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Measure Theory & 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. Probability Theory is then discussed, with topics including independence, conditional probabilities, and the Law of Large Numbers.

Unit of study details

Unit of study level: Senior

Credit points: 6

Commencing semesters: 2

Further unit of study information

Unit of study handbook: MATH3969

Costs and scholarships information: Costs and Scholarships

Final dates to withdraw from units of study: Census Dates

Available for study abroad and exchange: Yes

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