# Fall 2019 Discrete Math

**Fall 2019 Discrete Math Syllabus**

**Math 2345 Discrete Math Fall 2019**

Section 58 CRN 82613, TR 5:00-6:15pm, D120

Section 59 CRN 82614, TR 6:30-7:45pm, D120

Sarah Holliday Office: D216

Phone: 470-567-4923 E-mail: shollid4@kennesaw.edu

**Office Hours**:

TR . And by appointment

**Text**:

Discrete Mathematics with Applications, 3rd ed.(or 4th if you already bought it),
Susanna S. Epp.

**Prerequisites**:

MATH 1113.

**Technology**:

You may want a calculator for large data set arithmetic. The TI-83/84 or TI-89 is
acceptable, as are many other calculators. You may NOT share calculators during quizzes
or exams. The use of cell phones, pagers, text or other messaging devices is not allowed
during class.

**Course objectives**:

An introduction to the fundamentals of discrete mathematics. Topics include sets,
formal logic, methods of proof, counting, relations, functions, and graphs & trees..

Upon completing this course students should be able to:

1. Write a correct formal proof.

2. Write the converse, contrapositive, and negation of a statement.

3. Determine whether a relation is reflexive, symmetric, or transitive.

4. Identify isomorphism invariants of graphs.

5. Construct minimal spanning trees for weighted graphs using Kruskal's and Prim's
algorithms.

**Homework, Quizzes and Examinations**:

Homework will be assigned daily, but will not be collected without advance warning.
Questions on homework problems can be answered in Office Hours and/or in class. Quizzes
will occur frequently, and occasionally without warning. Quiz questions will typically
come from homework problems. There will be three in-class examinations, and a final

**Grading Policy**:

In-class examinations will be valued at 15% each, quizzes/homework will total to 30%,
and the final will be valued at 25%.

A 90% or greater average will be awarded A

An 80% or greater average will be awarded B

A 70% or greater average will be awarded C

A 60% or greater average will be awarded D

**Academic Integrity**

Every KSU student is responsible for upholding the provisions of the Statement of Student Rights and Responsibilities, as published in the Undergraduate and Graduate Catalogs. Section II of the Statement of Student Rights and Responsibilities addresses the University's policy on academic honesty, including provisions regarding plagiarism and cheating, unauthorized access to University materials, misrepresentation/falsification of University records or academic work, malicious removal, retention, or destruction of library materials, malicious/intentional misuse of computer facilities and/or services, and misuse of student identification cards. Incidents of alleged academic misconduct will be handled through the established procedures of the Department of Student Conduct and Academic Integrity (SCAI), which includes either an "informal" resolution by a faculty member, resulting in a grade adjustment, or a formal hearing procedure, which may subject a student to the Code of Conduct's minimal one semester suspension requirement.

**Absence:**

If I am contacted with an acceptable excuse before the date of the quiz or exam, then
a makeup can be arranged. An acceptable excuse is in writing, contains the student's
name, the date of the absence, a signature from a faculty member sponsoring the trip,
contact information for the faculty member, and a brief mention of the nature of the
trip.

**ADA**

"Important notice: Any student who, because of a disabling condition, may require
some special arrangements in order to meet the course requirements should contact
the instructor as soon as possible to arrange the necessary accommodations. Students
should present appropriate verification from KSU Student Disability Services. No requirements
exists that accommodations be made prior to completion of this approved University
process."

**Dates**:

First day of classes Monday August 19

Drop add ends Friday August 23

Labor Day Holiday Monday September 2

First Test Thursday September 19

Last day to withdraw Wednesday October 9

Second Test Thursday October 17

Third Test Thursday November 21

Fall Break November 25-29

Last day of classes Monday December 9

Exams December 10-16

Section 51 December 10, 1-3pm, in this room.

Section 58 December 10, 6-8pm, in this room.

Section 59 December 12, 6-8pm, in this room.

Grades due December 19

**Withdrawal**

Students who find that they cannot continue in college for the entire semester after being enrolled, because of illness or any other reason, need to complete an online form. To completely or partially withdraw from classes at KSU, a student must withdraw online at www.kennesaw.edu, under Owl Express, Student Services.

