Instructor: Richard Stark, SB 172, ext. 4371, email: richard@stark.smcm.edu

Office Hours: M-W-F 10:30 - 11:30 a.m. Other times are available upon appointment.

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.

Content: Numbers, groups, metric spaces.
The second semester begins with a construction of the natural numbers following Peano's axioms. This is followed by a brief survey of number theory. Next the integers and rational numbers are introduced as equivalence classes of pairs of natural numbers and integers. The real numbers are constructed using Dedekind cuts. Complex numbers are defined and discussed.
A discussion of geometrical symmetries, permutations, and systems of arithmetic leads us to introduce the concept of a group. Subgroups and Lagrange's theorem are presented. Normal subgroups, factor groups, and homomorphisms are introduced. The discussion culminates in proving an important homomorphism theorem.
Finally, the notion of distance is generalized and metric spaces are introduced. Open and closed sets, compact sets, and connected sets are treated and some important theorems on continuous functions are proved.

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, and by 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. Frequent quizzes should help you to keep up-to-date. Feel free to speak up and join the class discussions.

Teaching Assistant: Amber Wagner, an upper division mathematics major, will again be the teaching assistant.

Help: It is very important that you should seek help whenever you need it. Both Amber and I are freely available and invite you to seek our assistance. Regular outside-of-class help sessions will be conducted.

Homework: Homework will not be collected but turn in problems that you have worked if you are not sure about your answers or need some feedback. Homework problems will be discussed in class at your request.

Evaluation: This will be discussed in the first class meeting. Tests and quizzes should be as helpful to you as possible in your learning and understanding, and I want your opinion on the best ways to organize testing.