## Course Syllabus

Department of Mathematics and Computer Science, Lincoln University

 COURSE ID: MAT-220 COURSE NAME: Set Theory and Logic CREDITS: 3

TEXT BOOK:

Eccles, Peter J. An Introduction to Mathematical Reasoning. Cambridge University Press: Cambridge,UK 2004.

INSTRUCTOR INFORMATION:

***To be provided for each section***

COURSE DESCRIPTION:

This course consists of the study of sets and equivalence classes, Boolean algebra, the role of axiomatics in the structure of mathematics, basic principles of logic involving rules of modus ponens, reduction and absurdum, prepositional calculus, first order logic and the nature of mathematical proof.

PREREQUISITE:          MAT-121 (Calculus I) or permission of the instructor

COURSE GOALS- STUDENT LEARNER OUTCOMES:

Upon completion of this course, the student should be able to:
• Porperly use the vocabulary and symbolic notation of higher mathematics in definitions, theorems, and problems.
• Analyze the logical structure of statements symbolically, including the proper use of logical connectives, predicates, and quantifiers.
• Construct truth tables, prove or disprove a hypothesis, and evaluate the truth of a statement using the principles of logic.
• Identify and use a variety of methods of proof, including direct, indirect, contradiction, contrapositive, by example/counterexample, and mathematical induction.
• Solve problems and write proofs using the concepts of set theory, including the methods of Venn diagrams, pick-a-point, and truth tables.
• Solve problems and write proofs using the basic definitions and the fundamental properties of subsets and operations on the real numbers, integers, rational and irrational, even and odd, multiples or factors of whole numbers.
• Solve problems and write proofs using the basic definitions, properties and operations of relations and functions, including the concepts of injective, surjective, bijective, and inverse.

TENTATIVE SCHEDULE OF WEEKLY ASSIGNMENTS:

Part I Mathematical Statements and Proofs (Weeks 1-6)
Introductory Concepts
1. The Language of Mathematics
2. Implications
3. Proofs
5. The Induction Principle
Test 1

Part II Sets and Functions (Weeks 7-12)
6. The Language of Set Theory
7. Quantifiers
8. Functions
9. Injections, Surjections, and Bijections
Test 2

Part III Numbers and Counting (Weeks 13-16)
10. Counting
11. Properties of Finite Sets
12. Number Systems
13. Counting Infinite Sets
Test 3

COURSE ASSESSMENT- LEARNING OPPORTUNITIES:*

• Homework

Daily homework will be given on material covered in class, reviewed the next day, and may be collected and graded on an unannounced basis. On all assignments, all work must be shown for credit.

Students are encouraged to work cooperatively. The objective of group work is to develop individual skills while learning to work effectively as a team, to think and talk about problem solving and the underlying mathematical concepts, and to develop the ability to ask and answer questions as they arise. However, each student is responsible for all the assigned material, in other words, students can work together, but should not simply copy work from each other. Students are also encouraged to make regular visits during office hours, to meet in study groups, and to use the Math Lab or the Math Tutors from the School of Natural Sciences.

• Quizzes, Tests and Final Exam

Short quizzes will be given on an unannounced basis. One hour in- class exams will be announced at least a week in advance. A cumulative two hour Final Exam will be given as scheduled by the Registrar. ALL work must be shown for full credit.

• Late Work And Make-Ups

All graded assignments, quizzes and exams must be completed when scheduled. Late assignments or make-up tests or quizzes will only be allowed with official documentation and grades may be lowered. To qualify for a make-up, a student must have notified the professor and rescheduled in a timely manner.

 Participation+ 30% Tests 50% Final 20%
 A 92-100% A- 88-91% B+ 85-87% B 82-84% B- 78-81% C+ 75-77% C 72-74% C- 68-71% D+ 65-67% D 58-64% F 0-57%

UNIVERSITY POLICY:

1) Attendance:

Lincoln University uses the class method of teaching, which assumes that each student has something to contribute and something to gain by attending class. It further assumes that there is much more instruction absorbed in the classroom than can be tested on examinations. Therefore, students are expected to attend all regularly scheduled class meetings and should exhibit good faith in this regard. For the control of absences, the faculty adopted the following regulations:

• Four absences may result in an automatic failure in the course.
• Three tardy arrivals may be counted as one absence.
• Absences will be counted starting with whatever day is specified by the instructor but not later than the deadline for adding or dropping courses.
• In case of illness, death in the family, or other extenuating circumstances, the student must present documented evidence of inability to attend classes to the Vice President for Student Affairs and Enrollment Management. However, in such cases the student is responsible for all work missed during those absences.
• Students representing the University in athletic events or other University sanctioned activities will be excused from class (es) with the responsibility of making up all work and examinations. The Registrar will issue the excused format to the faculty member in charge of the off- or on-campus activity for delivery by the student(s) to their instructors.

Students are responsible for proper conduct and integrity in all of their scholastic work. They must follow a professor's instructions when completing tests, homework, and laboratory reports, and must ask for clarification if the instructions are not clear. In general, students should not give or receive aid when taking exams, or exceed the time limitations specified by the professor. In seeking the truth, in learning to think critically, and in preparing for a life of constructive service, honesty is imperative. Honesty in the classroom and in the preparation of papers is therefore expected of all students. Each student has the responsibility to submit work that is uniquely his or her own. All of this work must be done in accordance with established principles of academic integrity.

An act of academic dishonesty or plagiarism may result in failure for a project or in a course. Plagiarism involves representing another person's ideas or scholarship, including material from the Internet, as your own. Cheating or acts of academic dishonesty include (but are not limited to) fabricating data, tampering with grades, copying, and offering or receiving unauthorized assistance or information.

3) The Student Conduct Code:

Students will be held to the rules and regulations of the Student Conduct Code as described in the Lincoln University Student Handbook. In particular, excessive talking, leaving and reentering class, phones or pagers, or other means of disrupting the class will not be tolerated and students may be asked to leave. Students who constantly disrupt class may be asked to leave permanently and will receive an F.

4) The Core Curriculum Learner Competencies:

All courses offered through the Department of Mathematics and Computer Science require students to meet at least the following out of the 8 Core Curriculum Learner Competencies:

(1) Listen and effectively communicate ideas through written, spoken, and visual means;
(2) Think critically via classifying, analyzing, comparing, contrasting, hypothesizing, synthesizing, extrapolating, and evaluating ideas;

(6) Apply and evaluate quantitative reasoning through the disciplines of mathematics, computational science, laboratory science, selected social sciences and other like-minded approaches that require precision of thought;

(8) Demonstrate positive interpersonal skills by adhering to the principles of freedom, justice, equality, fairness, tolerance, open dialogue and concern for the common good.

Note:

* The instructor of a given section of the course may make some modifications to the evaluation as well as to the rest of the syllabi including but not limited to; the grade weights, number of tests, and test total points.

**The grading scale guideline includes a 2-point flexibility.

Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this page _ last updated 9/10/2007.

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