MATH343-20S1 (C) Semester One 2020

Metric, Normed and Hilbert Spaces

15 points

Details:
Start Date: Monday, 17 February 2020
End Date: Sunday, 21 June 2020
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 28 February 2020
  • Without academic penalty (including no fee refund): Friday, 29 May 2020

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

Pre-requisites

Timetable 2020

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Monday 10:00 - 11:00 Online Delivery (23/3, 4/5-25/5)
E12 (17/2-16/3)
17 Feb - 29 Mar
4 May - 31 May
Lecture B
Activity Day Time Location Weeks
01 Wednesday 13:00 - 14:00 - (25/3, 22/4)
Online Delivery (29/4-27/5)
E16 Lecture Theatre (19/2-18/3)
17 Feb - 29 Mar
20 Apr - 31 May
Tutorial A
Activity Day Time Location Weeks
01 Tuesday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 26 Apr
02 Tuesday 10:00 - 11:00 Rehua 329 17 Feb - 5 Apr

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Thursday 08:00 - 20:00 20 Apr - 26 Apr

Course Coordinator / Lecturer

Ngin-Tee Koh

Lecturer

Christopher Price

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 $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.

All MATH343 Occurrences

  • MATH343-20S1 (C) Semester One 2020