See https://www.anu.edu.au/covid-19-advice. In Sem 1 2022, this course is delivered on campus with adjustments for remote participants.
This course is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.
Topics to be covered will normally include topics from the following, with some additions and variations each year
- Measure and Integration - Lebesgue outer measure, measurable sets and integration, Lebesgue integral and basic properties, convergence theorems, connection with Riemann integration, Fubini's theorem, approximation theorems for measurable sets, Lusin's theorem, Egorov's theorem, Lp spaces, general measure theory, Radon-Nikodym theorem
- Hilbert Spaces - elementary properties such as Cauchy Schwartz inequality and polarization, nearest point, orthogonal complements, linear operators, Riesz duality, adjoint operator, basic properties or unitary, self adjoint and normal operators, review and discussion of these operators in the complex and real setting, applications to L2 spaces and integral operators, projection operators, orthonormal sets, Bessel's inequality, Fourier expansion, Parseval's equality, applications to Fourier series.
This is an Honours Pathway Course. It emphasises mathematical rigour and proof and develops modern analysis from an abstract viewpoint.
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of advanced analysis such as Lebesgue measure and integration and Hilbert space theory and their role in modern mathematics and applied contexts
- Demonstrate accurate and efficient use of advanced analysis techniques
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced analysis
- Apply problem-solving using advanced analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts.
- 5 assignments (30) [LO 1,2,3,4]
- Mid semester exam (20-30%) (30) [LO 1,2,3,4]
- Final exam (40-50%) (40) [LO 1,2,3,4]
- Precise weights to be determined in consultation with the class at first lecture. (null) [LO null]
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The expected workload will consist of approximately 130-140 hours throughout the semester including:
• Face-to face component which will consist of 12 x 3 hours lectures per semester (36 hours) and 10 hours of workshops throughout the semester.
• Approximately 80-90 hours of self-study which will include preparation for lectures, workshops, assignments and exams.
To be determined.
Requisite and Incompatibility
No prescribed text.
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
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Offerings, Dates and Class Summary Links
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