CS 19 – Winter 2008

Discrete Mathematics
for
Computer Science




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Schedule

Date Day # Lecture Topic  Reading  Story Time I/O
01/07 M 1 Overview. Propositional Logic 1.1, 1.2 LeibnizOn 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 FunctionClay
 
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 ParadoxAnalysis Homework Two Due
Homework Three
01/28 M 10 Counting: Sum; Product;
Inclusion-Exclusion; Permutations
7.5 Fifteen PuzzleHistory  
01/30 W 11 Combinations; Double Counting; Binomial Theorem 5.5 GaussTopics 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 MachinesChurch-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 ProblemAfra'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 KonigsbergE53 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 ScienceAMS Article (pdf) Homework Eight Due
03/10 M Final 3 – 6 PM in Kemeny 007      

 

Computer Science
Dartmouth College