Syllabus for MAT-401

MATHEMATICAL LOGIC

Logic is is often defined as the analysis of methods of reasoning. The mathematical logic is the study of mathematical reasoning and proof. This course starts off with the introduction to propositional calculus, the basics to the course. Then it focuses on the first-order logic and model theory. Topics covered include the metatheorems dealing with the properties of soundness, completeness, decidability, and consistency. The final part of the course is about formal number theory.

- Propositional Calculus
- Truth tables
- Tautologies
- Axiom system for the propositional calculus
- First-Order Logic
- Quantifiers
- First-order languages and their Interpretations, satisfiability and truth, models
- First-order theories
- Properties of first-order theories
- Formal Number Theory

After completing this course, you should be able to:

- CO1 Illustrate the basics of logic using truth tables.
- CO2 Utilize different axiomatic theories to prove statements logically.
- CO3 Explain the first-order languages and their interpretations.
- CO4 Discuss the various first-order theories and their properties.
- CO5 Generalize the metatheorems of soundness, completeness, decideability, and consistency.
- CO6 Define various formal number theories and properties.

You will need the following materials to do the work of the course. The required textbook is available from the College’s textbook supplier, MBS Direct.

Required Textbook

- Mendelson, Elliott (2010). Introduction to Mathematical Logic, 5th ed. by Chapman and Hall/CRC

ISBN-13: 978-1584888765

Mathematical Logic is a three-credit online course, consisting of four (4) modules. Modules include an overview, topics, learning objectives, study materials, and activities. Module titles are listed below.

- Module 1: The Propositional Calculus
- Module 2: First-Order Logic and Model Theory, Part 1
- Module 3: First-Order Logic and Model Theory, Part 2
- Module 4: Formal Number Theory

For your formal work in the course, you are required to participate in online discussion forums, complete written assignments, a comprehensive midterm assignment, and a final project. See below for details.

Consult the course Calendar for due dates.

You are required to participate in four (4) graded discussion forums. Discussion forums are on a variety of topics associated with the course modules. There is also an ungraded but required introduction forum in Module 1. Click to view Online Discussion Grading Rubric.

You are required to complete four (4) written assignments. The written assignments draw on the exercises at the end of sections from the textbook. For each assignment, answer all assigned exercises, and show all work.

Assignments must be prepared electronically with a word processor, preferably using whatever equation editor comes with your word processing software. However, if your word processor is not compatible with your mentor's word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility. (Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.)

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. Be sure to include your name at the top of the paper, as well as the course name and code and the semester and year in which you are enrolled. To receive full credit for your answers, you must show all work and include complete solutions.

You are required to complete a comprehensive midterm assignment that covers modules 1 and 2. The midterm assignment consists of five (5) problems similar to exercises in written assignments . You will submit this assignment by Saturday of midterm assignment week (see the course Calendar), doing it in the same way you have for your other written assignments in this course.

You are free to use your textbook if desired when working on the midterm assignments.

The assignment is located in the Midterm Assignment area of the course Web site.

You are required to write a final paper instead of taking a proctored final exam. This paper will focus on the first three modules of the course that deal with propositional calculus and first-order logic and model theory.

You are required to choose a mathematician among a given list and write a biography about that mathematician and explain their contributions to mathematical logic.

See the Final Paper area of the course web site for further details.

Your grade in the course will be determined as follows:

- Discussion forums (4)—20%
- Written assignments (4)—30%
- Midterm assignment (Modules 1–2)—25%
- Final paper—25%

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:

A | = | 93–100 | C+ | = | 78–79 | |

A– | = | 90–92 | C | = | 73–77 | |

B+ | = | 88–89 | C– | = | 70–72 | |

B | = | 83–87 | D | = | 60–69 | |

B– | = | 80–82 | F | = | Below 60 |

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a nonarea of study course), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).

