| 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 |
Banach-Tarski 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 x-hour – Induction |
5.1, 5.2 |
Hilbert's Grand Hotel |
|
| 01/25 |
F |
9 |
Strong Induction; Well-ordering |
5.3, 5.4 |
Unexpected Hanging Paradox –
Analysis |
Homework Two Due
Homework Three |
| 01/28 |
M |
10 |
Counting: Sum; Product;
Inclusion-Exclusion; 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; Big-O; Logarithm |
3.3 |
Napier's Logs
Slide Rules –
Use One! |
1st Midterm: Moore B03, 7 &ndash 9 PM |
| 02/06 |
W |
14 |
Big-Omega & Theta; Binary Search;
Insertion Sort |
4.4 |
The Halting Problem |
|
| 02/07 |
θ |
15 |
Carnival x-hour – Recursive Algorithms; Recurrences; Merge Sort |
6.1, 6.2 |
Turing Machines – Church-Turing Thesis |
Homework Four Due
Homework Five |
| 02/08 |
F |
|
Carnival Holiday &ndash No Class |
|
|
|
| 02/11 |
M |
16 |
Quick-Sort; Probability Theory |
7.1 |
P vs. NP &ndash Clay–
36 "Solutions"! |
|
| 02/13 |
W |
17 |
Inclusion-Exclusion; 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 |
Pseudo-Random 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 |
|
|
|
Computer Science