01/07 
M 
1 
Overview. Propositional Logic 
1.1, 1.2 
Leibniz –
On Computers
Mechanical Calculators


01/09 
W 
2 
Propositional Logic; Predicate Logic 
1.3, 1.4 
Sir Belvedere's Logic 

01/11 
F 
3 
Quantifiers; Inference rules 
1.5, 1.6 
Gödel's Proof –
Outline
Book

Homework One

01/14 
M 
4 
Proofs 
1.7, 2.1 
Riemann Hypothesis
ζ Function –
Clay


01/16 
W 
5 
Set Theory 
8.1, 2.2 
BanachTarski Paradox


01/18 
F 
6 
Relations; Functions 
2.3, 2.4

Russell's Paradox (Also)

Homework One Due
Homework Two

01/21 
M 

MLK Holiday &ndash No Class 



01/23 
W 
7 
Bijections; Sequences; Sums 
4.1,4.2 
Cantor's Diagonalization 

01/24 
θ 
8 
MLK xhour – Induction 
5.1, 5.2 
Hilbert's Grand Hotel 

01/25 
F 
9 
Strong Induction; Wellordering 
5.3, 5.4 
Unexpected Hanging Paradox –
Analysis 
Homework Two Due
Homework Three 
01/28 
M 
10 
Counting: Sum; Product; InclusionExclusion; Permutations 
7.5 
Fifteen Puzzle –
History 

01/30 
W 
11 
Combinations; Double Counting; Binomial Theorem 
5.5 
Gauss – Topics named after Gauss 

02/01 
F 
12 
Repetitions; The Pigeonhole Principle 
3.1, 3.2 
Poincaré Series 1: Topology Deforming a Donut to a Mug 
Homework Three Due
Homework Four 
02/04 
M 
13 
Algorithm; BigO; Logarithm 
3.3 
Napier's Logs Slide Rules –
Use One! 
1st Midterm: Moore B03, 7 &ndash 9 PM 
02/06 
W 
14 
BigOmega & Theta; Binary Search;
Insertion Sort 
4.4 
The Halting Problem 

02/07 
θ 
15 
Carnival xhour – Recursive Algorithms; Recurrences; Merge Sort 
6.1, 6.2 
Turing Machines – ChurchTuring Thesis 
Homework Four Due Homework Five 
02/08 
F 

Carnival Holiday &ndash No Class 



02/11 
M 
16 
QuickSort; Probability Theory 
7.1 
P vs. NP &ndash Clay– 36 "Solutions"! 

02/13 
W 
17 
InclusionExclusion; Random Variables; Conditional Probability 
6.3 
Bertrand's Paradox 
MIF Results & Feedback 
02/15 
F 
18 
Expectation; Bernoulli trials; Geometric & Binomial distributions 
6.4 
Monty Hall Problem – Afra's Report 
Homework Five Due Homework Six 
02/18 
M 
19 
Properties of Expectation; Variance 

Poincaré Series 2: Manifolds 

02/20 
W 
20 
Chebyshev's Inequality; Bayes's Rule;
Average Case Complexity 

St. Petersburg Paradox &ndash Philosophical Responses 

02/22 
F 
21 
Hashing 
9.1, 9.2 
PseudoRandom Numbers &ndash Get some random numbers! 
Homework Six Due Homework Seven 
02/25 
M 
22 
Graph Theory 
9.3, 9.4 
Paul Erdös &ndash Erdös Number Project 
2nd Midterm: Moore B03, 7 &ndash 9 PM 
02/27 
W 
23 
Graphs: Representations; Isomorphism; Invariants 
9.6, 10.1 
Seven Bridges of Konigsberg
– E53 in Dartmouth's Euler Archive


02/29 
F 
24 
Connectivity; Weighted Graphs; Dijkstra's Algorithm 
10.2, 10.3 
Four Color Theorem (Also) – Proof 
Homework Seven Due Homework Eight 
03/03 
M 
25 
Trees; Structural Induction 
4.3 
Poincaré Series 3: The Conjecture &ndash Clay 

03/05 
W 
26 
Decision trees & Lower Bounds on Sorting;
Prefix Coding & Huffman 

Poincaré Series 4: Thurston's Geometrization Conjecture 

03/07 
F 
27 
Binary Search Trees; Walks on Trees;
Reverse Polish Notation 

Poincaré Series 5:
Coverage in Science –
AMS Article (pdf)

Homework Eight Due 
03/10 
M 

Final 3 – 6 PM in Kemeny 007 


