Syllabus for Math 297 Winter Term 2019 Classes MWF 1-2:30, 3866 East Hall Instructor: Stephen DeBacker Office: 4076 East Hall Phone: 724-763-3274 e-mail:
[email protected] Office hours: DeBacker’s: M: 10:45 – 11:45am; M: 8:30 – 9:30pm; T: 2 – 3pm ; θ: 11 pm – midnight Annie’s: W: 7 – 8pm (EH3866) Problem Session: T: 4 – 5pm (EH3866) Text: Abbott, Stephen. Understanding Analysis, Second edition. Undergraduate Texts in Mathematics. Springer, New York, 2015. ISBN: 978-1-4939-2711-1.1 Philosophy: “He was not fast. Speed means nothing. Math doesn’t depend on speed. It is about deep.” (Yuriu Burago commenting on Fields Medal winner Grigory Perelman in Sylvia Nasar and David Gruber, Manifold Destiny, The New Yorker, August 28, 2006, pp. 44–57.) An Overview: It is assumed that you have acquired a solid foundation in the theoretical aspects of linear algebra (as in Math 217). This includes familiarity with how to read and write proofs; the notions of linear independence, basis, spanning sets; linear transformations; eigenvalues and eigenvectors; the spectral theorem; and basic results about inner product spaces including the Gram-Schmidt process. This is a course in analysis, the study of how/why calculus works. Over the course of the semester, we will develop an appreciation for the importance of the completeness and ordering of R. We will also learn how to read, write, and understand "–δ style arguments as we cover topics including basic topology, uniform continuity, and the properties of derivatives, definite integrals, and infinite sequences and series. To the extent possible, we will carry out our investigations in the setting of inner product spaces.