Analysis - MATH701
This unit provides an advanced introduction to the key areas of research interest in modern analysis. We will study Lebesgue integration, positive Borel measures, and the all important function spaces Lp. Then we will study the elementary Hilbert space theory and Banach space techniques. This will provide familiarity with some of the major theorems which make up the analysis toolbox: Monotone and Dominated Convergence theorems; Fatou's lemma; Egorov's theorem; Lusin's theorem; Radon-Nikodym theorem; Fubini-Tonelli theorems about product measures and integration on product spaces; Uniform Boundedness; Fundamental Theorem of Calculus for Lebesgue Integrals; Minkowski's Inequality; Holder's Inequality; Jensen's Inequality; and Bessel's Inequality.
| Credit Points: | 4 |
| When Offered: | S1 Day - Session 1, North Ryde, Day |
| Staff Contact(s): | Mathematics staff |
| Prerequisites: |
Admission to MRes |
| Corequisites: | |
| NCCW(s): | |
| Unit Designation(s): | |
| Assessed As: | Graded |
| Offered By: | Department of Mathematics Faculty of Science and Engineering |
Course structures, including unit offerings, are subject to change.
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