Instructor: Sharad Keny.

Office Number, Phone & email: Sc 108C, 562-907-4200 ext 4454, skeny@whittier.edu

Web Address: http://web.whittier.edu/skeny

Office Hours : (tentative) Monday, Wednesday 3:30 - 4:30 p.m.

Course Number and Title : Math 280, Abstract Thinking

Time and Day of Meeting : Monday, Wednesday, Friday 2:30 -3:20 p.m. in Sc 208

Book : Doing Mathematics

This course is designed primarily to help you in your transition from lower division mathematics courses such as Calculus which are more application and computational skills oriented, to more theoretical and rigorous upper division courses where you are expected to read, understand and write mathematical proofs. In this course you will learn different methods of writing abstract proofs using the tools of inductive and deductive logic, and you will be expected to use these methods to write proofs of some elementary results in Modern Algebra and Analysis.

More specifically, this course has five major goals:

1. To help you to think and to express mathematically- to analyze a situation, extract pertinent facts and draw appropriate conclusions.
2. To develop your abstract reasoning skills.
3. To help you read and understand mathematical proofs.
4. To help you write some simple proofs.
5. To develop skills required of an independent learner of mathematics.

Course Content:

I hope to cover chapters 1 through 4 and parts of chapters 5 and 6.

In chapter 1 we will learn the basic tools of logic used in mathematical arguments.

Most of the material in chapters 2, 3 and 4 must be familiar to all of you. We will use the tools of chapter 1 to read and write proofs of results in these three chapters. In chapter 5 we will study the concept of the cardinality of a set and write simple proofs of some beautiful results like the countability of rational numbers. Finally in chapter 6 we will study some basic concepts in Modern Algebra and write elegant proofs of some simple results about groups.

Lectures :

Every class will begin with a discussion of any questions you might have about the topics previously covered in class. Please feel free to ask questions during or outside the class. I will be around almost every day till about 4 p.m. and even later if needed.

Grading:

You will take this class for a letter grade, Cr/NC is not an option. Your grade in this class will be based on your performance in two one hour tests, a two hour final, homework, presentations, and attendance and participation. These will be weighted as follows towards the final grade in the class :

By college policy, incomplete grades can be given only for reasons of health or serious personal problems, provided the student has satisfactorily met all course requirements except for certain assigned work or final examination. Academic overload, outside employment or improper management of time are not sufficient reasons for receiving an incomplete grade. (see page 43 of the college catalog)

Final:

The final exam is cumulative and will be based on all the material covered during the semester. It is compulsory. If you do not take the final your course grade will be an ‘F’. It will be administered on Wednesday, December 16 from 10:30 - 12:30 p.m which is the officially scheduled time for this course as published in the schedule of classes. By college final examination policy (see page 41 of the college catalog) final exam must be taken only at this time. Your grade in the final will count towards 25% of your semester grade.

Tests:

The two tests are not cumulative and together they will count towards 40% of your

semester grade. The tentative dates of the three tests are

First test: Friday, October 9 Second test : Wednesday, November 11

No make up tests will be given unless there is a valid reason, the nature of valid being determined by the instructor. Remember the make up tests will usually be harder than the scheduled tests in fairness to the students who take the tests on time. Arrangements for the make up tests must be made before the scheduled test is administered. Positively no make up tests will be given later than one week after the scheduled tests.

Homework:

This is a college level proof writing course and accordingly my expectation about your homework assignment will not only include correct mathematical solution but also clear explanation of your solutions using correct English language.

Homework problems will be assigned during every lecture and their solutions will be collected during the following lecture. Some of these problems will be graded and the assignment will be returned during the next class meeting. Positively no late homework will be accepted. It has to be turned in at the beginning of the class when it is due. The grades in these homework assignments will count towards 15% of your semester grade. Remember these 15% points must be easy for everybody. All you have to do is work regularly. I expect all of you to get all 15% of the homework grade.

This is a seminar course where students will be expected to lecture on previously assigned topics. These student presentations will be evaluated based on the quality of mathematical preparation, explanations of the results and the organization and delivery of the material. Your presentations will be evaluated by your ccolleagues in the class and the instructor.15% of the semester grade will be based on your performance in these presentations. You are encouraged to seek my help if necessary in preparing for these presentations.

Attendance and participation:

Attendance and participation is extremely crucial in this class since it will be run as a seminar where students will be lecturing on previously assigned topics. Please arrive a few minutes earlier so that we can start on time. Every student will be expected to be prepared with the topic under discussion so that he/she can actively participate in the class. If you miss a class, you will miss much more than just the 50 minutes of class time. 5% of your semester grade will be based on your attendance and participation.

Academic honesty is expected at all times and in all the work you do in class or outside the classroom. Cheating or willful plagiarism in any work turned in for a grade will result in your getting grade zero in that work. Repeated plagiarism could result in your failing the course.

Students desiring accommodations on the basis of physical, learning, or psychological disability for this class are to contact Disability Services.  Disability Services is located on the ground floor of the Library, room G003, and can be reached by calling extension 4825.