CS 19 – Winter 2010

Discrete Mathematics
in
Computer Science




Announcements
Syllabus
Schedule
Resources
Grades




 

Schedule

Date Day # Lecture Topic  Reading  Story Time I/O
01/04 M 1 Overview. Propositional Logic 1.1, 1.2 LeibnizOn 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 FunctionClay
Homework One
Proof Methods
01/13 W 5 Proofs 2 1.7, 2.1 Euclid's PostulatesParallel Postulate
Spherical EaselNonEuclid
 
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 cartoonSouvenirs!
 
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 SetCantor 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-KhwarizmiAlgebra 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 machineChurch-Turing ThesisTuring 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 ProblemAfra's Report  
02/19 F 21 Variance; Chebyshev's Inequality;   Persi DiaconisCoin Toss (NPR) &ndash Paper (pdf)  
02/22 M 22 Bayes Theorem; Average case analysis; Hashing 9.1, 9.2 P vs NP (Clay)Complexity ZooPartial Map Homework Six Due
Homework Seven
02/24 W 23 Chaining analysis; Graphs 9.3, 9.4 Seven Bridges of KonigsbergPaper 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 NumbersCheating in PokerGet 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
Dartmouth College