The date the withdrawal is submitted online will be considered the official KSU withdrawal date which will be used in the calculation of any tuition refund or refund to Federal student aid and/or HOPE scholarship programs. It is advisable to print the final page of the withdrawal for your records. Withdrawals submitted online prior to midnight on the last day to withdraw without academic penalty will receive a “W” grade. Withdrawals after midnight will receive a “WF”. Failure to complete the online withdrawal process will produce no withdrawal from classes. Call the Registrar’s Office at 770-423-6200 during business hours if assistance is needed.

Students may, by means of the same online withdrawal and with the approval of the university Dean, withdraw from individual courses while retaining other courses on their schedules. This option may be exercised up until October 9, 2019.

This is the date to withdraw without academic penalty for Fall Term, 2019 classes. Failure to withdraw by the date above will mean that the student has elected to receive the final grade(s) earned in the course(s). The only exception to those withdrawal regulations will be for those instances that involve unusual and fully documented circumstances.

**Assistance**:

For help with your homework, or questions about the lectures, you have a lot of options.
I will take a limited number of questions during class, as time permits. I am available
in my office for help during my posted office hours, and any unscheduled time my door
is open. For additional help, there are campus-wide resources I will announce as soon
as I have the details.

**Practice homework (3rd edition here, 4th edition below):**

Section 1.1 Logical Form & Logical Equivalence #6, 7, 8, 9, 14, 15, 16, 17, 18, 19,
23, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 41, 42, 43, 44, 47, 49

Section 1.2 Conditional Statements #5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 28,
29, 30, 32, 33, 35, 42, 43, 44, 45, 46, 47, 48

Section 2.1 Introduction to Predicates and Quantified Statements I (no Tarski) #1,
3, 9, 11, 13, 14, 15, 16, 17, 18, 19, 27, 31

Section 2.2 Introduction to Predicates and Quantified Statements II #1, 2, 3, 4, 9,
10, 11, 13, 18, 19, 25, 27, 28, 38, 37, 40, 43, 45, 46.

Section 2.3 Statements Containing Multiple Quantifiers (no Prolog) #15, 17, 19, 21,
35, 37, 38.

Section 3.1 Direct Proof and Counterexample I: Introduction #1, 4, 5, 6, 7, 8, 9,
11, 12, 13, 17, 24, 27, 28, 29, 31, 39, 41, 44, 47, 48, 49, 53, 54, 56

Section 3.3 Direct Proof and Counterexamble III: Divisibility #3, 7, 12, 15, 18, 19,
20, 21, 22, 23, 24, 25, 26

Section 3.6 Indirect Argument: Contradiction and Contraposition #3, 5, 12, 14, 17,
19, 23, 24, 26

Section 4.1 Sequences #1, 3, 7, 11, 12, 15, 20, 22, 26, 27, 33, 35, 39, 41, 42, 43,
44, 45, 46, 47, 48

The first term in 4.1.15 should be 0.

Section 4.2 Mathematical Induction I #1, 6, 8, 11, 12, 15, 16, 19, 20, 21, 22, 23,
24, 25, 26, 27, 28, 31

Section 4.3 Mathematical Induction II #2, 4, 9, 11, 12, 16, 17, 19, 20, 22

Section 5.1 Basic Definitions of Set Theory #1, 3, 5, 8, 9, 10, 12, 13, 18, 19, 21,
26, 27, 28, 29, 30

Section 6.2 Possibility Trees and the Multiplication Rule #2, 4, 8, 9, 10, 11abc,
12, 14, 15, 17, 20, 28, 29, 30, 31, 32, 33, 34, 35, 36

Section 6.3 Counting Elements of Disjoint Sets: The Addition Rule #1, 3, 4, 6, 9,
11, 14, 17, 20, 21

Section 6.4 Counting Subsets of a Set; Combinations #4, 3, 4, 6, 9, 11, 14, 17, 20,
21

Section 6.5 r-Combinations with Repetition Allowed #2, 3, 4a, 4b, 10, 11, 12, 13,
14, 15a, 16a

Section 6.7 The Binomial Theorem #1, 3, 5, 10, 11, 13, 15, 17, 18, 24, 25, 27, 31,
34

