| MATH 281 | Foundations of Mathematics | Fall 2002 |
| Instructor: | Richard Stark SB 172 x4371, email: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. Kristine Roinestad, 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. |
| Schedule: | Tests: Friday, September 27; Friday, November 1; Friday, December 6.
Final exam -- Tuesday, December 17, 9 – 11 a.m.. |