ndash
Topics named after Gauss

Mathematical Induction

01/29 
F 
12 
Binomial theorem; Counting with repetitions

5.5

Euler Characteristic


02/03 
M 
13 
Repetitions; Pigeonhole principle

3.1

Peano Axioms

Homework Three Due
Homework Four

02/03 
W 
14 
BigO; Logarithm

3.2, 3.3

AlKhwarizmi –
Algebra

Midterm One: 7 – 9 PM, Kemeny 105

02/05 
F 
15 
BigΩ ; BigΘ ; Binary Search; Insertion Sort

4.4


Graded Midterms

02/08 
M 
16 
Recursive algorithms; recurrence relations

6.1

Halting Problem

Homework Four Due
Homework Five
Results & Response to MIF

02/10 
W 
17 
Discrete Probability Theory

6.2

Turing machine
–
ChurchTuring Thesis –
Turing Prize


02/11 
Θ 
18 
Carnival xhour – InclusionExclusion; Conditional probability;
Random Variables


Bertrand's Paradox


02/12 
F 

Carnival Holiday &ndash No Class 



02/15 
M 
19 
Expectation; Bernoulli trials

7.1, 6.3

St. Petersburg Paradox – Philosophical Responses

Homework Five Due
Homework Six
Probability handout (hardcopy)

02/17 
W 
20 
Geometric and binomial distributions;
Variance

6.4

Monty Hall Problem – Afra's Report


02/19 
F 
21 
Variance; Chebyshev's Inequality;


Persi Diaconis – Coin Toss (NPR) &ndash Paper (pdf)


02/22 
M 
22 
Bayes Theorem; Average case analysis; Hashing

9.1, 9.2

P vs NP (Clay) – Complexity Zoo – Partial Map

Homework Six Due
Homework Seven

02/24 
W 
23 
Chaining analysis; Graphs

9.3, 9.4

Seven Bridges of Konigsberg
– Paper E53 in Dartmouth's Euler Archive

Midterm Two: 7 – 9 PM, Kemeny 105

02/26 
F 
24 
Special graphs; Graph representation & isomorphism

9.6

Paul Erdös &ndash Erdös Number Project 

03/01 
M 
25 
Invariants; Connectivity

10.1

Four Color Theorem (Also) – Proof

Homework Seven Due
Homework Eight

03/03 
W 
26 
Dijkstra's algorithm; Trees

4.3, 10.2

PseudoRandom Numbers –
Cheating in Poker –
Get random!


03/05 
F 
27 
Decision trees; lower bound on sorting

10.3

3x+1 Problem (xkcd) – Borsuk's Conjecture


03/08 
M 
28 
Last Lecture


The Known Universe

Homework Eight Due

03/14 
U 

Final: 8 AM – 11 in Kemeny 105 


