Syllabus
MATH 281			   Foundations of Mathematics                        Fall 2001


Instructor:	Richard Stark,  SB 172,  ext. 4371,  e-mail: richard@stark.smcm.edu
		Other members of the mathematics faculty may also participate.

Time/Place:  	MWF 9:20 -10:30,  SB 161

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 should 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 and of rational 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 offfice for help, or just for a chat.  Bring your questions
		and discuss your problems with me. 
		Amber Wagner, 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.  All homework problems 
		can be discussed in class at your request.

Evaluation:	There will be (very) frequent unannounced quizzes, some to be taken in pairs or
		groups of three persons, and three tests.  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:	Dates for the tests will be announced in class.
		Final exam  --  Monday December 10, 9:00 - 11:00 a.m.