CS 215 – Discrete Structure Syllabus An introduction to methods of analytical, abstract and critical thinking, deductive reasoning, and logical and mathematical tools used in information sciences. The topics include propositional and predicate logic, natural deduction proof system, sets, functions and relations, proof methods in mathematics, mathematical induction, and graph theory.

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CS 215 – Discrete Structure Syllabus

Instructor: Dr. Gongjun Yan

Office: BE 2046 Telephone: 812-228-5073 email: gyan@usi.edu

Web site: blackboard

Meeting Hours: Online Class.

Office hours: 1) Monday 9:00-1:00 2) Wednesday 9:00-1:00. You can also make an

appointment to meet with me. Please email me or call me for an appointment.

Text: Discrete Mathematics and its Applications 7th edition

By Kenneth H. Rosen

Knowledge Areas that contain topics and learning outcomes

covered in the course (per ACM CS Curricula 2013)

USI Course CS215

Description Core-Tier 1 Core-Tier 2 Elective

DS/SetsRelationsAndFunctions 4

DS/BasicLogic 9

DS/ProofTechniques 10 1

DS/BasicsOfCounting 5

DS/GraphsAndTrees 1

DS/DiscreteProbability 4 1

This course will develop advanced mathematics skills appropriate for students pursuing STEM studies such as Engineering, Science, Computer Science, and Mathematics. Topics include sets, numbers, algorithms, logic, computer arithmetic, applied modern algebra, combinations, recursion principles, graph theory, trees, discrete probability, and digraphs. This course earns 3 credit hours and consists of 3 lecture hours per week for 14 weeks. Discrete Mathematics offered at USI currently meets twice per week for 75 minutes each. Students are assessed on a combination of homework, quizzes/tests, group activities, discussion, projects, and a comprehensive final exam. Students are expected to complete homework assignments

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Course Objectives:

Upon successful completion of this course, students will be able to: • Demonstrate critical thinking, analytical reasoning, and problem solving skills • Apply appropriate mathematical and statistical concepts and operations to interpret data and to solve problems • Identify a problem and analyze it in terms of its significant parts and the information needed to solve it • Formulate and evaluate possible solutions to problems, and select and defend the chosen solutions • Construct graphs and charts, interpret them, and draw appropriate conclusions

You have taken math courses before and you know that they are cumulative, that is the material

covered in a chapter tends to be applied to material covered in the following chapters. Therefore, you

must keep up with the assignments. Practice problems will be assigned for each class. It is important to

do these assignments in order to understand the material. The effort that you expend on the

assignments will ultimately be reflected in your exam scores. Mathematics is not a spectator sport.

You must do the work in order to learn the material. You cannot learn by merely watching.

Although attendance will not be taken, the student is responsible for all material presented in class.

This course supports the expected characteristics, capabilities and skills for computer science graduates

of the USI Computer Science program of study in the following ways:

