Introduction to Mathematical Logic Math 253 Fall 2004 Instructor: Office: Phone: Email: Web Page Office Hours: Textbook: Course Description: Dr. Kathy V. Rodgers SC 3273 812-465-7093 (office) 270-389-0011 (home) firstname.lastname@example.org http://www.usi.edu/science/math/krodgers/index.htm MTWF (10-12) and lots of other times by appointment Discrete Mathematics with Applications 3rd ed., Susanna S. Epps This course is designed to introduce you to basic concepts and procedures used in calculus and upper level mathematics courses. The topics to be discussed are the logic of compound statements, the logic of quantified statements, elementary number theory and methods of proof, sequences and mathematical induction, set theory, and functions.
This course fulfills the A2 requirement of the University Core Curriculum. In the context of number theory, quantified statements, and proofs, students will strengthen old algebraic skills and develop new ones. From the study of logical forms and equivalences, conditional statements, valid and invalid arguments, and mathematical induction, students will develop their ability to think abstractly. Students will also gain an appreciation for the power of “recursive thinking” and the verification of solutions by mathematical induction. In general, this class presents mathematical topics in a variety of contexts used to solve problems in a broad range of applied situations. This course also provides the foundation for the student to begin communicating in mathematical terms.
Satisfactory Placement Score or successful completion of Math 111 (College Algebra) or Math 118 (College Algebra and Trigonometry). Math 253 may be taken concurrently with Math 230 (Calculus I ). The grades for this course will be based on four one-hour exams, a comprehensive final exam and a homework/quiz score. Each one-hour exam will be worth 100 points, the final exam will be worth 200 points and the homework/quiz score will be worth 100 points. The course grades will be assigned as follows:
90-100% 88-89% 78-79% 68-69% Below 60% A B+ C+ D+ F 80-87% 70-77% 60-67% B C D
Students are expected to be present for every class meeting. Make-up exams will be given under extenuating circumstances only. The instructor must be notified in advance and the exam taken prior to the next class meeting. Homework is due at the beginning of class; late homework will not be accepted; place your homework on the instructor’s desk at the beginning of class. If you have a disability that will affect your work in this class, please notify the instructor immediately. Students are expected to abide by the University’s honesty policy as outlined in the University of Southern Indiana Bulletin, 2003-2005, p. 295. Part of this policy is listed below.
“The benchmarks of any great university are high academic standards for both faculty and students. For this reason, truth and honesty are necessary to a university community. The University expects both students and faculty to adhere to these principles and to foster them daily. Put simply, this expectation requires each student to do his or her academic work without recourse to unauthorized means of any kind. Both students and faculty are expected to report violations of academic honesty…” Cheating: A student must not intentionally use or attempt to use unauthorized materials, information, or study aids in any academic exercise. 1. A student must not use external assistance during any examination unless the instructor has specifically authorized such assistance. This prohibition includes (but is not limited to) the use of tutors, books, calculators, notes, formula lists, cues on a computer, photographs, and symbolic representations. A student must not copy from another student’s work, including (but not limited to) a test paper, project, product, performance, or electronic document or file. (For Math 253, students are not to copy others’ homework.) A student must not take a test for someone else or permit someone else to take a test for him or her. A student must not knowingly allow another student to copy one’s work in a test. A student must not submit, during the same semester, substantial portions of the same academic work for credit or honors more than once without permission from all of the instructors who may be involved. In the event a student seeks to submit in a current course a substantial portion of the same academic work submitted in a previous course, then only the current instructor need approve.
You may read the rest of this policy as well as the penalties in the Bulletin on pages 295 and 296.
Math 253 Fall 2004 Assignment Sheet for Chapters 1 and 2
All assignments are due at the beginning of class on the date indicated. Late homework will not be accepted.
Section 1.1 Logical Form and Logical Equivalences Conditional Statements
Date Due 3-36 and 42-52 multiples 9/3 of 3 1, 4, 5, 8, 12, 13b, 14 a, 14b, 16, 19, 20c, 20g, 22d, 23g, 28, 29, 32,35, 36, 37, 38,39, 43, 47, 49 1-29 odd, 33, 34, 37, 38a, 41, 42 9/8
No class 2.1
Valid and Invalid Arguments Labor Day Introduction to Predicates and Quantified Statements I Introduction to Predicates and Quantified Statements II Statements Containing Multiple Quantifiers Arguments and Quantified Statements Direct Proof and Counter Examples
3-27 multiples of 3, 30a, 30b, 31b, 31c
3-24 multiples of 3, 29, 38, 40, 42
3-54 multiples of 3
3-30 multiples of 3
3-54 multiples of 3
Chapters 1 and 2