Instructor     John Bishir,   236 Harrelson,   515-3350,   bishir@math.ncsu.edu

Office Hours --   9:30 - 10: 30    MWF            and by appointment

Text --        Bond & Keane         An Introduction to Abstract Mathematics

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Course Purpose and Coverage
 
 

         This course is designed to provide a transition from calculus to your upper level

courses.  The primary objective is to help you learn to communicate

mathematically. Emphasis will be  placed on understanding and clear

expression of mathematical ideas, both orally and in writing. In this regard,

problems and homework should be viewed as aids to understanding, not as

ends in themselves. This view is different from your experience in calculus, so you

may find this course a bit perplexing at first. In the end, though, you should be well

prepared for your advanced courses.
 

        Logic, Sets, and Functions - covered in the first 3 chapters of the text -

constitute the bulk of the course material, with relatively fewer days spent

on other topics. By the end of the course, you should be able to
 

   1.    Read and understand basic mathematical discussions and proofs.

   2.    Apply the basic methods of proof - direct, contrapositive, contradiction.

   3.    Critique proofs and explanations, spotting errors in logic and

              correcting these errors.

   4.    Formulate mathematical conjectures of your own.

   5.    Use universal and existential quantifiers in discussions and proofs.

   6.    Formulate proofs based on the method of mathematical induction.

   7.    Apply your knowledge of logic and proofs to basic concepts and results

               concerning sets, functions, and other topics.
 
 
 
 

Course Activities and Grading - MA 225
 
 

Major Tests and the Final Exam    (81% of the course grade)

        There will be 3 tests during the semester, with the test average counting 54%

of the course grade.   The final exam, scheduled for Monday, December 17,

at 1 PM, will count 27% of the grade.
 
 

Classwork and Homework   (19% of the grade)

       Homework will be assigned and collected each class day.  Since many of the

problem solutions will be placed on reserve, HW will not be graded, but I will

usually look over 1 or 2 problems and make suggestions for possible improvements.

If you wish, you can work with other members of the class on these problems.

In that case, hand in only one paper, with everyone's name on it.  I will also respond

to any questions you indicate.

         The Homework Grade will be based on Homework Tests (10%) which will be

given during several Wednesday class periods, and on your Homework

Preparation and Class Participation (9%).  The tests will contain two types of

questions--
 

      1)    Problems from recent homework assignments --    Such problems will

               typically involve proofs of theorems, or ask for explanations or

               descriptions of mathematical ideas and concepts. Naturally, it will help

               to have worked the problems in advance; the tests, however, will be

               closed book and notes.

      2)    Definitions --    These are extremely important because in order to

                                            communicate well, or to understand what you are studying,

                                            you must know the meanings of the words you use.   It will

                                            help to make a list of

                                            definitions as you encounter them and to review it daily.

                                            Be very specific; precise wording is crucial in mathematics.

                                            I will collect these

                                            from time to time to see how you are doing.
 
 

         Good luck with the course.   My goal is that everyone will earn an ‘A’.   Please

come see me at the first sign of trouble.   If my posted office hours do not work for

you, we can always find another time; I'm around most of every day.