Dr. Robert Brabenec's Schedule
Monday, November 9, 2009
9:00 - 9:50 a.m., Mercer 133: "Cantor's Theory of the Infinite"
Noon - 1:45 p.m., Dining Hall: Lunch conversations with students and faculty
2:00 - 2:50 p.m., Mercer 133: "Some Important Algebraic Structures"
7:30 p.m., Library First Floor: “An Historical Overview of Mathematics”
Mathematics has developed within the context and through the influence of many other parts of our culture. The lecture paints a broad picture of the development of mathematics during the previous four and one-half centuries, including its interactions with other disciplines.
Tuesday, November 10, 2009
11:30 - 1:30: Rhea County Room: Lunch conversation--philosophy of mathematics
4:15 p.m., Mercer 242: “The Axiomatic Method”
The axiomatic method has become the basis of modern mathematics, yet even math majors are not usually aware of its significance. Using a simple example like the axioms for a group, we discuss the meaning of consistency, completeness, dependence, and independence of axioms along with the use of models to establish some of these results. The meaning of non-Euclidean geometry becomes clearer when we identify the need to show that the parallel postulate is independent. The question of whether Christ’s parables can be considered as axiom systems can be discussed. Other examples can be included, such as how we obtain the identities for the exponential or logarithmic functions or how we choose the axioms to measure such diverse quantities as area of a region, cardinal number of a set, or the Lebesgue measure of a set. Gödel’s theorem can be viewed as a statement about consistency and completeness of a general axiom system.
7:30 p.m., Library First Floor: “Thinking Philosophically about Mathematics”
The prevailing 1880 - 1930 mathematics philosophies were developed mainly in response to questions raised by Cantor’s theory of the infinite. But individuals have thought philosophically about mathematics throughout history. This talk will survey the ideas of people like Plato, Pythagoras, Augustine, Descartes, Pascal, Leibniz, Berkeley, and Kant. The philosophy of mathematics has again become an area of interest to mathematicians during the past few decades.
Wednesday, November 11, 2009
11:00 a.m., Rudd Auditorium: “Connecting Mathematics with a Christian Perspective”
A popular misconception is that one’s philosophical or religious stance cannot have or should not have any bearing on his or her methodology, view of, or use of mathematics. A little digging into foundational questions, however, reveals that mathematics—just as any other area of intellectual endeavor—is shot through with presuppositions and assumptions that are not justified or verified by mathematics itself. This talk looks specifically at the interface between mathematics and Christianity.