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Unit of study_

Measure Theory and Fourier Analysis (Adv) - MATH3969

Year - 2018

Measure theory is the study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900. Moreover, it is the basis for modern probability theory. The course starts by setting up measure theory and integration, establishing important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. This is then applied to Fourier Analysis, and results such as the Inversion Formula and Plancherel's Theorem are derived. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Probability theory is then discussed with topics including distributions and conditional expectation.

Classes
Three 1 hour lectures and one 1 hour tutorials per week.

Assessment
One 2 hour exam, assignments, quizzes (100%)

Assumed knowledge
At least 6 credit points of (Intermediate Advanced Mathematics or Senior Advanced Mathematics units)

Pre-requisites

Credit average or greater in 12 credit points Intermediate Mathematics

Prohibitions

MATH3909

Details

Faculty: Science

Semester 2

30 Jul 2018

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2018
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
Courses that offer this unit

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