Syllabus for MAT-401

MATHEMATICAL LOGIC

# COURSE DESCRIPTION

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.

# COURSE TOPICS

1. Propositional Calculus
2. Truth tables
3. Tautologies
4. Axiom system for the propositional calculus
5. First-Order Logic
6. Quantifiers
7. First-order languages and their Interpretations, satisfiability and truth, models
8. First-order theories
9. Properties of first-order theories
10. Formal Number Theory

# COURSE OBJECTIVES

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.

# COURSE MATERIALS

You will need the following materials to do the work of the course. The required textbook is available from the University’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

# COURSE STRUCTURE

Mathematical Logic is a three-credit online course, consisting of four 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

# ASSESSMENT METHODS

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.

## Discussion Forums

You are required to participate in four 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.

## Written Assignments

You are required to complete four 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.

## Comprehensive Midterm Assignment

You are required to complete a comprehensive midterm assignment that covers modules 1 and 2. The midterm assignment consists of five 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.

## Final Paper

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.

### Turnitin Requirement for Final Paper

You are required to submit the final paper in this course to Turnitin.com, an academic plagiarism prevention site, prior to submitting the project within your course space. You will receive immediate written feedback from Turnitin regarding writing style as well as a plagiarism gauge with tips for proper citations. You then have the opportunity to edit your assignment with this feedback in mind and resubmit it to Turnitin for additional checking. Once you are satisfied with the paper, you are required to submit the Turnitin feedback (also known as the originality report) for the final version along with the paper itself within the course space.

Read carefully the information found at the following link, as it will provide instructions for this requirement:

Turnitin FAQ Web Page

The course ID and password that you will need in order to create an account may be found at the following link. Look within Step 1, locating your course ID and password by semester.

Course ID and Password by Semester

This information can also be found within Using Turnitin for Assignments. You can locate this document in the topic list area of your course space.

Students please note: You have the option of submitting any of your assignments to Turnitin.com. Submit any additional assignments through the slots with the optional label. However, submitting other assignments is NOT a requirement and you should not submit originality reports for these assignments to your mentor.

• Discussion forums (4)20%
• Written assignments (4)30%
• Midterm assignment (Modules 1–2)25%
• Final paper25%

 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 course not in your area of study), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).

# STRATEGIES FOR SUCCESS

### 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 University.
• 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.

Thomas Edison State University is committed to maintaining academic quality, excellence, and honesty. The University expects all members of its community to share the commitment to academic integrity, an essential component of a quality academic experience.

Students at Thomas Edison State University 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.

All members of the University community are responsible for reviewing the Academic Code of Conduct Policy in the University Catalog and online at www.tesu.edu.

Thomas Edison State University 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 University insist on strict standards of academic honesty in all courses. Academic dishonesty undermines this objective. Academic dishonesty can take the following forms:

• Cheating
• Submitting credentials that are false or altered in any way
• Plagiarizing (including copying and pasting from the Internet without using quotation marks and without acknowledging sources)
• Forgery, fabricating information or citations, or falsifying documents
• Submitting the work of another person in whole or in part as your own (including work obtained through document sharing sites, tutoring schools, term paper companies, or other sources)
• Submitting your own previously used assignments without prior permission from the mentor
• Facilitating acts of dishonesty by others (including making tests, papers, and other course assignments available to other students, either directly or through document sharing sites, tutoring schools, term paper companies, or other sources)
• Tampering with the academic work of other students

### Plagiarism

Thomas Edison State University is committed to helping students understand the seriousness of plagiarism, which is defined as using the work and ideas of others without proper citation. The University takes a strong stance against plagiarism, and students found to be plagiarizing are subject to discipline under the academic code of conduct policy.

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, or without identifying it as a direct quote, 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 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.

For examples of unintentional plagiarism, advice on when to quote and when to paraphrase, and information about writing assistance and originality report checking, click the links provided below.

Examples of Unintentional Plagiarism

When to Quote and When to Paraphrase

Writing Assistance at Smarthinking

Originality Report Checking at Turnitin

### Disciplinary Process for Plagiarism

Acts of both intentional and unintentional plagiarism violate the Academic Code of Conduct.

If an incident of plagiarism is an isolated minor oversight or an obvious result of ignorance of proper citation requirements, the mentor may handle the matter as a learning exercise. Appropriate consequences may include the completion of tutorials, assignment rewrites, or any other reasonable learning tool in addition to a lower grade for the assignment or course. The mentor will notify the student and appropriate dean of the consequence by e-mail.

If the plagiarism appears intentional and/or is more than an isolated incident, the mentor will refer the matter to the appropriate dean, who will gather information about the violation(s) from the mentor and student, as necessary. The dean will review the matter and notify the student in writing of the specifics of the charge and the sanction to be imposed.

Possible sanctions include:

• Lower or failing grade for an assignment
• Lower or failing grade for the course
• Rescinding credits
• Rescinding certificates or degrees
• Recording academic sanctions on the transcript
• Suspension from the University
• Dismissal from the University