MHF 4203/5207 Foundations of Mathematics: Syllabus

Course content:   The course covers fundamental principles of set theory. In it you will investigate the behavior of sets, relations and functions. Particular topics include the language and axioms of set theory, Boolean algebras, equivalence relations, orderings, ordinals, cardinals, the Axiom of Choice, other transfinite existence principles and the arithmetic of the infinite. The Axiom of Choice and its equivalent formulations are important particularly in topology and the study of the real line. Transfinite induction arguments and arguments based on cardinality are used in many branches of mathematics, including algebra, analysis and topology.

Instructional format:   The course will be taught seminar style, which means that the students will present (with guidance from the instructor) most of the material covered. The notes for the class include a list of more that one hundred problems whose solutions form the subject matter of the class. Students, working alone or in groups, will solve these problems and present them in class.

Exams and Grading:   There will be three 25-point exams during the term, and a final examination worth 25 points. In each test you are responsible for material covered up to that point. At the end of the term the lowest score from the three midterms and the final will be dropped in computing the final grade. There will be three Work Grades based on participation, homework, group work, and/or quizzes. Regular attendance is essential, and daily records of attendance and participation will be kept. The totals wi11 be scaled to 8, 8, and 9 points respectively. Makeup exams for medical reasons must have documentation. Makeups for other reasons will not be given except by agreement with the instructor arranged prior to the date of the exam.

Important Notes:

1. Please come on time to class prepared. Be kind to one another as you present material at the board and ask and answer questions so that all will benefit.
2. Your written work should be neat and show all steps.
3. You may study together, but you should be prepared to do problems on your own for quizzes and tests.
4. If you miss class, you are responsible for finding about homework and/or announcements made during the class. No late homework will be accepted; no makeup quizzes will be given.
5. If you have special needs or need to be excused from class for religious reasons, please let me know in the first two weeks of class.

6. You are expected to follow the Student Honor Code adopted by the Student Body:

   We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.

   Specifically, you are expected to refrain from cheating, to stop others from using your work to cheat, to be clear about giving credit to others rather than plagarizing, and to make only fair use of copyrighted materials and software.

7. Before requesting a classroom accommodation, you must first register with the Disability Resource Center of the Dean of Students Office. The Dean of Students Office will then provide documentation for you to give me when requesting an accommodation. Early notice will enable us to better serve you.
8. You are expected to abide by all University, College and Mathematics Department policies (see http://www.math.ufl.edu/~jal/c/mhfset/policies.html for details).