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Functional analysis is one of the major areas of modern mathematics. It can be thought of as an infinite-dimensional generalisation of linear algebra and involves the study of various properties of linear continuous transformations on normed infinite-dimensional spaces. Functional analysis plays a fundamental role in the theory of differential equations, particularly partial differential equations, representation theory, and probability. In this unit you will cover topics that include normed vector spaces, completions and Banach spaces; linear operators and operator norms; Hilbert spaces and the Stone-Weierstrass theorem; uniform boundedness and the open mapping theorem; dual spaces and the Hahn-Banach theorem; and spectral theory of compact self-adjoint operators. A thorough mechanistic grounding in these topics will lead to the development of your compositional skills in the formulation of solutions to multifaceted problems. By completing this unit you will become proficient in using a set of standard tools that are foundational in modern mathematics and will be equipped to proceed to research projects in PDEs, applied dynamics, representation theory, probability, and ergodic theory.
Study level | Undergraduate |
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Academic unit | Mathematics and Statistics Academic Operations |
Credit points | 6 |
Prerequisites:
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None |
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Corequisites:
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None |
Prohibitions:
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None |
Assumed knowledge:
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Real Analysis and abstract linear algebra (e.g., MATH2X23 and MATH2X22 or equivalent), and, preferably, knowledge of Metric Spaces |
At the completion of this unit, you should be able to:
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
Session | MoA ? | Location | Outline ? |
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Semester 1 2024
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Normal day | Camperdown/Darlington, Sydney |
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Session | MoA ? | Location | Outline ? |
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Semester 1 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Session | MoA ? | Location | Outline ? |
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Semester 1 2020
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2021
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2021
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Normal day | Remote |
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Semester 1 2022
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2022
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Normal day | Remote |
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Semester 1 2023
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2023
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Normal day | Remote |
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This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.