First Steps to Success

To succeed in this course, take the following first steps:

- Read carefully the entire Syllabus, making sure that all aspects of the course are clear to you and that you have all the materials required for the course.
- Take time to read the entire Online Student Handbook. The Handbook answers many questions about how to proceed through the course, and how to get the most from your educational experience at Thomas Edison State College.
- Familiarize yourself with the learning management systems environment—how to navigate it and what the various course areas contain. If you know what to expect as you navigate the course, you can better pace yourself and complete the work on time.
- If you are not familiar with Web-based learning be sure to review the processes for posting responses online and submitting assignments before class begins.

Study Tips

Consider the following study tips for success:

- To stay on track throughout the course, begin each week by consulting the course Calendar. The Calendar provides an overview of the course and indicates due dates for submitting assignments, posting discussions, and scheduling and taking examinations.
- Check Announcements regularly for new course information.

Students at Thomas Edison State College are expected to exhibit the highest level of academic citizenship. In particular, students are expected to read and follow all policies, procedures, and program information guidelines contained in publications; pursue their learning goals with honesty and integrity; demonstrate that they are progressing satisfactorily and in a timely fashion by meeting course deadlines and following outlined procedures; observe a code of mutual respect in dealing with mentors, staff, and other students; behave in a manner consistent with the standards and codes of the profession in which they are practicing; keep official records updated regarding changes in name, address, telephone number, or e-mail address; and meet financial obligations in a timely manner. Students not practicing good academic citizenship may be subject to disciplinary action including suspension, dismissal, or financial holds on records.

Academic Dishonesty

Thomas Edison State College expects all of its students to approach their education with academic integrity—the pursuit of scholarly activity free from fraud and deception. All mentors and administrative staff members at the College insist on strict standards of academic honesty in all courses. Academic dishonesty undermines this objective. Academic dishonesty takes the following forms:

- Cheating
- Plagiarizing (including copying and pasting from the Internet without using quotation marks and without acknowledging sources)
- Fabricating information or citations
- Facilitating acts of dishonesty by others
- Unauthorized access to examinations or the use of unauthorized materials during exam administration
- Submitting the work of another person or work previously used without informing the mentor
- Tampering with the academic work of other students

Academic dishonesty will result in disciplinary action and possible dismissal from the College. Students who submit papers that are found to be plagiarized will receive an F on the plagiarized assignment, may receive a grade of F for the course, and may face dismissal from the College.

A student who is charged with academic dishonesty will be given oral or written notice of the charge. If a mentor or the College official believes the infraction is serious enough to warrant referral of the case to the academic dean, or if the mentor awards a final grade of F in the course because of the infraction, the student and the mentor will be afforded formal due process.

If a student is found cheating or using unauthorized materials on an examination, he or she will automatically receive a grade of F on that examination. Students who believe they have been falsely accused of academic dishonesty should seek redress through informal discussions with the mentor, through the office of the dean, or through an executive officer of Thomas Edison State College.

Plagiarism

Using someone else’s work as your own is plagiarism. Although it may seem like simple dishonesty, plagiarism is against the law. Thomas Edison State College takes a strong stance against plagiarism, and students found to be plagiarizing will be severely penalized. If you copy phrases, sentences, paragraphs, or whole documents word-for-word—or if you paraphrase by changing a word here and there—without identifying the author, then you are plagiarizing. Please keep in mind that this type of identification applies to Internet sources as well as to print-based sources. Copying and pasting from the Internet, without using quotation marks and without acknowledging sources, constitutes plagiarism. (For information about how to cite Internet sources, see Online Student Handbook > Academic Standards > “Citing Sources.”)

Accidentally copying the words and ideas of another writer does not excuse the charge of plagiarism. It is easy to jot down notes and ideas from many sources and then write your own paper without knowing which words are your own and which are someone else’s. It is more difficult to keep track of each and every source. However, the conscientious writer who wishes to avoid plagiarizing never fails to keep careful track of sources.

Always be aware that if you write without acknowledging the sources of your ideas, you run the risk of being charged with plagiarism.

Clearly, plagiarism, no matter the degree of the intent to deceive, defeats the purpose of education. If you plagiarize deliberately, you are not educating yourself, and you are wasting your time on courses meant to improve your skills. If you plagiarize through carelessness, you are deceiving yourself.

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