MTH150: Discrete Mathematics (Fall 2009)

Course Number	Time	Location	Instructor	Office Hours	E-mail
66373	MWF 1100-1150	B&L 106	Andrew Ledoan	TTh 1400-1530	ledoan at math dot rochester dot edu

Recitation Location	Time	Teaching Assistant	E-mail
Hylan 201	W 1815-1905	Jaime Sorenson	jsorens2 at u dot rochester dot edu
Morey 525	Th 1815-1905	Jaime Sorenson	jsorens2 at u dot rochester dot edu

Prerequisites

There is no course at the University of Rochester which is a prerequisite for MTH150.

Textbooks

We will use the following textbook:

Kenneth H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, McGraw-Hill Science/Engineering/Math, 2006 (ISBN-10: 0073229725, ISBN-13: 978-0073229720).

Objectives

My main objectives are to help you develop and refine basic mathematical skills and to promote problem-solving and critical thinking skills that are crucial to your future work in engineering, computer science, and mathematics.

Syllabus

MTH150 is an undergraduate course on discrete mathematics. We will more or less follow the textbook and cover Chapters 1, 2, 3, 4, 5, 7, 8, and 9. The topics that we will study are logic, functions, algorithms, mathematical reasoning, mathematical induction, recurrence relations, techniques of counting, equivalence relations, graphs, trees, as well as specific questions given by the “Towers of Hanoi,” and Euler’s “7 bridges of Konigsberg problem.” A detailed weekly schedule is provided below.

Grading Policy

The course grade will be derived from the following four components:

WeBWorK 25%
Midterm Exams 30%
Final Exam 40%
Participation 5%

MTH150A students usually take MTH171Q concurrently. For these students, their semester grades will be based solely on their WeBWorK and exam scores.

All scoring will be done by a computer program, and you will be able to access your accumulated scores and view your current grade at any time. The grading program we will use is called BlackBoard. You can access your grades by loging in at http://my.rochester.edu/.

A grade of Incomplete will be given only in the event that a documented emergency or illness prevents the student who is doing acceptable work from completing a small percentage of the course requirements. Failing to recover from falling behind in the course is not an acceptable reason for seeking an Incomplete. Please note that regular attendance is mandatory. Failure to regularly attend class will result in a student receiving the grade E if the student is unsuccessful in dropping the course.

WeBWorK

Each WeBWorK problems set (these are presented and graded electronically) is due Friday morning at 0500, a little over one week after it was assigned (Wednesday at 1000). The solutions will be posted each Friday at 0600. There are no makeups on homework. Any changes to the due dates will be indicated in the Weekly Schedule. There will be 10 WeBWorK sets (Set 0, Set 1, Set 2, ... , Set 9). Set 0 is meant to familiarize you with WeBWorK and will not count toward your grade. Additional problems will be assigned toward the end of the term to cover Chapters 8 and 9.

Exams

The exam schedule is as follows.

Midterm Exam 1, Friday, October 23, 1100 to 1150, Sections 1.1 thorugh 3.4
Midterm Exam 2, Monday, November 23, 1100 to 1150, Sections 3.5 through 7.2
Final Exam, Sunday, December 20, 1230 to 1530, Sections 1.1 through 9.7

Most exam problems will closely mirror the problems from the Lectures and WebWorK Sets. However, there will be some problems which require a deeper understanding of the material than can be learned by memorization. For the midterm exams, you may bring one single-sided sheet of handwritten notes and a calculator. For the final exam, your sheet of handwritten notes may be double-sided.

If you learn that you will not be able to take the exams on the given dates, please contact me as soon as possible and be ready to provide the necessary documentation. As a rule, I do not give make-ups on exams. If you miss a Midterm Exam, you will receive a score of 0. The Final Exam is cummulative. It will cover all the sections listed in the Weekly Schedule below. Failure to take the Final Exam at the proper time and place will result in an automatc E in the course. Other arrangements must be made a long time in advance.

If you have a disability and need assistance, please let me know as early as possible. Special arrangements can be made to accomodate most needs. You should also contact Learning Assistance Services (LAS) in 10 Lattimore (telephone number (585)275-9049), or visit their web site. Any accomodations for exams must be arranged a week in advance and will require a letter or e-mail from the LAS.

Recitations

There will be sign-up sheets for Recitations posted on the first floor of Hylan (on the walls near the elevators) during the week of September 6. You must register for Recitations and attend the meetings regularly. Attendance will be enforced. It will count toward your class participation.

Weekly Schedule

The Weekly Schedule below describes exactly what will be discussed in Recitations in the following week. You are responsible for reading the textbook sections that are covered in the Lectures.


