MATH6110 Analysis 1: Metric spaces and Applications

Offered By	Department of Mathematics
Academic Career	Graduate Coursework
Course Subject	Mathematics
Offered in	First Semester, 2009 and First Semester, 2010
Unit Value	6 units
Course Description	This course introduces the key concepts of modern real analysis. The philosophy of this course is that modern analysis play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. Topics to be covered include: Review of the real number system The foundations of calculus Elementary set theory Metric spaces Sequences, series and power series Uniform convergence Continuity The contraction mapping principle Foundations of multidimensional calculus Applications to the calculus of variations Integral equations Differential equations. Note: Graduate students attend joint classes with undergraduates but are assessed separately. This course will have shared lectures with MATH2320 and MATH 3116 but will have different tutorials and assessment which will emphasize the application of techniques.
Learning Outcomes	On satisfying the requirements of this course, students will have the knowledge and skills to: 1. Explain the fundamental concepts of real analysis and their role in modern mathematics and applied contexts 2. Demonstrate accurate and efficient use of real analysis techniques 3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from real analysis 4. Apply problem-solving using real analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts
Indicative Assessment	Assessment will be based on: Tutorials (10%; LO 1-4) Assignments (10%; LO 1-4) Mid-semester exam (30%; LO 1-4) Final exam (50%; LO 1-4)
Course Classification(s)	AdvancedAdvanced courses are designed for students having reached 'first degree' level of assumed knowledge, which provide a deep understanding of contemporary issues; or 'second degree' and higher levels of knowledge; or for transition to research training programs. and SpecialistSpecialist courses are designed for students having reached 'first degree' level of assumed knowledge, which provide for the acquisition of specialist skills; or 'second degree' and higher level of knowledge; or for transition to research training programs; or knowledge associated with professional accreditation.
Areas of Interest	Mathematics
Eligibility	Bachelor degree; with first year Mathematics.
Requisite Statement	First year Mathematics is required.
Consent Required	Departmental consent is required to enrol in this course.
Programs	Master of Mathematical Sciences
Academic Contact	Dr Ben Andrews

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