Leeds University Library

Module Reading List

Linear Analysis 1, 2017/18, Semester 1
Dr Vladimir Kisil
Tutor information is taken from the Module Catalogue

W. Rudin, Real and complex analysis , McGraw-Hill, 1987.  This books covers some of the analysis you should already know, as well as much of this course and its partner, MATH5016.

W. Rudin, Functional analysis , McGraw-Hill, 1991.  This book is good for both parts of the course (that is, MATH5016 as well) but is written at quite a high level, and contains (much) more than you need.

D. Cohn,Measure theory, Birkhauser, 1980.  This book covers the measure theory part of the course, and goes much further than the course does.

A. Weir, "Lebesgue integration and measure" - This is a nicely paced book which carefully develops the theory of the Lebesgue integral on the line. Our course goes further than this, but will heavily use the Lebesgue integral as an example.

W. Rudin, "Principles of mathematical analysis." - This would be a good book to revise the basics which are assumed by this course. The final chapter deals with Lebesgue integration in a nicely motivated way.

B. Rynne, M. Youngson, "Linear functional analysis" - This covers much of the Banach space side of the course in a careful, motivated manner. It assumes that you know some measure theory, but those sections could be skipped on a first reading.

B. Bollobas, "Linear analysis: an introductory course" - This is a classic, but goes much beyond the course. The first few chapters are most appropriate.  Only covers the abstract Banach space side of the course, but also useful for MATH5016.

E. Kreyszig, "Introductory Functional Analysis With Applications" - This is a classic, and goes much beyond the course. Chapters 1, 2 and 4 are most appropriate. Many people recommend this book, but personally, I find it hard to read and rather verbose.

This list was last updated on 28/07/2009