Syllabus

MATH 281 Foundations of Mathematics Fall 2003

Instructor:      Richard Stark,  SB 172,  ext. 4371,  e-mail: rkstark@smcm.edu

Time and Place:  MWF 9:20 -10:30,  SB 134

Text: Foundations of Abstract Mathematics -- A set of notes written for this course by the St.         

                        Mary's mathematics faculty; available in class.

Content:        This is the first semester of a two-term course that will introduce you to the basic                      

                        ideas, concepts, and thought processes that underlie today's mathematics.

                        The course begins with an informal discussion of the logical foundations of mathematics.     

                        Then the terms "definition", "theorem", "proof", and "axioms" are explained and explored.        

                        The first part of the course ends with a short description of formal logic.

                        Next, set theory, relations and functions, and the concept of mathematical infinity are               

                        discussed.

                        The first semester ends with a systematic construction of the natural numbers based on       

                        Peano's axioms, followed by a description of the systems of integers, of rational                       

                        Numbers, real numbers, and complex numbers.

Classes:       There will be lectures, discussions, and working of problems.  To keep up in the course, it    

                        is important that you prepare for each class by reviewing the material covered earlier, by         

                        trying to read ahead in the text book, and by answering the study questions and working         

                        the problems.  Most of your work should be in writing -- English sentences, not just                  

                        formulas -- and you are encouraged to discuss your work with other students in the class.     

                        Occasionally, the class will split into small groups to discuss problems and work examples

                        together.  In-class quizzes should help you to keep up-to-date.

                        You are invited and should not hesitate to speak up in class.

Help:              Feel free to come to my office for help, or just for a chat.  Bring your questions and

                        discuss your problems with me.

                        Gwyneth Whieldon, an upper-division mathematics major, will be teaching assistant for this

                        class, and she is also available for help.  She will attend classes and schedule weekly help

                        sessions.

Homework:   Homework will not be collected but please turn in problems that you have worked if you          

                        are not sure about your answers or need some feedback.  Any homework problems can        

                        be discussed in class at your request.

Evaluation:    There will be a quiz every Wednesday and three tests.  Some of the quizzes will be taken  in pairs or groups of three.  For the final, you may select to take a written test or write                                                                               

                        a paper summarizing and discussing the course.

                        Quizzes -- 20%;  each test -- 20%;  final paper -- 20%.

Schedule:     Tests:  Friday, September 26;  Friday, October 31;  Friday, December 5.

                       Final exam  --  Wednesday, December 17, 9 – 11:15 a.m..