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Unit of study_

Measure Theory and Fourier Analysis (Adv) - MATH3969

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
3x1-hr lectures; 1x1-hr tutorial/wk

Assessment
Assignments (20%), quizzes (20%); 2-hr final exam (60%),

Assumed knowledge
(MATH2921 and MATH2922) or MATH2961

Pre-requisites

A mark of 65 or greater in 12 credit points of MATH2XXX units of study

Prohibitions

MATH4069

Details

Faculty: Science

Semester 2

05 Aug 2019

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2019
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
More details
Unit of Study coordinator: Florica Cirstea
HECS Band: 2
Courses that offer this unit

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