Can the infinite be tamed? Many people say that the human mind cannot comprehend the infinite. From Zeno to Bertrand Russell, mathematicians and philosophers who have tried have been plunged into paradox. This course moves from philosophical perplexity about such paradoxes to mathematical theories of the infinite. Mathematics provides a microcosm for central issues of epistemology and metaphysics. Is there a reality independent of thought? Can humans know anything with certainty, and if so, how? Is knowledge confined to the senses, or is reason a source of knowledge? Course inquiry is informed by mathematical theorizing, developing techniques of abstraction, definition, proof, and calculation. Affiliate department: Philosophy.
Prerequisites: Strong background in high school mathematics, including successful completion of a pre-calculus course.