Definitions, Proofs and Examples

**Dr Joel Feinstein, Mathematical
Sciences**

Dr Joel Feinstein is an Associate
Professor in Pure Mathematics at the University of Nottingham. After reading
mathematics at Cambridge, he carried out research for his doctorate at Leeds. He
held a postdoctoral position in Leeds for one year, and then spent two years as
a lecturer at Maynooth (Ireland) before taking up a permanent position at
Nottingham. His main research interest is in functional analysis, especially
commutative Banach algebras.

During the academic year 2011-12, Dr Joel Feinstein gave
five optional example classes to his second-year Mathematical Analysis students
on** **Definitions, Proofs and Examples. Dr Feinstein recorded videos of
these classes (presented here) to go along with his previous videos on 'How and
why we do mathematical proofs'.

These sessions are intended to
reinforce material from lectures, while also providing more opportunities for
students to hone their skills in a number of areas, including the following:

- working with formal definitions

- making deductions from information given

- writing relatively routine proofs

- investigating the properties of examples

- thinking up examples with specified
combinations of properties

**Background knowledge required:** knowledge of the relevant definitions
from Mathematical Analysis, especially in the setting of the real line,
including the following: bounded sets; interior points and open sets;
convergent sequences; continuous functions.

Dr Feinstein writes an online blog for mathematics which can be followed by using the link below

http://explainingmaths.wordpress.com/