Unit of study_

# Measure Theory and Fourier Analysis - MATH4069

Year - 2020

Measure theory is the study of fundamental ideas as length, area, volume, arc length and surface area. It is the basis for Lebesgue integration theory used in advanced mathematics ever since its development in about 1900. Measure theory is also a key foundation for modern probability theory. The course starts by establishing the basics of measure theory and the theory of Lebesgue integration, including important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. These ideas are applied to Fourier Analysis which leads to results such as the Inversion Formula and Plancherel's Theorem. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Key ideas of this theory are applied in detail to probability theory to provide a rigorous framework for probability which takes in and generalizes familiar ideas such as distributions and conditional expectation. When you complete this unit you will have acquired a new generalized way of thinking about key mathematical concepts such as length, area, integration and probability. This will give you a powerful set of intellectual tools and equip you for further study in mathematics and probability.

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

Assessment
2 x quiz (20%), 2 x written assignment (20%), final exam (60%)

Assumed knowledge
(MATH2921 and MATH2922) or MATH2961

Pre-requisites

(A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from the following units (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)]

Prohibitions

MATH3969

### Details

Faculty: Science

Semester 2

03 Aug 2020

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2020
Unit of study level: Honours
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: Dr Leo Tzou
HECS Band: 2
##### Courses that offer this unit

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