# Discrete Structures

**Course Code:**MATU 251

**Credits:**4 semester credits

**Through UMass Global**

Enroll Now (Credit)

View the Noncredit Option

**Credit Information**

Course Title: | Discrete Structures |

Course Code: | MATU 251 |

Credits: | 4 Semester Credits |

Credit Provider: | UMass Global |

Transfer: | 4-year degree applicable |

Grading Mode: | Standard letter grade |

**Course Requirements**

Enrollment Type: | Rolling | Sign up and start any day of the year. |

Requires Textbook? | No | All of the course materials are online. |

Proctored Final: | Yes | The credit version of this course has a proctored final. |

**Course Description**

This course was designed for students in math and computer science. Logic is emphasized in this course, and topics include proof and theory (including inductive and deductive proofs), propositional and predicate logic, set theory, algorithms (including recursion), trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs (including Dijkstra's shortest path algorithm). Additionally, an introduction to complexity of algorithms and recurrence relations are included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.

Discrete Structures is an Omega Math

^{TM}Course.

**Prerequisite:**College Algebra or Precalculus with a grade of C or better.

**Course Pricing**

The full cost of the course is $728.00; however, you may use the payment plan to split the cost into two payments.

**Payment Plan:**

1st payment: $403.90 (Start your class immediately!)

2nd payment: $331.10 (Automatically charged 30 days later.)

Enroll Now - Credit - $728 View Noncredit Option - $509

**Helpful Links:**

Math Placement Test

View a free Omega Math Demo Lesson

See the Transcript & Preapproval tab for more details on this topic.

**Enrollment Information**

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able, with a minimum coursework time of at least four weeks. Most students finish the lower level courses in four weeks to three months. The upper level math courses, such as calculus and above, usually take students 2 - 4 months.

Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.

**Textbook Requirement:**

No outside textbook is needed. Our Omega Math

^{TM}courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.

**Proctored Final Requirement:**

This course requires a proctored final. Your college is accepting this course because it goes through a regionally accredited university, which tells them the class will have a proctored final, and the 60% rule will apply (50% for science courses). Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met. Before the registrar at a college accepts a transcript, many of them call and ask to us verify that their student has indeed taken a proctored final at an approved testing location. The 60% rule(50% for science courses) requires that a student get at least 60% (50% for science courses) on the final in order to pass the class with a C or better. Note: 60% is right between an F and a D, so it is a fair requirement.

Notice: While the testing centers are closed due to COVID-19, we have an online proctor service that students can use if they have a computer and a web camera. This can be a laptop with a built in camera or a desktop with a web cam.

The final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near you: Find a Testing Center

**Student's Requirements:**

You must have internet access.

You must have access to email.

Omega Math

^{TM}Courses - you must be at or above a 7th grade reading level. Other courses require at least a 10th grade reading level.

**Payment Plan:**

The cost of each class can be divided into two payments by checking the payment plan box when you enroll. The first payment is 55% of the total amount, and the second payment is 45% of the total amount. Your first payment will be charged when you enroll, and the second payment will be charged in 30 days. Your course is activated once your first payment is made. There is a $3.50 additional fee for the credit card split for each of the two payments.

If paying by check, you can either send in a check for the two payments 30 days apart. Or you may send in both checks at the same time, with one post dated by 30 days for the 2nd payment. Just click on "Check by Mail" under Payment Information when you enroll. The form at the end of your enrollment will give you the address for mailing the checks.

**Transcript:**

Westcott Courses/Omega Math is the teacher of the course, and our exclusive partner university is UMass Global. UMass Global is regionally accredited by WASC, and awards the semester credits and transcript for the individual classes. Once you are finished with the course, we will post your grade with UMass Global and give you the instructions on how to order the transcript from UMass Global's records office. Since Westcott Courses is the teacher, we do not appear on the transcript. The official transcript from UMass Global will show our course the same way it would show a traditional class taken on their campus. See Transferring the Credit for more information.

Taking a course through this program does not require being enrolled in the university as a regular student; anyone can receive the credits for these classes. Any student has the opportunity to earn university credits through UMass Global, part of the Chapman University System!

**Transfer Information:**4-year degree applicable

Your college will require any class you wish to transfer to them to be from a regionally accredited college that awards academic semester or quarter credits. They will also want the course description of the course to match their own. UMass Global is regionally accredited and issues academic semester credits. Our course description will match or exceed your college's description; thus, your college will most likely accept the course and apply it towards your degree. If you would like preapproval from your school, please send your counselor or registrar's office the link at the bottom of this page.Your college may be one of the many schools that we are associated with, so check the Associated School link before asking for preapproval. Students are responsible for verifying that courses taken via Westcott/UMass Global satisfy program requirements at their home institution. Additionally, the acceptance of any transfer credit is the decision of the accepting (home) institution.

