- Code MATH6212
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
This course has been adjusted for remote participation in Sem 1 2021 due to COVID-19 restrictions. On-campus activities will also be available.
This course is intended both for continuing mathematics students 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.
Note: Graduate students attend joint classes with undergraduates.
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of advanced analysis such as topology and Lebeque integration 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
- Use deep knowledge and understanding of advanced analysis, such as topology and Lebesgue integration, to formulate responses to complex concrete and abstract problems.
- 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
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
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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Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.