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Mathematical Sciences Institute · ANU College of Systems and Society
Analysis 1 is a foundational course in Mathematics, leading on to other areas of analysis, such as topology and measure theory, complex analysis, functional analysis, and harmonic analysis. It also provides important tools for application areas such as theoretical computer science, physics, 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. Note: This is an Honours Pathway Course : It emphasises mathematical rigour and proof and develops the application of the theory to topics such as differential equations.
Regular written assignments (20-30%)
Learning outcomes 1, 2, 3, 4
Mid semester exam (30-40%)
Learning outcomes 1, 2, 3, 4
Final exam (40-50%)
Learning outcomes 1, 2, 3, 4
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). - Approximately 84 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.