Spring 2007 Course Syllabus
Course: W141.001.
Course Title: Basic Concepts of Mathematics.
Time: TR 11:40-1:00.
Place: TL 302.
Instructor: Chein, Orin N.
Instructor Office: WA 612.
Instructor Email: orin.chein@temple.edu
Instructor Phone: 215-204-7846.
Office Hours: TR 10=11:20 and by appointment.
Prerequisites: Pre/co-requisites: Two semesters of Calculus (or permission of the instructor).
Textbook: A Transition to Advanced Mathematics.
Course Goals: Students should develop a familiarity with the following mathematical concepts: mathematical induction, equivalence and order relations, injective and surjective mappings, algebraic operations. They also should develop the ability to recognize and to produce a straightforward mathematical proof. Finally, they should be able to construct the real (or at least the rational) numbers from Peanos postulates.
Topics Covered: The course begins by considering the nature of mathematics as the study of axiomatic systems and the implications this has for the relationship between mathematics and the real world. Chapter 1 introduces the tools of propositional logic, the rules of inference and methods of proof. Chapter 2 deals with the basic notions of set theory. It also considers mathematical induction (a very important technique for proving certain types of theorems) and some techniques of counting. Chapter 3 is concerned with the notion of mathematical relations. In particular, it considers equivalence relations and their connection with partitions, as well as order relations. Chapter 4 examines the notion of a function, as a particular kind of relation. It also considers what it means for a function to be injective (one-to-one), surjective (onto) or bijective (a one-to-one correspondence). Chapter 5 considers the notion of cardinality as an example of an equivalence relation. We will probably not have time to cover this chapter in class, but some of the concepts of the chapter will be assigned as homework. Chapter 6 is an introduction to group theory. We will only consider the beginning of the chapter, discussing what is meant by an algebraic operation and what is meant by a group. Chapter 7 deals with the axiomatic structure of the real number system. As with Chapter 6, this chapter delves too deeply into topics covered in more advanced courses. Instead of following the thread of the text, your will be assigned a term project (see below) through which you will construct the real numbers as an application of the concepts found in the earlier parts of the course. Sections covered: Chapter 1, sections 1-6 Chapter 2, sections 1-6 Chapter 3, sections 1-4 Chapter 4, sections 1-4 Chapter 5 will not be covered in class but will form the basis of assigned homework. Chapter 6, section 1 & selected topics from section 4 Chapter 7 will not be covered in class but will form the basis of your term project.
Course Grading: There will be two midterm examinations, each worth approximately 20% of the final grade, and a cumulative final examination, worth approximately 25%. Grades for the written homework assignments will be worth 20%, the term project will be worth the remaining 10%, and class participation will be worth 5%. In the case of borderline grades, class participation (attendance as well as asking and answering questions) may be the deciding factor.
Exam Dates: The midterm examinations are tentatively scheduled for Thursday, March 1 and for Tuesday, April 24. The final examination is scheduled for Tuesday, May 8, from 11:00-1:30.
Attendance Policy: It is expected that you attend class regularly and on time. While I do not have any hard and fast rules such as "five absences means an automatic F", I do take attendance (formally at first until I get to know everyone, and visually thereafter). Excessive unexcused absence or lateness will lower your class participation grade. You are also expected to be present for each scheduled exam. If you determine in advance that you will not be able to be present on the date of a scheduled exam, I expect you to notify me immediately of that fact, so that we can discuss alternate arrangements. If a last minute emergency prevents you from being able to take a scheduled exam, I expect you to call my office AS SOON AS POSSIBLE. (If you are ill or your car won't start, I expect to hear from you on the morning of the exam. If you are in a coma, then when you emerge from the coma will be soon enough, assuming that you have a doctor's note attesting to the fact that you were in the coma!) If I am not available when you call, leave a message on my voice mail stating your name, the class you are in, your reason for missing the exam and a phone number at which I can reach you later that day. If you don't follow these instructions, I am likely to treat your absence as unexcused. If we have not made arrangements in advance for you to take a make-up exam, you should be prepared to take a make-up on the day you return to campus. In general, I find it difficult to compose two exams that are truly comparable, so I prefer not to. For an excused absence, I may decide to give a make-up on the day you return, or I may decide to disregard the exam and to increase the percentages which your other exams and/or writing grades contribute your final grade. (This is my decision, not yours.) Exams that are missed due to unexcused absence will receive the grade of zero. Students who miss more than one exam may receive a zero for the second exam, regardless of the reason for the absence, unless advance arrangements have been made.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:
During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.