Jeff Kinne - CS240 Summer 2007 Schedule

CS 240 - Introduction to Discrete Mathematics, Summer 2007

Course Schedule

The textbook is copious in the number of topics covered and the number of examples for each topic. We will not be covering all topics and examples in the book, so the assigned reading will be kept to a manageable amount. This web-page will be kept up to date with the suggested reading to perform before each lecture. We will also list practice exercises that you can work through to test your knowledge, as well as the key concepts that should be learned from the reading.

Homework assignments are due each Thursday at the beginning of class (except for the first week of class).

The following table gives a tentative outline of the semester. Below the outline are the details for each lecture. Each of these will be updated throughout the semester as things change.

Course Introduction June 18

Mathematical structures and background June 19, June 20, June 21
June 25, June 26
Algorithms: analysis, proof, and design June 26, June 27, June 28,
July 2, July 3, July 5,
July 9, July 10
First Exam - July 16. handout (PS, PDF). sample exam (PS, PDF).

Probability Theory and Randomized Algorithms July 11, July 12,
July 17, July 18, July 19,
July 23, July 24, July 25, July 26
Integer Arithmetic: Algorithms and Uses July 30, July 31, August 1, August 2,
August 6, August 7
Miscellaneous Day August 8

Second Exam - August 9. handout (PS, PDF). sample exam (PS, PDF).

June 18: Introduction/Mazes
Reading: handout - PS, PDF
Exercises: none
Key Concepts: Graph, Algorithm, Running time
June 19: Propositional Proofs
Reading: 1-11, 21-25, 30-42, 50-55, 63-67, 70
Exercises: Pgs 106-107, #s 1, 5, 7, 11, 13, 15, 19, 31
Key Concepts: Translating sentences between English and logical form, Logical operators, Rules of inference, Truth table

June 20: Sets and Functions
Reading: 111-116, 121-127, 133-144, 158-160
Exercises: Pgs 164-165, #s 1, 3, 5, 9, 11, 13
Key Concepts: Sets, Set operations and basic properties, Functions, Basic function properties and definitions, Countable, Uncountable

June 21: Cardinality, Graphs
Reading: 158-160, 589-593, 597-605
Exercises: Pg 596, #s 3, 7, 19; Pgs 608-609, #s 3, 13, 19
Key Concepts:Cardinality of infinite sets, Basic Graph terminology

June 25: Graphs, Relations
Reading: 117-118, 246-249, 519-524, 611-614, 615-616
Exercises: Pg. 120 #s 23, 27, 31; Pgs. 254-255 #s 1, 5, 7; Pg 528 # 7; Pgs 618-619 #s 3, 7, 13, 35
Key Concepts: Relation, Equivalence Relation, Adjacency Matrix, Adjacency List, Graph Isomorphism, Cartesian Product, Matrix

June 26: Graph Isomorphism, Algorithms
Reading: 167-171, 180-190, 193-194
Exercises: Pg 177 #s 3, 5, 9; Pg 191-192 #s 1, 3, 7, 15, 23, 41; Pg 199 #s 3, 5, 7
Key Concepts: Graph isomorphism, algorithm correctness, algorithm running time, big-O, big-Omega, big-Theta

June 27: Asymptotic running time, Induction, Recursion
Reading: 180-190, 263-266, 311-312, 315, 322-327
Exercises: Pg 191 #s 9, 11, 13, 19; Pg 321 #s 9, 23; Pgs 327-328 #s 1, 3, 7
Key Concepts: Big-O, Big-Omega, Big-Theta, Recursion, Proving algorithm correctness using Induction

June 28: Induction for proving formulae
Reading: 267-271, 283-284, 287
Exercises: Pg 279 #s 3, 9, 11, 39, 43; Pg 291-292 #s 3, 9
Key Concepts: Induction, sum of geometric series, number of bit strings of length n, inequalities, well-ordering

July 2: Connectivity and Shortest Path
Reading: 621-624, 647-653, 175
Exercises: Pgs 629-631 #s 1, 3, 27; Pgs 655-656 #s 3, 5, 15
Key Concepts: Connectivity, Path, Shortest Path, Breadth First Search, Weighted Graph, Dijkstra's Algorithm, Greedy Algorithm

July 3: Merge Sort and Running time of recursive algorithms
Reading: 317-320, 449-454, 474-479
Exercises: Pgs 456-457 #s 1, 11, 17, 19; Pgs 482-483 #s 7, 19
Key Concepts: Merge Sort, Recurrence relation, Recursion tree, Master theorem, Recursively defined structures

July 4: Independence day - no class

July 5: Topological sort and Partial Orders
Reading: 566-572, 576-578
Exercises: Pgs 578-579 #s 1, 3, 5, 9, 21
Key Concepts: Partially ordered set, Hasse diagram, Topological sort

