# Summer 22 Discrete Math

Math 2345 Discrete Math Summer 2022

Sarah Holliday

Office: https://us02web.zoom.us/j/84100142478?pwd=STJ5ZHpFSjlZY0JrRFo3MlN3V1NVUT09

E-mail: shollid4@kennesaw.edu

Office Hours: By appointment on zoom

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 four in-class tests, and a final

Tests will be valued at 15% each, quizzes/homework will total to 20%, and the final will be valued at 20%.
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

Dates:
First day of classes 6/1/22
Holiday 6/20/22
First Test Due by 6/12/22
Second Test Due by 6/25/22
Last day to withdraw 6/29/22
Third Test Due by 7/8/22
Fourth Test Due by 7/24/22
Last day of classes 7/27/22
Exams 7/28-8/1/22

Delivery

This is a fully online asynchronous class with all content delivered through D2L.  You may work ahead.  There are deadlines approximately every four days (to keep us all on track).

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.

"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."

Withdrawal

Students who officially withdraw from this course before Wednesday June 29 at 11:45pm will receive a grade of "W" and receive no credit. Students who withdraw after the Wednesday June 29 deadline and before the last week of classes, or who have exceeded the maximum number of withdrawals, will receive a grade of "WF," which will be counted as an "F" in the calculation of their grade point average.

The only exceptions to these withdrawal regulations will be for instances involving unusual circumstances, which must be fully documented. 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. 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.

Science and Math Academic Resource and Tutoring (SMART) Center at KSU:
In the SMART Center you will find people and resources to help with most general education Mathematics, Chemistry, and Physics courses along with select Engineering classes offered at KSU. No appointments are necessary to use the SMART Center’s services, stop by any time they are open for help in your classes. For more information about hours and tutor schedule see: https://uc.kennesaw.edu/academicinitiatives/smart/index.php

Diversity statement:
Kennesaw State University prides itself on offering a premiere, personalized educational experience for leadership and engagement within a diverse nation and world. This educational experience is achieved through recognition and appreciation of the differing backgrounds and experiences reflected within the University community. It is my intent that students from all diverse backgrounds and perspectives be well served by this course, that students’ learning needs be addressed both in and out of class, and that the diversity that students bring to this class be viewed as a resource, strength and benefit.

Course Delivery
KSU may shift the method of course delivery at any time during the semester in compliance with University System of Georgia health and safety guidelines. In this case, alternate teaching modalities that may be adopted include hyflex, hybrid, synchronous online, or asynchronous online instruction.

COVID-19 illness
If you are feeling ill, please stay home and contact your health professional. In addition, please email your instructor to say you are missing class due to illness. Signs of COVID-19 illness include, but are not limited to, the following:

· Cough

· Fever of 100.4 or higher

· Runny nose or new sinus congestion

· Shortness of breath or difficulty breathing

· Chills

· Sore Throat

· New loss of taste and/or smell

COVID-19 vaccines are a critical tool in “Protecting the Nest.” If you have not already, you are strongly encouraged to get vaccinated immediately to advance the health and safety of our campus community. As an enrolled KSU student, you are eligible to receive the vaccine on campus. Please call (470) 578-6644 to schedule your vaccination appointment or you may walk into one of our student health clinics.

For more information regarding COVID-19 (including testing, vaccines, extended illness procedures and accommodations), see KSU’s official Covid-19 website.

Face Coverings
Based on guidance from the University System of Georgia (USG), all vaccinated and unvaccinated individuals are encouraged to wear a face covering while inside campus facilities. Unvaccinated individuals are also strongly encouraged to continue to socially distance while inside campus facilities, when possible.

Practice homework (3rd edition here, 4th edition & 5th available):
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, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 22, 25, 28, 31
Section 4.3 Mathematical Induction II #2, 4, 9, 11, 12, 16, 17, 19, 20, 22, 29
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, 17
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, 16, 18, 20, 22, 24, 25, 27, 28, 30, 47, 48, 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