Mathematics 381 - TOPICS IN ANALYSIS

Topics course. The analysis of the real line, begun in MTH 243 is developed further here, starting with Lebesgue's theory of measure. Our intuition leads us to statements (some ancient, some less than a year old) that are paradoxical. Attempts to resolve the paradoxes leads us to statements that can be neither proved nor disproved. This in turn leads us to alternatives to the standard real line, both smaller (the constructive numbers) and larger (the hyperreal numbers, the surreal numbers). Prerequisite: MTH 243

Topic: Lebesque measure, the Banach-Tarski paradox, Axioms of Choice and Determinancy, and analysis with Nelson's Internal Set Theory.