Discrete Mathematics for Computing II
CS 3305.501
Fall 2009
Advanced counting: Recurrences, solving recurrences, generating functions, and the inclusion-exclusion principle.
Relations: Properties of binary relations, representing relations, equivalence relations, partial orders.
Graphs: graph representation, isomorphism, Euler paths, shortest path algorithms, planar graphs, graph coloring.
Trees: tree applications, tree traversal, trees and sorting, spanning trees.
Further introduce students to mathematical reasoning, the art and practice of understanding and formulating logical arguments and constructing and evaluating proofs.
Present computer algorithms that implement step-by-step solutions to many of the abstract problems discussed in class.
Introduce students to the art of mathematical modeling, representing a real-world problem as equations or abstract problems that can be solved using the other components of the course.
Discuss numerous applications of mathematical modeling to real-life problems from computer science, biology, linguistics, and other fields.
Provide students with the specific knowledge outlined under “Specific Course Learning Objectives” below.
Ability to construct and solve recurrence relations
Ability to use the principle of inclusion and exclusion to solve problems
Ability to understand binary relations and their applications
Ability to recognize and use equivalence relations and partial orderings
Ability to use and construct graphs and graph terminology
Ability to apply the graph theory concepts of Euler and Hamilton circuits
Ability to identify and use planar graphs and shortest path problems
Ability to use and construct trees and understand tree terminology
Ability to use and construct binary search trees
CS 2305, Discrete Math for Computing I. You should be familiar with
Propositional logic and proofs
Basic mathematical structures: sets, functions, sequences
The concept of an algorithm
Integers and matrices
Mathematical induction and recursion
Basic counting principles: permutations and combinations
Elementary concepts of discrete probability
“Discrete Mathematics and its Applications”, 6th edition, by Kenneth H. Rosen, McGraw-Hill, 2007.
ISBN 978-0-07-288008-3
Available at the UTD Bookstore and at Barnesandnoble.com or Amazon.com ($142)
We will cover select material from chapters 7-10.
“Student's Solutions Guide to accompany Discrete Mathematics and Its Applications” by Kenneth H. Rosen and Jerrold W. Grossman, McGraw-Hill, 2007.
ISBN 0073107794
Available at the UTD bookstore, and at Barnesandnoble.com or Amazon.com ($48)
Obtaining the newest 6th edition of the text book is recommended. For the benefit of those students who wish to continue using an earlier edition purchased for their Discrete Mathematics for Computing I course, the instructor will provide reprints of the homework problems. It is still recommended that such students consult from time to time the newer edition currently used in the course for any differences.
Grading
Class participation: 20%
Homework assignments: Four to five assignments, approximately three weeks apart, two weeks to turn in each, 30% total
Quizzes: Two short in-class quizzes, multiple-choice or very short answers, 10% total
Midterm: 15%
Final exam: 25%
Topic
Time
Lecture Notes
Textbook Reference
Introduction
Monday 8/24
N/A
Recurrence Relations
Wednesday 8/26
Section 7.1
Linear Recurrence Relations, part 1
Monday 8/31
Section 7.2
Linear Recurrence Relations, part 2
Wednesday 9/2
Section 7.2
Non-homogeneous Recurrence Relations
Wednesday 9/9
Section 7.2
Divide and Conquer Algorithms, part 1
Monday 9/14
Section 7.3
Divide and Conquer Algorithms, part 2
Wednesday 9/16
Section 7.3
Divide and Conquer Algorithms, part 3
Monday 9/21
Section 7.3
Generating Functions, part 1
Wednesday 9/23
Sections 7.3-7.4
Generating Functions, part 2
Monday 9/28
Section 7.4
Quiz 1. Discussion of quiz and homeworks.
Wednesday 9/30
No slides
None
Generating Functions, part 3
Monday 10/5
Section 7.4
Midterm Exam
Wednesday 10/7
No slides
None
Counting with Generating Functions
Monday 10/12
Section 7.4
The Principle of Inclusion-Exclusion
Wednesday 10/14
Sections 7.4 - 7.5
Applications of Inclusion-Exclusion, part 1
Monday 10/19
Sections 7.5 - 7.6
Applications of Inclusion-Exclusion, part 2
Wednesday 10/21
Section 7.6
Relations
Monday 10/26
Section 8.1
Databases
Wednesday 10/28
Section 8.1-8.2
Relation Representation and Closures
Monday 11/2
Sections 8.3-8.4
Equivalence Relations
Wednesday 11/4
Sections 8.4-8.6
Partial Orders
Monday 11/9
Section 8.6
Lattices and Graphs
Wednesday 11/11
Sections 8.6 - 9.2
Graph Representation
Monday 11/16
Sections 9.2 - 9.3
Isomorphism
Wednesday 11/18
Lecture #23
Sections 9.3 - 9.4
Additional lecture information will be added to the table above as the course progresses.
Information about homework
Homework #1: Assigned Monday 9/14,
Homework #2: Assigned Wednesday 9/30, due Wednesday 10/14.
Homework #3: Assigned Monday 11/2, due Monday 11/16.
Homework #4: Assigned Wednesday 11/18, due Wednesday 12/2.
Submission Instructions: You may submit your homework by one of the following methods:
Drop a hard copy in the box outside my office by 8:15pm on the due date.
Bring a hard copy by the end of class (8:15pm) on the due date.
Email the homework to me (vh (at) hlt.utdallas.edu) by 11:59pm on the due date. You must send me a single attachment which is a PDF, Word, Postscript, or text file. The file's name should include your name and the words "Discrete Math II" and "HW 3".
Late Submissions: I will accept late submissions for Homework 3 up to the start of class on Wednesday 11/18, for a penalty of up to 20%.