| 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
|
Banach-Tarski 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 x-hour – 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, Inclusion-Exclusion
|
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 |
Big-O; Logarithm
|
3.2, 3.3
|
Al-Khwarizmi –
Algebra
|
Midterm One: 7 – 9 PM, Kemeny 105
|
| 02/05 |
F |
15 |
Big-Ω ; Big-Θ ; 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
–
Church-Turing Thesis –
Turing Prize
|
|
| 02/11 |
Θ |
18 |
Carnival x-hour – Inclusion-Exclusion; 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
|
Pseudo-Random 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 |
|
|
|
Computer Science