# Methods of Proof in Mathematics

**Course Code:**MATU 220

**Credits:**4 semester credits

**Through Brandman University**

Enroll Now (Credit)

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**Credit Information**

Course Title: | Methods of Proof in Mathematics |

Course Code: | MATU 220 |

Credits: | 4 Semester Credits |

Credit Provider: | Brandman University |

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? | Yes | This course requires a textbook. |

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

**Course Description**

This course is an introduction to abstract mathematics, with an emphasis on the techniques of mathematical proof (direct, contradiction, conditional, contraposition). Topics to be covered include logic, set theory, relations, functions and cardinality.

Note: This course is proof based. All homework assignments, exams and the final are graded by the instructor.

**Prerequisite:**Calculus l, Calculus ll and Calculus lll (Or Business Calculus, Calculus ll and Calculus lll.)

**Course Pricing**

The full cost of the course is $973.00; however, you may use the payment plan to split the cost into two payments.

**Payment Plan:**

1st payment: $538.65 (Start your class immediately!)

2nd payment: $441.35 (Automatically charged 30 days later.)

Enroll Now - Credit - $973 View Noncredit Option - $693

**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. Most students finish the lower level courses in 1 - 3 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:**

Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition)

- Chartrand, Gary; Polimeni, Albert; Zhang, Ping

- Textbook ISBN-10: 0321797094

- Textbook ISBN-13: 978-0321797094

Text Book on Amazon

Check the price on abebooks.com, as their price is usually lower than Amazon.**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. 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 requires that a student get at least 60% on the final in order to pass the class with a C or better. This is a fair rule, as 60% is right between an F and a D.

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 Brandman University. Brandman University 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 Brandman and give you the instructions on how to order the transcript from Brandman's records office. Since Westcott Courses is the teacher, we do not appear on the transcript. The official transcript from Brandman University 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 Brandman University, 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. Brandman University 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.

(K-12 use)

**Brandman University's Accreditation:**

You can verify that Brandman University is regionally accredited via the Department of Education's web site. Enter Brandman University into the search field. Brandman University has 26 campuses, so just click on the first link and it will show they are regionally accredited by WASC.

**Preapproval from your College:**

If you would like to make sure your college will accept this course from Brandman University, 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 220 - Methods of Proof in Mathematics through Brandman University. Brandman University is regionally accredited by WASC.

You will find the course description for this course, as well as other pertinent information on Brandman's web site at this URL: https://www.brandman.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 Brandman University. If your school is not on this list, it just means they have not contacted us to establish an articulation agreement.

## Course Information

Course Title: | Methods of Proof in Mathematics |

Course Code: | MATU 220 |

Credits: | 4 credits |

Credit Provider: | Brandman University |

Grading Mode: | Standard letter grade |

Proctored Final: | Yes |

**Textbook Requirement:**

Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition)

- Chartrand, Gary; Polimeni, Albert; Zhang, Ping

- Textbook ISBN-10: 0321797094

- Textbook ISBN-13: 978-0321797094

Text Book on Amazon

Check the price on abebooks.com, as their price is usually lower than Amazon.

## Course Description

This course is an introduction to abstract mathematics, with an emphasis on the techniques of mathematical proof (direct, contradiction, conditional, contraposition). Topics to be covered include logic, set theory, relations, functions and cardinality.Note: This course is proof based. All homework assignments, exams and the final are graded by the instructor.

**Prerequisite:**Calculus l, Calculus ll and Calculus lll (Or Business Calculus, Calculus ll and Calculus lll.)

## Learning Outcomes

At the conclusion of this course, students should be able to:- Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments.
- Perform set operations on finite and infinite collections of sets.
- Determine equivalence relations on sets and equivalence classes.
- Identify functions, surjections, injections, and bijections and work with inverse images and inverse functions.
- Apply multiple techniques of mathematical proof (direct, contradiction, conditional, contraposition, and induction).
- Write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence.

## Methods Of Evaluation

Homework quizzes 15%Chapter Tests (5) 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:**

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 using the concepts to solve problems. Each lesson contains a set of homework problems.

**Chapter Tests (5):**

The chapter tests are designed to cover a broader area of the text and test your understanding of the material.

#### Proctored Final:

This course goes towards a 4-year degree; thus, it 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. Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met.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 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 math 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.

## Content Menu

#### Course Content Menu:

**Chapter 1. Sets**

1.1. Describing a Set

1.2. Subsets

1.3. Set Operations

1.4. Indexed Collections of Sets

1.5. Partitions of Sets

1.6. Cartesian Products of Sets

**Chapter 2. Logic**

2.1. Statements

2.2. The Negation of a Statement

2.3. The Disjunction and Conjunction of Statements

2.4. The Implication

2.5. More on Implications

2.6. The Biconditional

2.7. Tautologies and Contradictions

2.8. Logical Equivalence

2.9. Some Fundamental Properties of Logical Equivalence

2.10. Quantified Statements

2.11. Characterizations of Statements

**Chapter 3. Direct Proof and Proof by Contraposition**

3.1. Trivial and Vacuous Proofs

3.2. Direct Proofs

3.3. Proof by Contrapositive

3.4. Proof by Cases

3.5. Proof Evaluations

**Chapter 4. More on Direct Proof and Proof by Contrapositive**

4.1. Proofs Involving Divisibility of Integers

4.2. Proofs Involving Congruence of Integers

4.3. Proofs Involving Real Numbers

4.4. Proofs Involving Sets

4.5. Fundamental Properties of Set Operations

4.6. Proofs Involving Cartesian Products of Sets

**Chapter 5. Existence and Proof by Contradiction**

5.1. Counterexamples

5.2. Proof by Contradiction

5.3. A Review of Three Proof Techniques

5.4. Existence Proofs

5.5. Disproving Existence Statements

**Chapter 6. Mathematical Induction **

6.1. The Principle of Mathematical Induction

6.2. A More General Principle of Mathematical Induction

6.3. Proof By Minimum Counterexample

6.4. The Strong Principle of Mathematical Induction

**Chapter 8. Equivalence Relations**

8.1. Relations

8.2. Properties of Relations

8.3. Equivalence Relations

8.4. Properties of Equivalence Classes

8.5. Congruence Modulo n

8.6. The Integers Modulo n

**Chapter 9. Functions**

9.1. The Definition of a Function

9.2. The Set of All Functions from A to B

9.3. One-to-one and Onto Functions

9.4. Bijective Functions

9.5. Composition of Functions

9.6. Inverse Functions

9.7. Permutations

**Chapter 10. Cardinalities of Sets**

10.1. Numerically Equivalent Sets

10.2. Denumerable Sets

10.3. Uncountable Sets

Exam #4

**Final Exam for Methods of Proof**

## 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.## 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.

**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, we offer 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, Brandman University 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.