1 9193 Please contact MATHSadmin@maths.anu.edu.au for consent to enrol in this course true MATH3325 <p>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.</p><p>Topics to be covered include: </p><p>Measure theory- functions of bounded variation over R, absolute continuity and integration, examples of more general measures (Radon, Hausdorff, probability measures), Fubini-Tonelli theorem, Radon-Nikodym theorem. </p><p>Banach spaces and linear operators - classical function and sequence spaces, Hahn-Banach theorem, closed graph and open mapping theorems, and uniform boundedness principles, sequential version of Banach-Alaoglu theorem, spectrum of an operator and analysis of the compact self-adjoint case, Fredholm alternative theorem.</p><p>Note: This is an HPC. It emphasises mathematical rigour and proof and continues the development of modern analysis from an abstract viewpoint.</p> C 1 false 12616 <p>with MATH3022.</p> <p>Assessment will be based on:</p><ul><li>Three assignments (30% total; LO 1-4)</li><li>Essay paper (20%; LO 1-4)</li><li>Take home exam (50%; LO 1-4)</li></ul> 1 1 <p>On satisfying the requirements of this course, students will have the knowledge and skills to:</p>1. Explain the fundamental concepts of functional analysis and their role in modern mathematics and applied contexts<br />2. Demonstrate accurate and efficient use of functional analysis techniques<br />3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from functional analysis<br />4. Apply problem-solving using functional analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts 2 Analysis 3 Honours: Functional analysis, Spectral theory and Applications 6 6 6 <p>A mark of 60 or more in MATH3320.</p> Analysis 3 Honours Band 2 NP Mathematics u8606170 2 <p>36 lectures, tutorials by arrangement</p> 2010