Math 290 -- Foundations of Mathematics -- Spring 1999

Place: Science and Technology II Room 15

Time: Tuesday/Thursday: 3:00 - 4:15

Text: Mathematical Thinking by John D'Angelo and Douglas West

Instructor: Michael R. Gabel, Department of Mathematical Sciences: Science and Technology I, Room 241

Phones:

E-Mail: mgabel@gmu.edu or mgabel@osf1.gmu.edu

Office Hours: Tuesday/Thursday 2:00 - 2:45 and by appointment

Material Covered: We will cover much of Chapters 1 through 8 and parts of Chapters 13 (and 14, if possible).

Philosophy of the Course: Courses of this type serve as a transition to mathematics in the sense that, for many students, this will be the first course where they will be asked to understand and create proofs. The course is foundational in two senses: not only will the course help to bring about this transition, but also the material itself is about basic/foundational topics: set theory, logic, induction, properties of numbers (from the integers to the real numbers). Chapters 13 (and 14) are more advanced, and start the process of a careful creation of calculus.

Now, just because this course is foundational, that does not mean it is easy, for, prior to this course, your success in mathematics has generally been measured by assessing your computational, manipulative, and memorization skills. In this course, success will be measured by the assignment of the correctness and coherence of your arguments (proofs). Additionally, even though the topics are foundational, parts the material may seem deceptively easy. But, in fact, a solid understanding of many of these foundational ideas has been developing over the centuries (even over the millennia), and, thus clearly must be rather subtle. In fact, we will brush aside, even in this foundational course, some of the more deeper subtleties of the structure of mathematics, which are covered at the advanced undergraduate or graduate level.

Final Exam: All or part of this final exam may be take-home. The take-home component will be due at 1:30 pm on Tuesday, May 18, 1999. The "in-class" part of the final, if there is one, will be on Tuesday, May 18, 1999 from 1:30 to 4:15.

Homework: Homework will be assigned each day. Students will keep homework notebooks, which will be collected and reviewed periodically.

Exams/Quizzes: In addition to the final exam, there will be two (possibly three) exams, components of which may be take-home. There may be several in-class quizzes.

Presentations: Each student will present to the class one (perhaps two) proofs of theorems coming either from our text (most likely) or from other sources. It may be that some of the presentations will be by pairs of students.

Grades: The final grade will be based on the exams, (any) quizzes, your class presentation(s), and, particularly, the final exam. Performance on homework will be used to decide borderline grades. The final exam will be worth approximately 35% of your grade.

Honor Code: Except when explicitly stated to the contrary, all work is to be your own work.

NOTE: If you feel you must miss an exam or other graded assignment due to illness or other problem, you must notify me in person (or via the telephone) before the exam in order to determine what (if any) make-up procedure will be used. Alone, an e-mail correspondence is not sufficient.

DROP DATE: (without a Dean's permission): 5 pm February 26, 1999