MATH343-18S1 (C) Semester One 2018

Metric, Normed and Hilbert Spaces

15 points

Details:
Start Date: Monday, 19 February 2018
End Date: Sunday, 24 June 2018
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 4 March 2018
  • Without academic penalty (including no fee refund): Sunday, 20 May 2018

Description

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.

Learning Outcomes

  • This course will:
  • develop metric space theory and its applications including convergence, open and closed sets, completeness, and compactness
  • look at standard infinite dimensional spaces and the similarities and differences between them and finite dimensional spaces
  • introduce normed and Hilbert spaces

      • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Prerequisites

Course Coordinator / Lecturer

Rick Beatson

Lecturer

Christopher Price

Assessment

Assessment Due Date Percentage 
Tutorials 10%
Test 35%
Final Examination 55%

Textbooks / Resources

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.

Indicative Fees

Domestic fee $749.00

International fee $3,788.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH343 Occurrences

  • MATH343-18S1 (C) Semester One 2018
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