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Mathematical Sciences Institute · ANU College of Systems and Society
This course introduces the key concepts of modern abstract analysis. The philosophy of this course is that modern analysis plays a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. Topics to be covered include elementary set theory, metric spaces, sequences, uniform convergence, continuity, the contraction mapping principle, integral equations and differential equations, topological spaces. The special topic for MATH6110 students has, for example, previously included an introduction to one or more of the following topics: axiomatic set theory; the construction of the natural numbers, integers, rationals and reals; the p-adic numbers; harmonic analysis; numerical analysis; the prime number theorem. Note: This course is partially co-taught with the undergraduate course MATH2320 but will be assessed separately. Masters students will have a separate additional class each week on an additional special topic, and additional assessment item(s).
Assignments (15-22.5%)
Learning outcomes 1, 2, 3, 4
Mid semester exam (22.5%-30%)
Learning outcomes 1, 2, 3, 4
Final exam (30-37.5%)
Learning outcomes 1, 2, 3, 4
Written report or assignments on special topic.Regardless of performance on other assessment items, a minimum score of 35% on this report is required to pass the course. (This is known as a 'course hurdle'.)
Learning outcomes 1, 2, 3, 4, 5
The expected workload will consist of approximately 130 hours throughout the semester including: - Face-to face component which will consist of three 1-hour lectures each week for 12 weeks (36 hours) and ten 1-hour workshops (one each week in ten of twelve weeks) throughout the semester (10 hours). - 12 x 1 hour extension lectures per semester (12 hours). - Approximately 72 hours of self-directed study which will include preparation for lectures, workshops, assignments and exams.
No prescribed texts. Preliminary Reading - W. Rudin, Principles of Mathematical Analysis, McGraw-Hill. - J. Giles, Introduction to the Analysis of Metric Spaces, Australian Mathematical Society lecture series no. 3. - G. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill. - H. Royden, Real Analysis, Prentice-Hall, various editions. - T.W. Korner, A Companion to Analysis, American Mathematical Society.