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An introduction to those parts of modern analysis essential for many aspects of pure and applied mathematics, physics, economics and finance.
An introductory course into the parts of modern mathematics that arise from the idea of distance in finite and infinite dimensions. It is useful in understanding numerical algorithms, the basis of calculus, approximation methods, and the theoretical underpinnings of quantum mechanics and theoretical economics.MATH343 provides useful background material for many 400-level courses, including Approximation Theory, Hilbert Spaces, Dynamical Systems, Fourier Transforms & Distribution Theory, and Topology.
This course will:develop metric space theory and its applications including convergence, open and closed sets, completeness, and compactnesslook at standard infinite dimensional spaces and the similarities and differences between them and finite dimensional spacesintroduce normed and Hilbert spaces
30 points from MATH201, MATH202, MATH203, MATH240, MATH270, EMTH210, EMTH211 orEMTH271.
Students must attend one activity from each section.
Recommended reading: • William F. Trench, Introduction to Real Analysis. This is an excellent real analysis text put in the public domain by its author Prof. William Trench. • Satish Shirali and Harkrishan L. Vasudeva, Metric Spaces, Springer, 2006. • Graeme Cohen, A course in Modern Analysis and its Applications, Cambridge University Press, 2003. • W. Rudin, Principles of Mathematical Analysis, McGraw-Hill.
General information for students
Domestic fee $780.00
International fee $4,250.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.