MAT 3120 (Fall 2010)

Analysis III

About The Course

This is a course in abstract analysis. Our general setting will be that of a metric space. A metric space is a set with a notion of distance that satisfies certain natural properties. Examples include the real numbers (or Rn in general), normed vector spaces, and various spaces of functions. We will discuss mappings between metric spaces as well as their topology. We will also investigate convergence of sequences in metric spaces.

Official Course Description

Real numbers; completeness properties. Metric spaces; compactness and connectedness, continuous functions. Contraction mappings. Sequences and series of functions; modes of convergence, power series. Topics on function spaces such as: Weierstrass approximation, Fourier series and L2 spaces.

Prerequisites

MAT 2121 (Analysis II).

Course Text

Official course text:

  • Graeme L. Cohen, A Course in Modern Analysis and its Applications, Cambridge University Press, 2003. ISBN: 9780521526272.

This book can be purchased at the University Bookstore. An electronic version is also available for purchase here (for less than the hard copy).

Other useful resources:

Students looking for additional references are advised to look at the following texts.

  • Kenneth R. Davidson and Allan P. Donsig, Real Analysis and Applications, Springer, 2009. ISBN: 9780387980973. From on-campus computers, this text available for free download here.
  • Mícheál Ó Searcóid, Metric Spaces, Springer, 2006. ISBN: 9781846283697. From on-campus computers, this text is available for free download here.

For students interested in French textbooks, the following are recommended. They can be purchased from amazon.fr (they will be shipped from Europe and so will take a week or two to arrive).

  • Guy Auliac et Jean-Yves Caby, Mathématiques pour la Licence – 3e année. Tome 2 : Topologie et Analyse, Éditions Dunod, 2005. ISBN: 9782100483334. Purchase here.
  • Georges Skandalis, Mathématiques pour la licence - 3e année. Tome 3: Topologie et Analyse, Éditions Dunod. ISBN: 9782100488865. Purchase here.

Course Outline

A more detailed syllabus can be found here.

Course Webpage

There are two main online locations for information regarding the course:

  • https://alistairsavage.ca/mat3120. This is the course home page. It will be updated regularly and contains important material for the course. Announcements will also be posted here.
  • Virtual Campus. Students can access their grades via Virtual Campus.