Date	Lecture and Reading Topics	WeBWorK Assignments	Class Notes	Remarks
9/2	Course Overview, Section 1.1 Propositional Logic	Set 0 (introduces WeBWorK; due 0500 Friday 09/11; will not be graded)	lec1
9/4	Section 1.2 Propositional Equivalences	Set 1 (covers Sections 1.1 through 1.4; due 0500 Friday 09/18)	lec2
9/9	Section 1.3 Predicates and Quantifiers		lec3
9/11	Section 1.4 Nested Quantifiers		lec4
9/14	Section 1.5 Rules of Inference		lec5
9/16	Section 1.6 Introduction to Proofs		lec6
9/18	Section 1.7 Proof Methods and Strategy		lec7
9/21	Section 2.1 Sets	Set 2 (covers Sections 2.1 through 2.2; due 0500 Friday 10/02)	lec8
9/23	Section 2.2 Set Operations		lec9
9/25	Section 2.3 Functions		lec10 (has 3 typos)
9/28	Section 2.4 Sequences and Summations		lec11
9/30	Section 3.1 Algorithms		lec12
10/2	Section 3.2 The Growth of Functions		lec13
10/7	Section 3.3 Complexity of Algorithms	Set 3 (covers Sections 2.3 through 3.3; due 0500 Friday 10/16)	lec14
10/9	Section 3.4 The Integers and Division		lec15
10/12	Section 3.5 Primes and Greatest Common Divisors	Set 4 (covers Sections 3.2 through 3.4; due 0500 Friday 10/23)	lec16
10/14	Section 3.6 Integers and Algorithms		lec17
10/16	Section 3.7 Applications to Number Theory	Set 5 (covers Sections 3.4 through 3.7; due 0500 Friday 11/06)	lec18
10/19	Section 4.1 Mathematical Induction		lec19
10/21	Section 4.2 Strong Induction and Well-Ordering		lec20
10/23	Midterm Exam 1, Sections 1.1 through 3.4
10/26	Section 4.3 Recursive Definitions and Structural Induction	Set 7 (due 0500 Friday 11/13)	lec21
10/28	Section 4.4 Recursive Algorithms
10/30	Section 5.1 The Basics of Counting		lec23
11/2	Section 5.2 The Pigeonhole Principle		lec24
11/4	Section 5.3 Permutations and Combinations		lec25
11/6	Section 7.1 Recurrence Relations		lec26
11/9	Section 7.2 Solving Linear Recurrence Relations		lec27
11/11	Section 7.3 Divide-and-Conquer Algorithms and Recurrence Relations
11/13	Section 8.1 Relations and Their Properties	Set 8 (due 0500 Friday 12/04)
11/16	Section 8.5 Equivalence Relations
11/18	Section 9.1 Graphs and Graph Models
11/20	Section 9.2 Graph Terminology and Special Types of Graphs
11/23	Midterm Exam 2, Sections 3.5 through 7.2
11/30	Section 9.3 Representing Graphs and Graph Isomorphism
12/2	Section 9.4 Connectivity
12/4	Section 9.5 Euler and Hamilton Graphs
12/7	Section 9.7 Planar Graphs
12/9	Final Exam Review
12/20	Final Exam, Sections 1.1 through 9.7

Bulletin Board

08/03/2009 This course web page was created and posted online today. Check this Bulletin Board regularly for important announcements, sample exams, study guides, and so on.
08/05/2009 Two copies of the textbook are now available at the Reserve Desk in Carlson Library.
10/16/2009 Midterm Exam 1 will be given in class on Friday, October 23. The exam will cover Sections 1.1 through 3.4. There will be a review session next Thursday, October 22. More information will be posted here.
10/20/2009 A sample Midterm Exam I will be posted here this Thursday, October 22. There will be a review session this Thursday, October 22, from 1700 to 1750, in CSB 209. For MTH150A students, Midterm Exam I will be given this Friday, October 23, from 1600 to 1700, in Hylan 101.
10/22/2009 Here is the Sample Midterm Exam 1.
10/28/2009 Here are the Midterm Exam 1 Solutions. For MTH150, the average is 83.63, the median is 83, and the standard deviation is 4.9. For MTH150A, the average is 76.52, the median is 82, and the standard deviation is 17.95.
11/18/2009 The review session for Midterm Exam 2 will be given on Friday, November 20, from 1600 to 1700, in 101 Hylan. The makeup midterm exam for MTH150A will be given on Monday, November 23, from 1600 to 1700, in 1101 Hylan.
11/20/2009 Here are some Sample Problems for Midterm Exam 2 and their Solutions. There are other problems in the lecture notes that you are responsible for. Please review them carefully.