Mastery of Computer Science technical foundations

Recognition of common Computer Science themes and Principles

Recognition of interplay between theory and practice

Effective problem solving and critical thinking skills

Commitment to life-long learning, and professional and ethical responsibility

Correlation of Program Objectives, Student Learning

Outcomes, and Assessment Methods

Program

Objectives

Student Learning Outcomes Assessment

Methods Demonstrate critical

thinking, analytical

reasoning, and

problem solving

skills

Recognize, identify, and solve problems using set

theory, elementary number theory, and discrete

probability Recognize, identify, and apply the

concepts of functions and relations and graph

theory in problem solving Apply proof

techniques in logic

Written: Homework

assignments, examinations

in class, and projects to be

completed at home

Verbal: Classroom exercises

and discussion

Apply appropriate

mathematical and

Recognize, identify, and solve problems using set

theory, elementary number theory, and discrete

Written: Homework

assignments, examinations

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statistical concepts

and operations to

interpret data and to

solve problems

probability Recognize, identify, and apply the

concepts of functions and relations and graph

theory in problem solving

in class, and projects to be

completed at home

Verbal: Classroom exercises

and discussion

Identify a problem

and analyze it in

terms of its

significant parts and

the information

needed to solve it

Recognize, identify, and solve problems using set

theory, elementary number theory, and discrete

probability Recognize, identify, and apply the

concepts of functions and relations and graph

theory in problem solving Apply proof

techniques in logic

Written: Homework

assignments, examinations in

class, and projects to be

completed at home

Verbal: Classroom exercises

and discussion

Formulate and

evaluate possible

solutions to

problems, and select

and defend the

chosen solutions

Recognize, identify, and solve problems using set

theory , elementary number theory, and discrete

probability Recognize, identify, and apply the

concepts of functions and relations and graph

theory in problem solving Apply proof

techniques in logic

Written: Homework

assignments, examinations in

class, and projects to be

completed at home

Verbal: Classroom exercises

and discussion

Construct graphs and

charts, interpret

them, and draw

appropriate

conclusions

Recognize, identify, and apply the concepts of

functions and relations and graph theory in

problem solving

Written: Homework

assignments, examinations in

class, and projects to be

completed at home

Verbal: Classroom exercises

and discussion

Course Contents:

The course will cover at least the following sections from Rosen

1.1-1.8, 2.1-2.4, 3.2, 4.1-4.4, 5.1-5.3, 6.1-6.3, 7.1, 8.1, 8.5 9.1, 9.3, 9.5, 10.1, 10.4, 11.1

First we learn a general methodology for solving problems. This methodology is going to be

followed in solving problems, and in proving theorems throughout this course.

The next subject is logic. It is a language that captures the essence of our reasoning, and correct

reasoning must follow the rules of this language. We start with logic of sentences called

propositional logic, and study elements of logic, (logical) relationships between propositions, and

reasoning. Then we learn a little more powerful logic called predicate logic. It allows us to

reason with statements involving variables among others.

We also study sets, relations between sets, and operations on sets. Just about everything is

described based on sets, when rigor is required. It is the basis of every theory in computer

science and mathematics.

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We learn recursive definitions and mathematical reasoning, in particular induction. There are

sets, operations and functions that can be defined precisely by recursive definitions. Properties of

those recursively defined objects can be established rigorously using proof by induction.

We study relations as well. They are one of the key concepts in the discussion of many subjects

on computer and computation. For example, a database is viewed as a set of relations and

database query languages are constructed based on operations on relations and sets. Graphs are

also covered briefly here. They are an example of discrete structures and they are one of the most

useful models for computer scientists and engineers in solving problems. More in-depth

coverage of graph and tree can be found in the class as well.

We will cover the discrete probability in the class. It is fundamental concepts for future classes.

Finally, we briefly study functions. They are a special type of relation and basically the same

kind of concept as the ones we see in calculus. However, it is one of the most important concepts

in the discussion of many subjects on computer and computation such as data structures,

database, formal languages and automata, and analysis of algorithms which is briefly covered in

class.

Right to change information Although every effort has been made to be complete and accurate, unforeseen circumstances

arising during the semester could require the adjustment of any material given here.

Consequently, given due notice to students, the instructor reserves the right to change any

information on this syllabus or in other course materials.

Grading

The course grade will contain the following components:

(Note that these percentages are only approximate and are subject to change, but by no more than

10%.)

Class Participation 5%

Assignments 50%

Exam 1 15%

Exam 2 15%

Exam 3 15%

The grading scale is as follows (+ and - modifiers will be applied as appropriate):

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90-100 A

87-89 B+

83-86 B

80-82 B-

77-79 C+

73-76 C

70-72 C-

67-69 D+

63-66 D

60-62 D-

0-59 F

Late Submissions

Any assignment submitted after its deadline is considered late. Assignments that are submitted

within 24 hours after the original deadline are considered to be "one day late," within 48 hours

"two days late," etc. Weekends count just like weekdays in determining the number of days late.

Five percent (5%) of the assignment's total value will be deducted for each day an assignment is

late. Assignments will not be accepted after they are more than 3 days late. I reserve the right to

specify that late submissions will not be accepted for any assignment.

Turned in less than

or equal to... Penalty

24 hours (1 day) late - 5%

48 hours (2 days) late - 10%

72 hours (3 days) late - 15%

etc. etc.

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Course Policies and Responsibilities

The time to ask questions is during class. Please participate actively. You are responsible for

knowing and following University regulations. This includes such areas as withdrawals,

incompletes, pass/fail options, and ethics. Start early in case the unforeseen happens near grading

dates (disk failure, working overtime, or whatever). Make backup copies as needed.

Exams will cover the material in the text (mostly) and lectures (some questions not in the

readings). Graded items missed for a valid reason are handled by taking a makeup. Makeup

exams will use your individual score to calculate both individual and team components of the

exam value (9% & 6% respectively).

Learning computing skills is supported by in-class small group activities, but you will likely

need to devote additional time towards building proficiencies prior to being graded on individual

skills. This is your homework assignment, after readings are done.