July 9: Spanning Trees
Reading: 683-684, 690, 724-730, 737-741
Exercises: Pgs 734-736 #s 1, 5, 13, 25; Pg 742 #s 1, 3, 11
Key Concepts: Tree, Spanning Tree, Minimum Spanning Tree, Depth First Search

July 10: Review- Mathematical Structures, Proof, and Algorithms
Reading: None
Exercises: None
Key Concepts: Greedy, Divide and Conquer, and recursive algorithms, Proof techniques, Algorithm analysis

July 11: Basic Probability Theory and Counting
Reading: 393-398, 335-343, 355-358, 499-504
Exercises: Pg 344 #s 1, 7, 11; Pgs 360-361 #s 3, 5, 9, 13, 19; Pgs 398-399 #s 3, 5, 7, 21, 37; Pg 504 #s 1, 3, 5
Key Concepts: Random events, Discrete probability, Methods for counting (permutations, combinations, sum/product rules, inclusion-exclusion), Monty Hall 3-door problem, Birthday paradox

July 12: Basic Probability Theory and Counting (continued)

July 16: First exam

July 17: Binomial Distribution
Reading: 400-414, 363-366
Exercises: Pg 414-415 #s 1, 3, 7, 11, 15, 17, 21
Key Concepts: Conditional probability, Random variable, Independent random variables, Bernoulli trials, Binomial Distribution, Binomial Theorem

July 18: Bayes' Theorem and Conditional Probability
Reading: 417-423
Exercises: Pg 369 #s 3, 9, 15; Pg 424 #s 1, 3, 5, 7, 11
Key Concepts: Bayes' Theorem, Applications of Bayes' Theorem (spam filter, Bayesian inference)

July 19: Probabilistic Method, Problem Session
Reading: 413-414, 352
Exercises: None
Key Concepts: Probabilistic Method, Ramsey number

July 23: Expected Value and Variance
Reading: 426-439
Exercises: Pgs 439-441 #s 1, 3, 5, 11, 19, 23, 25, 29, 33
Key Concepts: Expected Value, Linearity of Expection, Variance, Rules for Expectation and Variance for independent variables, Chebyshev's inequality

July 24: Expected Value and Variance (continued)

July 25: Randomized Algorithms
Reading: Randomized Algorithm - Wikipedia,
Exercises: Pg. 440-441 #s 13, 15, 31, 33
Key Concepts: Definitions of Randomized Algorithm, Simple randomized algorithm, Markov's rule, Geometric Distribution
July 26: Randomized Selection
Reading: Sections 1 and 2 of Deterministic and Randomized Selection Algorithms
Exercises: None
Key Concepts: Randomized algorithm, Randomized Selection
July 30: Integer and Modular Arithmetic
Reading: 200-206, 219-225
Exercises: Pgs 208-209 #s 1, 3, 5, 9, 19, 23, 25; Pg 230 #s 49, 51, 53, 55
Key Concepts: Algorithms for +, *, Modular arithmetic, Divisibility

July 31: Modular Arithmetic, Euclidean Algorithm
Reading: 226-229, 298-299
Exercises: Pg 218 #s 21, 27; Pg 230 #s 23, 27, 29
Key Concepts: Euclidean Algorithm, gcd

August 1: Primality, Finger-printing
Reading: 210-217, Fingerprinting
Exercises: Pgs 217-218 #s 5, 15, 31, 35
Key Concepts: Infinitude of primes, distribution of primes, unique factorization
August 2: Chinese Remainder Theorem
Reading: 216, 231-238
Exercises: Pgs 244-245 #s 5, 11, 19, 25
Key Concepts: Relatively prime, Chinese Remainder Theorem, arithmetic with large integers

August 6: Primality Testing and Factoring
Reading: 238-240, 412-413, Pg 244 # 17
Exercises: Pg 245 #s 27, 29, 35
Key Concepts: Fermat's little theorem, Pseudoprimes

August 7: Cryptography - RSA
Reading: 226-227, 241-244, 507-509
Exercises: None
Key Concepts: Modular Exponentiation, Sieve of Eratosthenes, Public key cryptography, RSA cryptosystem

August 8: Miscellaneous Day
Reading: None
Exercises: None
Key Concepts: (Course evaluation, finishing up loose ends, etc.)

August 9: Final exam

Computer Sciences | UW Home

Feedback or content questions: send email to "jkinne" at the cs.wisc.edu server
Technical or accessibility issues: lab@cs.wisc.edu
Copyright © 2002, 2003, 2004, 2005, 2006, 2007 The Board of Regents of the University of Wisconsin System.