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Final Exam: [pdf]
[ps]
Midterm Exam due 5:00
pm on Nov. 3: [pdf]
[ps]
Homework:
~~~~~ The first term of Math 110 will cover a variety of topics in
Real
Analysis. In many cases we will revisit familiar ideas from a previous
course and present them at a greater level of generality. A tentative
order of presentation is listed below, however this is subject to
amendment and alteration at any time.
Lebesgue integration with respect to measures on a sigma-algebra.
Hölder and Minkowski's inequalities, convergence theorems, properties of the
space Lp(dμ).
Fourier series on the unit circle. Convolution and approximate identities,
density of trigonometric polynomials, Plancherel's theorem.
Linear maps between normed vector spaces. Weak-star topologies, Dual spaces,
Hahn-Banach theorem, Riesz representation theorem and signed measures. Baire
category theorem and its consequences.
Differentiation of rough functions and measures. Radon-Nikodym
theorem,maximal functions and the Lebesgue differentiation theorem.
Textbook: Real Analysis: Modern Techniques and their Applications,
second edition, by Gerald Folland. (required)
Grading: 50% weekly homework, 20% midterm exam, 30% final exam, 2%
round-off errors. Late work will be accepted only with a well-documented
explanation.
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