CS 215 Discrete Structure Syllabus

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.

CS 215 – Discrete Structure Syllabus

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Instructor: Dr. Gongjun Yan

Office: BE 2046 Telephone: 812-228-5073 email: [email protected]

Web site: http://collabra.usi.edu/~teaching/discretemath/ (right now only classroom access, IT people are working on the public access or wireless access.)

Meeting Hours: 1:30-2:45pm BE1034.

CS 215.-002 11845 Class 1:30 pm-2:45 pm BE 1034

Office hours: 1) Monday 9:00-12:00 2) Wednesday 9:00-11:00. 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

Course Objectives:

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.

The main objectives of this course are

1. to explain basic mathematical concepts such as sets, relations, functions, and graphs, relationships between them, and their properties, 2. to reason correctly, 3. to show techniques for solving problems, 4. to cultivate the ability to extrapolate, and 5. to become proficient in using mathematical notations (both in reading and writing).

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

http://collabra.usi.edu/~teaching/discretemath/


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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.

Course Contents:

The course will cover at least the following sections from Rosen

1.1-1.5, 2.1-2.3, 3.1, 3.4, 3.5, 5.1-5.3, 9.1, 9.3, 10.1-10.5

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 covered in Chapter 1 of the textbook. 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.

In Chapter 2, 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.

In Chapter 5, 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.

Then in Chapters 9 we study relations. 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 can be found in Chapter 10.

Finally, back in Chapter 2 again, 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 Chapter 3.

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


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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%

Random Quiz 10%

Assignments 25%

Exam 1 30%

Exam 2 30%

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

97-100 A+

93-96 A

90-92 A-

87-89 B+

83-86 B

80-82 B-

77-79 C+

73-76 C

70-72 C-

67-69 D+


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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.

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). Quizzes taken late will have extra requirements to adjust

for the student having had additional preparation time.

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.


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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 attend class and to arrive on time. Your grade may be affected if you are

consistently tardy. If you have to miss a class, you are responsible checking the course website to

find any assignments or notes you may have missed. Students may leave after 15 minutes if the

instructor or a guest lecturer does not arrive in that time.

Exams There are two in-class 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.

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

Class Participation


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

assignment submission (20%); 3) class discussion (20%); 4) discussion offline by

email or other ways (10%).

Quiz:

Quiz is given randomly. The purposes of quiz include two: 1) attend class; 2) review

the content. If you miss a quiz, there will be no make-up for quiz.

Email

Students should activate their IU Kokomo 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

Please be respectful of your classmates and instructor by minimizing distractions during class.

Cell phones must be turned off during class. Disruptive classroom behavior will not be tolerated.

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.

Cell phones, electronic devices, and calculators.

Please turn off or silence your cell phone during class. The use of cell phones, ipods, MP3

players, or any other electronic devices will be strictly forbidden during the exams and during

lectures. Only non-programmable calculators will be authorized during exams.

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

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.

http://www.usi.edu/disabilities


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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

Task 1: Read the following: 1. Introduction to Discrete Structures 2. Problem Solving Framework 3. Problem Solving Example 1

Unit 2


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Task 1: Read the following: 1. Problem Solving Examples

Unit 3

Task 1: Read the following: 1. Introduction to Logic 2. What is Proposition 3. Elements of Propositional Logic 4. Truth Table 5. Connectives 6. Construction of Proposition 7. Converse and Contrapositive

These materials can also be found in Textbook 1.1 - 1.2.

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

Unit 4

Task 1: Read the following: 1. Variations of if_then 2. From English to Proposition



Unit 5

Task 1: Read the following: 1. Introduction to Reasoning 2. Identities of Propositions and Dual 3. Example of Use of Identities



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Unit 6

Task 1: Read the following: 1. Implications 2. Reasoning with Propositions 3. Proof of Identities 4. Proof of Implications

These materials can also be found in Textbook 1.1 - 1.2 and pp. 56 - 61.


Unit 7

Task 1: Read the following: 1. Why Predicate Logic ? 2. Predicate 3. Quantification 4. Constructing Formulas (Wffs)

These materials can also be found in Textbook 1.3 and 1.4 .


Unit 8

Task 1: Read the following: 1. From Wff to Proposition 2. English to Logic Translation

These materials can also be found in Textbook 1.3 and 1.4.


Unit 9

Task 1: Read the following:


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1. Reasoning with Predicate Logic

These materials can also be found in Textbook 1.3, 1.4 and 1.5 .


Unit 10

Task 1: Read the following: 1. Quantifiers and Connectives

These materials can also be found in Textbook 1.3.


Unit 11

Task 1: Read the following: 1. Introduction to Sets 2. Representation of Set 3. Equality, Subset, etc.



Unit 12

Task 1: Read the following: 1. Mathematical Reasoning 2. Set Operations


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


Unit 13


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Task 1: Read the following: 1. Properties of Set Operation



TEST: Covers Unit 3 - Unit 12 inclusive.

Unit 14

Task 1: Read the following: 1. Recursive Definition 2. Generalized Set Operations



Unit 15

Task 1: Read the following: 1. Recursive Definition of Function 2. Recursive Algorithm



Unit 16

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




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Unit 17

Task 1: Read the following: 1. Example of Use of Induction 2. 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.


Unit 18

Task 1: Read the following: 1. Introduction to Relation 2. Binary Relation 3. Definition of Relation (general relation) 4. Equality of Relations 5. Recursive Definition of Relation



Unit 19

Task 1: Read the following: 1. Digraph 2. Digraph Representation of Binary Relation 3. Properties of Binary Relation

These materials can also be found in Textbook 7.3, 8.1 and 8.2.


Unit 20

Task 1: Read the following: 1. Operations on Binary Relations 2. Closures of Binary Relation



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Unit 21

Task 1: Read the following: 1. Equivalence Relation 2. Order Relation (Partial, Total, and Quasi Orders)



Unit 22

Task 1: Read the following: 1. Order Relation (Minimal Element and the rest)

These materials can also be found in Textbook 7.6 .


Unit 23

Task 1: Read the following: 1. Definitions on Function 2. Growth of Functions

These materials can also be found in Textbook 1.8, 2.2 and 2.3.


Unit 24

Task 1: Read the following: 1. Growth of Functions (Calculation of Big-Oh Relation)



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FINAL EXAM: Covers Unit 3 - Unit 24 inclusive.

Documents

CS 215 Discrete Structure Syllabus