(K-12 use)

**Preapproval from your College:**

If you would like to make sure your college will accept this course from UMass Global, you can ask your school for preapproval. Send the following email to your counselor or registrar's office:

Dear counselor,

I would like to request preapproval to take MATU 251 - Discrete Structures through UMass Global. UMass Global is regionally accredited by WASC.

You will find the course description for this course, as well as other pertinent information on UMass Global's web site at this URL: https://www.umassglobal.edu/westcott

Note: Your college may be one of the many schools that we are already have agreements with, so check the Associated School page before asking for preapproval. If your school is listed, it will let you know that they accept the course through UMass Global. If your school is not on this list, it just means they have not contacted us to establish an articulation agreement. Students are responsible for verifying that courses taken via Westcott/UMass Global satisfy program requirements at their home institution. Additionally, the acceptance of any transfer credit is the decision of the accepting (home) institution.

## Course Information

Course Title: | Discrete Structures |

Course Code: | MATU 251 |

Credits: | 4 credits |

Credit Provider: | UMass Global |

Grading Mode: | Standard letter grade |

Proctored Final: | Yes |

**Textbook Requirement:**

No outside textbook is needed. Our Omega Math

^{TM}courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.

## Course Description

This course was designed for students in math and computer science. Logic is emphasized in this course, and topics include proof and theory (including inductive and deductive proofs), propositional and predicate logic, set theory, algorithms (including recursion), trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs (including Dijkstra's shortest path algorithm). Additionally, an introduction to complexity of algorithms and recurrence relations are included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.Discrete Structures is an Omega Math

^{TM}Course.

**Prerequisite:**College Algebra or Precalculus with a grade of C or better.

## Learning Outcomes

Upon successful completion of Discrete Structures, a student should be able to:- Effectively express themselves in a precise written form.
- Demonstrate the ability to think critically and logically.
- Students should be able to distinguish between a definition and a theorem, and apply them correctly.
- Read, comprehend and construct mathematical arguments.
- Construct standard proofs, using direct, contradiction, contrapositive, if and only if and inductive arguments.
- Demonstrate the ability to integrate knowledge and ideas in a coherent and meaningful manner.
- Represent discrete objects using the abstract mathematical structures such as sets, permutations, relations, functions, trees and graphs.
- Demonstrate appropriate techniques for specific problems in graph theory, and be able to develop and apply algorithms to solve these problems.
- Demonstrate competencies, and thought processes in the fundamental concepts of graph theory, set theory, and combinatorics, at a level necessary for more advanced mathematics courses.
- Demonstrate real-world problem solving skills. Analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

## Methods Of Evaluation

Homework quizzes 15%Chapter tests 60%

Final Exam 25%

(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.#### Proctored Final: 25%

This course goes towards a 4-year degree; thus, it requires a proctored final.Students are responsible for proctoring fees.

We have an approved online proctor service that students can use if they have a web camera with their computer. This can be a laptop with a built in camera or a desktop with a web cam. This service charges $60 for group sessions and double for private sessions. A student can also be proctored at college testing center, Sylvan Learning Center, Prometric Testing center, or Pearson Vue Testing Center. No other options are available.

A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final

The final exam is a comprehensive final covering all of the chapters of the course. Other than scratch paper, you may view the "Authorized Materials" list for the final exam for each class.

^{*}Students must obtain a 60% or better on the final exam in order to get a C or better in the class.

The 60% rule was set in place to protect the integrity of online education by requiring a display of competency in exchange for a grade. All schools which are regionally accredited adhere to online standards. Your college is accepting this course because it goes through a regionally accredited university, which tells your college that standards have been met. Your college will not accept a class from a school that is not regionally accredited, because they know the standards won't be met.

## Assessment

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.

C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.

D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.

