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Area/Catalogue
MATH 3026

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Course Level
Undergraduate

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Offered Externally
No

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Course ID
101192

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Unit Value
4.5

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University-wide elective course
No

Course owner

Course owner
School of Information Technology and Mathematical Sciences

Course aim

To discuss selected key theorems of mathematical analysis. The discuss should include the history of the theorems, their motivation, their impact on the systematic development of mathematical notation, their rigorous proof and their contribution to the study of particular topics.

Course content

Classical Abstract spaces in Modern Functional Analysis: Topological spaces, Metric spaces, Normed Vector spaces, Space of Lebesgue Measurable Functions, and Hilbert spaces; Fundamental Theorems of Analysis: Hahn-Banach Theorem, Uniform Boundedness Theorem, The Open Mapping Theorem. Dual Spaces: Weak and Weak* topology, Riesz’s Representation Theorem, Closed Graph Theorem, Adjoint Operators in Hilbert spaces, Lp spaces. Differential Calculus in Normed Vector Spaces: Differentiability of functionals (Gateaux and Frechet differentiability).

Textbook(s)

Kurdila, AJ & Zabarankin, M 2005, Convex Funtional Analysis, Birkauser

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number Course Name
MATH 2027 Fundamentals of Real Analysis

Corequisite(s)

Nil

Teaching method

Component Duration
INTERNAL, MAWSON LAKES
Lecture 3 hours x 13 weeks
Tutorial 1 hour x 13 weeks
Directed Study N/A x N/A

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.


Assessment

Task Length Weighting Duration
INTERNAL, MAWSON LAKES
Assignment 1 1250 word equivalent 15% N/A
Assignment 2 1250 word equivalent 20% N/A
Examination 2000 word equivalent 65% N/A

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
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Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation

Course Coordinators

School of Information Technology and Mathematical

Degrees this course is offered in

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