Academic Integrity

Please refer to the statement on academic integrity of the university. Cheating is ZERO tolerance. Any evidence of cheating will result in a 0 grade for the assignment/exam, and the incident will be submitted to the department for further review.

Attendance

I expect you to arrange your own study time and schedule. We don’t have attendance

requirement.

Exams There are three online exams. The format of the exams may include any combination of multiple

choice, short answer, essay, and problem solving questions. Exams will include materials from

the textbook, reading assignments, handouts and classroom discussion.

There is No Make-up exam for this class. In extreme cases, students might be permitted to

replace the grade for the missed exam by overall course grade. However, in these extreme cases,

students should receive PRIOR permission to be absent during the regular exam period. Such

permission will be granted only if the student demonstrates a strong need. Any uncoordinated

absence from an exam will result in a score of 0 for the exam.

Students are responsible for preparing the exams and exam material.

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Assignments Homework will be turned in based on due time. Homework is due at the beginning of class (or

discussion section) the day it is due. At the beginning means before or within the first 10 minutes

of class. If you are later than 10 minutes to class without an excused absence (as

described below) your homework will not be accepted. Late penalty for homework is 10% each

day.

There are more than TEN assignments. I only include the highest scores of TEN assignments

in the final grades.

You must work alone on your homework, and homework must be written legibly, single-sided

on your own lined paper, or typed, with the answers clearly labeled and in the sequential order as

assigned. You must write your name and university ID number in the upper right-hand corner of

your homework. Scan all pages together and be sure that your name appears on every sheet.

Class Participation

The grading for the class participation includes: 1) class activity completion (50%); 2)

assignment submission (20%); 3) discussion to instructor or through forum (20%); 4)

discussion offline by email or other ways (10%).

Email

Students should activate their USI e-mail accounts and check them every day. If a student

chooses to have his/her messages forwarded to another account, it is the student's responsibility

to take the necessary steps to have them forwarded.

Classroom Conduct

Disruptive behavior will not be tolerated for any online activities and content. This includes

unnecessary chatting, text messaging, the use of a cell phone during lecture/exams, etc. Be

respectful of the learning environment.

Make-up Work

Make-ups for graded activities are possible only with a valid written medical or university

excuse. It is the student's responsibility to give the instructor the written excuse and to arrange

for any makeup work to be done.

Disability Services

If you have a disability for which you may require academic accommodations for this class,

please register with the Office of Disability Resources (ODR) as soon as possible. Students who

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have or who receive an accommodation letter from ODR are encouraged to meet privately with

me to discuss the provisions of those accommodations as early in the semester as possible. To

qualify for accommodation assistance, students must first register to use the disability resources

in ODR, Orr Center Rm. 095, 812/464-1961 http://www.usi.edu/disabilities. To help ensure that

accommodations will be available when needed, students are encouraged to meet with course

faculty at least 7 days prior to the actual need for the accommodation.

Seeking Help

The course website should be your first reference for questions about the class. The schedule will

be updated throughout the semester with links to assigned readings. Announcements and

frequently asked questions (FAQ) will also be posted to the course website.

The best way to get help is to come to office hours. If you cannot make office hours, please send

an email to setup an appointment. I am available via email, but do not expect or rely on an

immediate response.

Some keys to success.

Work hard: Foremost, students are urged to work hard! This class covers a lot of material in a short amount

of time – do not let yourself get behind. Work hard and keep up the pace! In designing this class,

efforts have been made to assist students in their learning by frequently allowing them to

exercise what they learn and quickly receive feedback. The class is designed so that if you work

hard and keep up on things you can succeed.

As a corollary to working hard, please feel free to ask the instructor questions, but please ponder,

read and reflect on your own before doing so.

Ask Questions and do exercises: It is students' responsibility to make sure (ask questions and do exercises) if they do not

understand all the lectures and materials. I will repeat and try as much as I can to help you

understand. It is not acceptable that students state that they do not understand the lecture or

material at the end of semester.

Attend class

Do homework independently

Read textbook

Do exercises

Study Units

Unit 1

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Task 1: Read the following: Introduction to Discrete Structures Problem Solving Framework Problem Solving Example 1

Unit 2

Task 1: Read the following: Introduction to Logic What is Proposition Elements of Propositional Logic Truth Table Connectives Construction of Proposition Converse and Contrapositive

These materials can also be found in Textbook 1.1 - 1.3.