F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

## Course Content Menu

Chapter 1 - Logic |

Lessons | Homework | Quiz |

1.1 - Nonlinear Inequalities | 1.1 | 1.1 |

1.2 - Truth Tables & Propositions | 1.2 | 1.2 |

1.3 - Logic Operators | 1.3 | 1.3 |

1.4 - Quantifiers | 1.4 | 1.4 |

1.5 - Nested Quantifiers | 1.5 | 1.5 |

Chapter 2 - Formal Proofs |

Lessons | Homework | Quiz |

2.1 - Truth Tables Proofs | 2.1 | 2.1 |

2.2 - Direct Proof | 2.2 | 2.2 |

2.3 - Proof by Contradiction | 2.3 | 2.3 |

2.4 - Proof by Contrapositive | 2.4 | 2.4 |

2.5 - If and only if Proof | 2.5 | 2.5 |

2.6 - Mathematical Induction | 2.6 | 2.6 |

Chapter 3 - Sets and Relations |

Lessons | Homework | Quiz |

3.1 - Introduction to Sets | 3.1 | 3.1 |

3.2 - Venn Diagrams | 3.2 | 3.2 |

3.3 - Binary Relations | 3.3 | 3.3 |

3.4 - Equivalence Relations | 3.4 | 3.4 |

3.5 - Matrices of Relations | 3.5 | 3.5 |

3.6 - Functions | 3.6 | 3.6 |

3.7 - Sequences & Strings | 3.7 | 3.7 |

Chapter 4 - Algorithms |

Lessons | Homework | Quiz |

4.1 - Introduction to Algorithms | 4.1 | 4.1 |

4.2 - The Euclidean Algorithm | 4.2 | 4.2 |

4.3 - Recursive Algorithms | 4.3 | 4.3 |

4.4 - Complexity of Algorithms | 4.4 | 4.4 |

Chapter 5 - Graph Theory |

Lessons | Homework | Quiz |

5.1 - Introduction to Graph Theory | 5.1 | 5.1 |

5.2 - Paths and Cycles | 5.2 | 5.2 |

5.3 - Hamiltonian Cycles | 5.3 | 5.3 |

5.4 - Matrix Representations of Graphs | 5.4 | 5.4 |

5.5 - Dijkstra's Algorithm | 5.5 | 5.5 |

5.6 - Isomorphic Graphs | 5.6 | 5.6 |

5.7 - Planar Graphs | 5.7 | 5.7 |

Chapter 6 - Trees |

Lessons | Homework | Quiz |

6.1 - Introduction to Trees | 6.1 | 6.1 |

6.2 - Depth First Search Algorithm | 6.2 | 6.2 |

6.3 - Breadth First Search Algorithm | 6.3 | 6.3 |

6.4 - Minimal Spanning Trees | 6.4 | 6.4 |

Chapter 7 - Recurrence Relations and Finite-State Machines |

Lessons | Homework | Quiz |

7.1 - Introduction to Recurrence Relations | 7.1 | 7.1 |

7.2 - Solving Recurrence Relations | 7.2 | 7.2 |

7.3 - Introduction to Finite-State Machines | 7.3 | 7.3 |

Chapter 8 - Counting and Probability |

Lessons | Homework | Quiz |

8.1 - Counting | 8.1 | 8.1 |

8.2 - Permutations and Combinations | 8.2 | 8.2 |

8.3 - Finite Basic Probabilities | 8.3 | 8.3 |

8.4 - Basic Laws of Probability | 8.4 | 8.4 |

## Time on Task

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.## Schedule

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able, with a minimum coursework time of at least six weeks.Week | Complete Sections |

1 | 1.1 - 1.3 |

2 | 1.4 - 1.5 |

3 | 2.1 - 2.2 |

4 | 2.3 - 2.4 |

5 | 2.5 - 2.6 |

6 | 3.1 - 3.2 |

7 | 3.3 - 3.5 |

8 | 3.6 - 3.7 |

9 | 4.1 - 4.3 |

10 | 4.4 - 5.1 |

11 | 5.2 - 5.4 |

12 | 5.5 - 5.6 |

13 | 5.7 - 6.1 |

14 | 6.2 - 6.4 |

15 | 7.1 - 7.3 |

16 | 8.1 - 8.2 |

17 | 8.3 - 8.4 |

Final Exam |

## Code of Conduct:

**Code of Ethics:**

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

**Respectful communications:**

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

**Grading information and proctored final policies:**

The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade. By agreeing to the terms of service agreement, you agree to read the 'Grading' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first log-in to notify us if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies. There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.

**Examples of academic misconduct:**

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you. Final exams are the intellectual property of Westcott Courses, and taking screen shots of a digital final or copying a paper test in any way is cheating and will result in an F in the course.

**Unauthorized collaboration:**

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

**Important Notes:**

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

#### Related Information:

#### How it Works

These courses are available to anyone in the public who'd like to enroll. Unlike traditional colleges where one must enroll in a degree program, Westcott Courses offers individual courses that are available instantly. Westcott Courses is the teacher of the course, and the official transcript with academic semester credits comes from our partner university, UMass Global who is regionally accredited by WASC. Westcott Courses doesn't appear on the transcript; the transcript shows our courses the same way it would show a traditional class taken at the university's campus.Read more about transferring the credits.

#### Teachers for the course:

The classes are self-paced; however, a teacher is attached to each course who holds at least a master's degree in their field of study (or related). Most of our teachers are teachers who teach the exact same course on either a California State University or Community college campus.#### Omega Math^{TM} Courses:

Courses that have the trademark of "Omega Math^{TM}" are courses that have been written by our Omega Math team, and have a format that students love! These courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Students can take each test and quiz twice, and only the higher of the two scores counts towards their grade. This feature enables students to figure out what they did wrong before pushing forward, providing them with a deeper understanding of the course material.