MATH343-21S1 (C) Semester One 2021

Metric, Normed and Hilbert Spaces

15 points

Start Date: Monday, 22 February 2021
End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 7 March 2021
  • Without academic penalty (including no fee refund): Friday, 14 May 2021


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


Timetable 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 11:00 - 12:00 John Britten 117 HP Seminar Room 22 Feb - 4 Apr
26 Apr - 6 Jun
Lecture B
Activity Day Time Location Weeks
01 Monday 09:00 - 10:00 John Britten 117 HP Seminar Room 22 Feb - 4 Apr
26 Apr - 6 Jun
Tutorial A
Activity Day Time Location Weeks
01 Friday 13:00 - 14:00 Psychology - Sociology 213 22 Feb - 4 Apr
26 Apr - 6 Jun
02 Friday 10:00 - 11:00 Jack Erskine 121 22 Feb - 4 Apr
26 Apr - 6 Jun

Course Coordinator / Lecturer

Ngin-Tee Koh


Christopher Price


Assessment Due Date Percentage 
Tutorials 16%
Test 28%
Final Examination 56%

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 $788.00

International fee $4,438.00

* 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.

All MATH343 Occurrences

  • MATH343-21S1 (C) Semester One 2021