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Final Exam (due Dec. 12):
[ps]
[pdf]
Midterm Exam- modified version posted 10/31
(due Nov. 4):
[ps]
[pdf]
Homework:
Handouts:
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List of topics (corrected 10/8): [ps]
[pdf]
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Proof that Q is not a countable intersection of open sets:
[ps]
[pdf]
~~~~~ This course covers the basic tools and techniques of real
analysis. While our primary focus is the calculus of functions on Rn,
we will also work in other settings inspired by the Real numbers. Core
topics include:
- Sequences and limits in the real line, metric spaces, and
normed linear spaces.
- Open and closed sets in Rn, continuous functions
- Compactness and its many consequences
- Convergence of sequences of functions, Weierstrass
Approximation Theorem
- Differentiation of functions from Rn to Rm.
Taylor polynomials
Additional ideas and topics will be presented as time permits.
Text: Robert Strichartz, The
Way of Analysis, revised ed. (2000)
Prerequisite: Ma 2 or equivalent or
instructor's permission. May be taken concurrently with Ma 109.
Grading: Weekly homework 50%,
midterm exam 20%, final exam 30%, instructor's discretion 2%. Late work
will only be accepted with a valid and well-documented explanation.
Collaboration Policy: You may
discuss homework problems with other students, but solutions should be
written up individually in your own words. Take-home exams must be your
own work, with outside references properly attributed.
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