01/05 
M 
1 
Overview. Propositional Logic 
1.1, 1.2 
Leibniz –
On Computers
Mechanical Calculators


01/07 
W 
2 
Propositional Logic; Predicate Logic 
1.3, 1.4 
Sir Belvedere's Logic 

01/09 
F 
3 
Quantifiers; Inference rules 
1.5, 1.6 
Gödel's Proof –
Outline
Book

Homework One

01/12 
M 
4 
Proofs 
1.7, 2.1

Riemann Hypothesis
ζ Function –
Clay


01/14 
W 
5 
Proofs; Set Theory 
8.1, 2.2

BanachTarski Paradox


01/15 
Θ 
6 
MLK xhour – Set Operations 
2.3, 2.4

Russell's Paradox (Also)

Proof Methods

01/16 
F 
7 
Relations, Functions

4.1, 4.2

Hilbert's Grand Hotel &ndash
Salon cartoon – Souvenirs!

Homework One Due
Homework Two

01/19 
M 

MLK Holiday &ndash No Class 



01/21 
W 
8 
Sequences; Sums; Induction 
5.1 
Cantor's Diagonalization 

01/23 
F 
9 
Induction; Strong Induction Guest lecture by
Ranganath Kondapally 
5.2, 5.3 

Homework Two Due
Homework Three

01/26 
M 
10 
Counting: Sum, Product, InclusionExclusion, Permutations 
5.4, 7.5 
Continuum Hypothesis


01/28 
W 
11 
Counting: Combinations, Double Counting 
5.5 
Cantor Set


01/30 
F 
12 
Counting with Repetitions 
3.1, 3.2 
Gauss &ndash
Topics named after Gauss

Homework Three Due
Homework Four

02/02 
M 
13 
Pigeonhole; BigO 
3.3 
AlKhwarizmi –
Algebra 
1st Midterm: 7 &ndash 9 PM in Kemeny 006 
02/04 
W 
14 
Logartithm; BigΩ ; BigΘ 
4.4 
Napier's Logs Slide Rules –
Use One!


02/06 
F 
15 
Binary Search; Insertion & Merge Sort;
Recursive algorithms & Recurrences

6.1, 6.2 
Halting Problem

Homework Four Due
Homework Five

02/09 
M 
16 
Quick Sort; Probability Theory

7.1, 6.3 
Turing machine
–
ChurchTuring Thesis


02/11 
W 
17 
InclusionExclusion; Uniform Distributions;
Conditional Probability


Bertrand's Paradox

Results & Response to MIF

02/12 
Θ 
18 
Carnival xhour: Random Variables; Expectation 
7.6, 6.4

Monty Hall Problem – Afra's Report

Homework Five Due
Homework Six

02/13 
F 

Carnival Holiday &ndash No Class 



02/16 
M 
19 
Bernoulli trials 

St. Petersburg Paradox – Philosophical Responses


02/18 
W 
20 
Properties of Expectation; Variance 

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


02/20 
F 
21 
Chebyshev's Inequality; Bayes's Theorem; Average Case Analysis 
9.1, 9.2

PseudoRandom Numbers –
Show me the Random Numbers!

Homework Six Due
Homework Seven

02/23 
M 
22 
Hashing 
9.3, 9.4 
Paul Erdös &ndash Erdös Number Project 
2nd Midterm: 7 &ndash 9 PM in Kemeny 006 
02/25 
W 
23 
Graphs 
9.6 


02/27 
F 
24 
Bipatite graphs; Graph representation & Isomorphism 
10.1, 10.2 
Seven Bridges of Konigsberg
– Paper E53 in Dartmouth's Euler Archive

Homework Seven Due
Homework Eight 
03/02 
M 
25 
Graph invariants; Connectivity
 10.3 
Four Color Theorem (Also) – Proof


03/04 
W 
26 
Trees; Structural Induction 
4.3 
P vs NP (Clay) – Complexity Zoo Partial Map –
Homer in 3D


03/06 
F 
27 
Dijkstra's Algorithm; Lower bound on sorting
 
Felix Klein – Klein bottle

Homework Eight Due 
03/09 
M 
28 
Last Lecture
 


03/13 
F 

Final 8 – 11 AM in Kemeny 105 


