Summer1 2010 Course Syllabus
Course: Mathematics 2196.011.
Course Title: Basic Mathematical Concepts.
Time: MTWR 12:55-2:25.
Place: CC 527.
Instructor: Chein, Orin N.
Instructor Office: CC 612.
Instructor Email: orin.chein@temple.edu
Instructor Phone: (215) 204-7846.
Course Web Page: I don't have a course URL, but there is a Bl;ackboard site for the course that I expect you to check regularly
Office Hours: M 2:30-3:15 or T 11:45-12:50 or W 11:45-12:50 or R 2:30-3:15.
Prerequisites: Two semesters of Calculus (or permission of the instructor).
Textbook: A Transition to Advanced Mathematics (Sixth Edition), by D. Smith, M. Eggen and R. St. Andre.
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 with a brief introduction to 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 may not have time to cover this chapter fully 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, you 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.
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 15%. In the case of borderline grades, class participation (attendance as well as asking and answering questions) may be the deciding factor. (See the syllabus on Blackboard for more details about grading.).
Exam Dates: The midterm examinations are tentatively scheduled for Thursday, May 27 and for Monday, June 14. The final examination is scheduled for Monday, June 28.
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 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.
WARNING: Because of the importance of this course in my opinion, I assign a large amount of work, and the course requires a great deal of time even during the regular school year. Because we only have six weeks during the summer, you should expect to devote many hours each day to doing the work that I require. If you cannot or do not wish to do this, you should not take this course during the summer.
Further Syllabus information: See the full syllabus under "Course Information" on the Blackboard site for this course. I expect that you read it thoroughly and carefully.
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:
- The first day of classes is Monday, May 17.
- The last day to drop/add (tuition refund available) is Monday, May 28.
- Memorial Day is Monday, May 31.
- The last day to withdraw (no refund) is Monday, June 14.
- The last day of classes is Monday, June 28.
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.