| 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
|
Banach-Tarski Paradox
|
|
| 01/15 |
Θ |
6 |
MLK x-hour – 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, Inclusion-Exclusion, 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; Big-O |
3.3 |
Al-Khwarizmi –
Algebra |
1st Midterm: 7 &ndash 9 PM in Kemeny 006 |
| 02/04 |
W |
14 |
Logartithm; Big-Ω ; Big-Θ |
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
–
Church-Turing Thesis
|
|
| 02/11 |
W |
17 |
Inclusion-Exclusion; Uniform Distributions;
Conditional Probability
|
|
Bertrand's Paradox
|
Results & Response to MIF
|
| 02/12 |
Θ |
18 |
Carnival x-hour: 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
|
Pseudo-Random 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 |
|
|
|
Computer Science