Discrete_Structures_3362.pdf

Name and Number: Discrete Structures – Math 3362

Instructor: Ricardo Teixeira

Term: Spring 2, from Mar 21 to May 13

Office Phone: (361) 570.4206

Email: teixeirar@uhv.edu (preferred method of communication)

Course Description: Mappings, relations, recurrence, logic, Boolean algebras, graphs,

induction, proofs, languages, state machines, history of artificial intelligence, Turing test, and

applications of these areas.

Prerequisites: MATH 1324 or MATH 2413.

Required Material: Webassign access for “Essentials of Discrete

Mathematics 4th Edition” By David J. Hunter.

Optional Material: The textbook ISBN: 1284184765.

Webassign: You must have access to a computer and a fast internet

connection. You also must have the textbook (at least the e-book) and

access Webassign regularly. Computer or internet problems will not be

valid justifications for asking for extensions on assignments. Access it

via www.webassign.net.

Class key:

uhv 4029 0369

The Big Idea:

1. Understand discrete mathematics ideas. 2. Apply discrete mathematics ideas to algorithms and other areas.

Course Objectives:

1. Students will be able to use logical notation and perform logical proofs. 2. Students will define relational thinking ideas such as graphs, sets, functions,

equivalences, and partial ordering.

3. Students will apply recursive functions and solve recurrence relations. 4. Students will apply basic and advanced principles of counting and calculate discrete

probabilities.

5. Students will describe useful standard library functions, create functions, declare parameters, and analyze algorithm complexity.

Course Map:

Module 1: Introduction to Course, and Intro to Logical Thinking (Chapter 1)

March 21 – March 26

MO1: Understand basic logic terminology

MO2: Describe truth tables

MO3: Describe proof sequences

Module 2: Logical Thinking (Chapter 1)

March 27 – April 2

MO1: Understand the duality of text and quantifiers in logic

MO2: Create and identify counterexamples

MO3: Choose and develop the most adequate method of proof in different cases

Module 3: Relational Thinking (Chapter 2)

April 3 – April 9

MO1: Understand graphs, sets and functions

MO2: Identify equivalence relations through graphs

MO3: Understand modular arithmetic

Module 4: Recursive Thinking (Chapter 3)

April 10 – April 16

MO1: Understand and model recurrence relations

MO2: Develop closed form solutions

MO3: Write recursive examples in geometry

MO4: Develop proofs through induction

MO5: Apply recursion to data structures

Module 5: Quantitative Thinking (Chapter 4)

April 17 – April 23

MO1: Define basic counting principles

MO2: Understand and distinguish permutations and combinations

MO3: Understand and apply the pigeonhole principle

MO4: Calculate expected value and conditional probability

MO5: Apply counting techniques to algorithms and codes

MO6: Compute Big-Oh of functions

Module 6: Analytical Thinking (Chapter 5)

April 24 – April 30

MO1: Understand pseudocodes

MO2: Develop traversal, greedy and divide-and-conquer algorithms

MO3: Approximate complexity on algorithms

MO4: Distinguish between verification and testing

MO5: Verify interactive algorithms

Module 7: Thinking through Applications (Chapter 6)

May 1 – May 7

MO1: Identify Mutations and calculate phylogenetic distance

MO2: Apply graph theory to social networks

MO3: Apply recursion to linguistics

MO4: Apply models to population models.

Assignments: It is essential that you study Mathematics several times in a week. The following

• Discussion Board (20%): on each module, students will participate in a discussion board involving one or more of the module’s concepts, and a reply to someone else’s

post in a way to show a deeper understanding of the content, or a possible application

of the concepts, if possible. Every week we will have one discussion board with a

minimum of two posts per student. They will be assigned through Blackboard

(elearning.uhv.edu).

• First post to be completed by Wednesday, • Second post to be completed by Friday.

• Homework assignments (30%): assignment will contain questions that cover basic knowledge, and also a deeper understanding of the content in theoretical or applied

situations. For each section from the book, we will have one assignment. These

assignments are not timed but will have deadlines. Due Saturdays. They will be on

Webassign (www.webassign.net).

• Midterm (25%): during week 4, this midterm will cover Modules 1 to 4. It will have around 50 questions, with questions taken from the same bank of questions as the

modules’ assignments. This test will be timed: 2 hours to complete it. Due Sunday

after Module 4. It will be on Webassign (www.webassign.net).

• Final exam (25%): Similar to midterm, it will be on week 8. It will not be cumulative. It will cover modules 5-7. It will be on Webassign (www.webassign.net).

There will be no make-up activities, unless there is an emergency, in which case a written

justification will be required. If you miss an activity, you will automatically receive zero.

Grade distribution: (the instructor reserves the right to modify these bounds only to benefit students, in other words, the “cutoff” for some letters may be slight less than what is described here).

A: 90 – 100 B: 80 – 89 C: 70 – 79 D: 60 – 69 F: below 60

Curves on Grades: The instructor will not make any curves on grades.

Blackboard use: We will use Blackboard and the Webassign system.

Announcements, syllabus, calendars, and more will be available on

Blackboard: https://elearning.uhv.edu

Important: Computer Science and Math majors must receive a grade of C or higher in all

Computer Science and Math courses used as prerequisite or transferred from other institutions.

Any such course in which a student received a D, F, or W must be repeated.