Section 10.1 Relations on Sets #1, 6, 7, 9, 10, 11, 15, 24, 25, 27

Section 10.2 Reflexivity, Symmetry, Transitivity #1, 2, 4, 6, 8, 9, 10, 11, 12, 14,
17, 18, 19, 20, 23, 25, 33, 37

Section 11.1 Graphs: An Introduction #1, 3, 5, 8, 15, 16, 17, 18, 19, 20, 21, 22,
23, 25, 27, 33, 34, 36, 44, 45

Section 11.2 Paths and Circuits #1, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 47a, 48a, 49

Section 11.4 Isomorphisms of Graphs #6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18

Section 11.5 Trees #3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23,
25, 27, 30

Section 11.6 Spanning Trees #1, 3, 4, 5, 6, 7, 8, 9, 11

4th edition:

Section 2.1 Logical Form & Logical Equivalence #6, 7, 8, 9, 14, 15, 16, 17, 18, 19,
23, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 41, 42, 43, 44, 47, 49

Section 2.2 Conditional Statements #5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 28,
29, 30, 32, 33, 35, 42, 43, 44, 45, 46, 47, 48

Section 3.1 Introduction to Predicates and Quantified Statements I (no Tarski) #1,
3, 9, 11, 13, 14, 15, 16, 17, 18, 19, 29, 32

Section 3.2 Introduction to Predicates and Quantified Statements II #1, 2, 3, 4, 9,
10, 11, 13, 16, 17, 22, 35, 37, 38, 39, 41, 44, 46, 47.

Section 3.3 Statements Containing Multiple Quantifiers (no Prolog) #14, 17, 19, 22,
36, 38, 39.

Section 4.1 Direct Proof and Counterexample I: Introduction #1, 4, 5, 6, 7, 8, 9,
11, 12, 13, 17, 24, 27, 28, 29, 35, 43, 45, 48, 51, 52, 53, 57, 58, 60

Section 4.3 Direct Proof and Counterexamble III: Divisibility #3, 7, 12, 15, 21, 22,
23, 24, 25, 26, 27, 28, 29

Section 4.6 Indirect Argument: Contradiction and Contraposition #3, 5, 13, 15, 19,
21, 25, 26, 29.

Section 5.1 Sequences #1, 3, 7, 11, 12, 15, 20, 22, 26, 27, 44, 46, 50, 52, 62, 63,
64, 65, 66, 67, 68.

Section 5.2 Mathematical Induction I #1, 6, 8, 11, 12, 15, 16, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 32

Section 5.3 Mathematical Induction II #2, 4, 9, 11, 12, 16, 17, 19, 20, 22

Section 5.1 Basic Definitions of Set Theory #1, 3, 5, 8, 9, 10, 12, 13, 18, 19, 21,
26, 27, 28, 29, 30

Section 9.2 Possibility Trees and the Multiplication Rule #2, 4, 8, 9, 10, 11, 12,
14, 15, 17, 19, 31, 32, 33, 34, 35, 36, 37, 38, 39

Section 9.3 Counting Elements of Disjoint Sets: The Addition Rule #1, 3, 4, 6, 11,
13, 16, 19, 22, 23

Section 9.5 Counting Subsets of a Set; Combinations #1, 3, 4, 5, 6, 9, 11, 14, 17,
20, 21

Section 9.6 r-Combinations with Repetition Allowed #2, 3, 4a, 4b, 10, 11, 12, 13,
14, 17a, 18a

Section 9.7 The Binomial Theorem #19, 21, 23, 28, 29, 31, 33, 36, 37, 43, 44, 46,
50, 53

Section 10.1 Relations on Sets #1, 6, 7, 9, 10, 11, 15, 24, 25, 27

Section 10.2 Reflexivity, Symmetry, Transitivity #1, 2, 4, 6, 8, 9, 10, 11, 12, 14,
17, 18, 19, 20, 23, 25, 33, 37

Section 11.1 Graphs: An Introduction #1, 3, 5, 8, 15, 16, 17, 18, 19, 20, 21, 22,
23, 25, 27, 33, 34, 36, 44, 45

Section 11.2 Paths and Circuits #1, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 47a, 48a, 49

Section 11.4 Isomorphisms of Graphs #6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18

Section 11.5 Trees #3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23,
25, 27, 30

Section 11.6 Spanning Trees #1, 3, 4, 5, 6, 7, 8, 9, 11