CS 19 – Winter 2009

Discrete Mathematics
for
Computer Science




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Schedule

Date Day # Lecture Topic  Reading  Story Time I/O
01/05 M 1 Overview. Propositional Logic 1.1, 1.2 LeibnizOn 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 FunctionClay
 
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 cartoonSouvenirs! 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-KhwarizmiAlgebra 1st Midterm: 7 &ndash 9 PM in Kemeny 006
02/04 W 14 Logartithm; Big-Ω ; Big-Θ 4.4 Napier's Logs
Slide RulesUse 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 machineChurch-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 ProblemAfra'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 DiaconisCoin Toss (NPR) &ndash Paper (pdf)  
02/20 F 21 Chebyshev's Inequality; Bayes's Theorem; Average Case Analysis 9.1, 9.2 Pseudo-Random NumbersShow 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 KonigsbergPaper 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 MapHomer in 3D
 
03/06 F 27 Dijkstra's Algorithm; Lower bound on sorting   Felix KleinKlein bottle Homework Eight Due
03/09 M 28 Last Lecture      
03/13 F Final 8 – 11 AM in Kemeny 105      

 

Computer Science
Dartmouth College