MATH2320 Analysis 1 Honours: Metric Spaces and Applications

Later Year Course

Offered By	Department of Mathematics
Academic Career	Undergraduate
Course Subject	Mathematics
Offered in	First Semester, 2009 and First Semester, 2010
Unit Value	6 units
Course Description	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: 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 and differential equations. Note: This course will have shared lectures with MATH3116 but will have different tutorials and assessment which will emphasise the application of techniques. Note: This is an HPC. It emphasises mathematical rigour and proof and develops the application of the theory to topics such as differential equations and the proofs of major theorems in multivariable calculus.
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)
Areas of Interest	Mathematics
Requisite Statement	A mark of 60 or more in MATH1021 or MATH1116.
Incompatibility	MATH2021 and MATH3116.
Consent Required	Departmental consent is required to enrol in this course.
Science Group	B
Academic Contact	Dr Ben Andrews

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