Netiquette: Use the following rule of thumb “if you wouldn’t do or say something in real life,

don’t do it online either.

2. Stay on topic, don’t post irrelevant links, comments, thoughts, or pictures. 3. Don’t type in ALL CAPS! If you do, it will look like you’re screaming. 4. Don’t write anything that sounds angry or sarcastic, even as a joke, because without

hearing your tone of voice, your peers might not realize you’re joking.

5. Always remember to say “Please” and “Thank you” when soliciting help from your classmates.

6. Respect the opinions of your classmates. If you feel the need to disagree, do so respectfully and acknowledge the valid points in your classmate’s argument.

Acknowledge that others are entitled to have their own perspective on the issue.

7. If you reply to a question from a classmate, make sure your answer is accurate! If you’re not 100% sure when the paper is due, DO NOT GUESS! Otherwise, you could

really mess things up for your classmates and they will not appreciate it.

8. If you ask a question and many people respond, summarize all answers and post that summary to benefit your whole class.

9. Be brief. If you write a long dissertation in response to a simple question, it’s unlikely that anyone will spend the time to read through it all.

10. Check the most recent comments before you reply to an older comment, since the issue might have already been resolved or opinions may have changed.

11. Run a spelling and grammar check before posting anything to the discussion board. It only takes a minute and can make the difference between sounding like a fool and

sounding knowledgeable.

STANDARD UHV COURSE POLICIES:

Academic Integrity: “Students. . . have a responsibility to fulfill, and indeed an investment to protect, in helping to

ensure that academic achievement is characterized by honesty and fair play” (UHV Student Handbook). The

University takes academic integrity very seriously. It is your responsibility to understand what behavior violates

academic honesty rules and to understand the consequences for such violations. Please refer to the UHV Student

Plagiarism: Plagiarism is an increasingly common form of academic misconduct. All of the following are

considered plagiarism:

• turning in someone else's work as your own

• copying words or ideas from someone else without giving credit

• failing to put a quotation in quotation marks

• giving incorrect information about the source of a quotation

• changing words but copying the sentence structure of a source without giving credit

• copying so many words or ideas from a source that it makes up the majority of your work, whether

you give credit or not.

Most cases of plagiarism can be avoided, however, by citing sources. Simply acknowledging that certain material

has been borrowed and providing your audience with the information necessary to find that source, is usually

enough to prevent plagiarism.

Services for Students with Disabilities: The University of Houston System complies with Section 504 of the

Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of

reasonable academic adjustments / auxiliary aids for students who have a disability. In accordance with Section 504

auxiliary aids to students who request and require them. If you believe that you have a disability requiring an

A; Office – 361-570-4287; Fax – 361-580-5504; Email - Disability Services (DisabilityServices@uhv.edu);

Website - Disability Services (www.uhv.edu/disability-services).

Student Services: The Academic Center offers writing assistance, subject-area tutoring, testing services, and

information resources. For additional information: call 361-570-4288 or Toll Free: 1-877-970-4848, ext. 288; or

visit their website: http://www.uhv.edu/ac.

UHV Student Handbook for additional information: http://www.uhv.edu/HandBook/

Title IX: Sexual Misconduct: The University of Houston System including UHV seeks to provide an educational

environment free from sex discrimination, including non-consensual sexual contact, sexual assault, sexual

harassment, interpersonal violence and stalking. We encourage you to report any sexual misconduct to UHV Title IX

Coordinators (361-570-4835; University West 116). If you report any sexual misconduct to me, I am required to

policy and counseling and support resources available to you, go to http://www.uhv.edu/title-ix

Student Conduct: Students are expected to participate in a mutually respectful learning environment. If your

behavior is disruptive, I will remove you from class and you will be referred to the Office of Student Affairs and/or

the Academic Dean. Disruptive behavior is defined by the Student Code of Conduct as:

“3.6 Disruptive Classroom Conduct – Disruptive classroom conduct means engaging in behavior that

substantially or repeatedly interrupts either the instructor’s ability to teach or student learning. The

classroom extends to any setting where a student is engaged in work toward academic credit or satisfaction

of program-based requirements or related activities.” (https://www.uhv.edu/handbook/code-of-conduct/)

Check List for the first week:

1. Register on Webassign and buy the access code (there is a small grace period before payment is due, so register ASAP):

a. Go to www.webassign.net b. Click on “I HAVE A CLASS KEY” (right of the page)

i. There will be three boxes, on the first box, enter uhv ii. On the second box, enter 4029 iii. On the third box, enter 0369

2. Get familiar with the rules on this syllabus. 3. Get familiar with Webassign. Learn how to access the textbook.

https://webassign.com/support/student-support/ 4. Optional: mark the important dates on a calendar app on your phone 5. Optional: browse the course content and review math you do not feel comfortable.

Typical week in the course:

1. Beginning of the week: a. Watch videos b. Read the textbook

2. By Wednesday 11:59pm: write the first post on Blackboard discussion Board (https://elearning.uhv.edu)

3. By Friday 11:59pm: reply to someone else’s post with a meaningful contribution to the topic. 4. By Saturday 11:59pm: Homework assignments from the modules are due (there are some different

homework assignments per module): www.webassign.net

Exams:

1. Midterm: due Sunday 11:59pm after Module 4, covering Modules 1-4 on www.webassign.net 2. Final exam: due Sunday on week 8 at 11:59pm, covering Modules 5-7 on www.webassign.net