Task 2: Do the textbook exercises.

These exercises are NOT homework questions.

They are for helping you understand the materials of this unit.

Unit 3

Task 1: Read the following: Implications English to Logic Translation From Wff to Proposition Variations of if_then From English to Proposition

These materials can also be found in Textbook 1.1 - 1.3.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 4

Task 1: Read the following:

Introduction to Reasoning Identities of Propositions and Dual Example of Use of Identities

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Reasoning with Propositions Proof of Identities Proof of Implications

These materials can also be found in Textbook 1.1 - 1.3 and 1.7.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 5

Task 1: Read the following: Why Predicate Logic ? Predicate Quantification Constructing Formulas (Wffs)

These materials can also be found in Textbook 1.4 - 1.6 .

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 6

Task 1: Read the following: Reasoning with Predicate Logic

These materials can also be found in Textbook 1.4 - 1.8.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 7

Task 1: Read the following: Quantifiers and Connectives

These materials can also be found in Textbook 1.4 - 1.6.

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Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 8

Task 1: Read the following: Introduction to Sets Representation of Set Equality, Subset, etc.

These materials can also be found in Textbook 2.1-2.2.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 9

Task 1: Read the following: Mathematical Reasoning Set Operations Properties of Set Operation

These materials can also be found in Textbook 1.8 and 2.2, 2.4, 2.6.

You must, however, read the Web pages for Mathematical Reasoning(see above).

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

TEST1 : Covers Unit 3 - Unit 9 inclusive.

Unit 10

Task 1: Read the following: Recursive Definition Generalized Set Operations

These materials can also be found in Textbook 5.1-5.3.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

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Unit 11

Task 1: Read the following: Recursive Definition of Function Recursive Algorithm

These materials can also be found in Textbook 5.1-5.3.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 12

Task 1: Read the following: First Principle of Mathematical Induction

These materials can also be found in Textbook 5.1-5.3.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 13

Task 1: Read the following: Example of Use of Induction Second Principle of Mathematical Induction

Task 2: Do the textbook exercises.

These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

These materials can also be found in Textbook 5.1-5.3.

Task 3: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 14

Task 1: Read the following:

1. Introduction to Relation

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2. Binary Relation 3. Definition of Relation (general relation) 4. Equality of Relations 5. Recursive Definition of Relation 6. Operations on Binary Relations

These materials can also be found in Textbook 9.1, 9.3, 9.5.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 15

Task 1: Read the following:

1. Equivalence Relation 2. Order Relation (Partial, Total, and Quasi Orders)

These materials can also be found in Textbook 9.3, 9.5.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Task 3: Read the following: Order Relation (Minimal Element and the rest)

These materials can also be found in Textbook 7.6 .

Unit 16

Task 1: Read the following: Definitions on Function Growth of Functions

These materials can also be found in Textbook 1.8, 2.3 and 3.2.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Task 3: Read the following: Growth of Functions (Calculation of Big-Oh Relation)

These materials can also be found in Textbook 3.2.

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Task 4: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 17

Task 1: Read the following: Basics of counting The pigeonhole Principle

These materials can also be found in Textbook 6.1 and 6.2.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

TEST2 : Covers Unit 10 – Unit 17 inclusive.

Unit 18

Task 1: Read the following: Permutation and combination

These materials can also be found in Textbook 6.3.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 19

Task 1: Read the following: Application of Recurrence relations

These materials can also be found in Textbook 8.1.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

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Unit 20

Task 1: Read the following: Inclusion-exclusion

These materials can also be found in Textbook 8.5.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 21

Task 1: Read the following: Definitions on Probability Finite probability Union of probability

These materials can also be found in Textbook 7.1-.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 22

Task 1: Read the following: Probability Theory Finite probability

These materials can also be found in Textbook 7.2.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 23

Task 1: Read the following: Bayes’ Theorem Applications of Bayes’ Theorem Expected value and variance

These materials can also be found in Textbook 7.3 and 7.4.

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Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 24

Task 1: Read the following: Expected value and variance

These materials can also be found in Textbook 7.3 and 7.4.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Unit 25

Task 1: Read the following: Tree, Graph and weighted graph

These materials can also be found in Textbook 10.1, 10.4 and 11.1.

Task 2: Do the textbook exercises. These exercises are NOT homework questions. They are for helping you understand the materials of this unit.

Task 3: Review for final exam.

FINAL EXAM: Covers Unit 18 - Unit 25 inclusive.