Foundations of Pure Mathematics University of Nottingham

 Courses

This module provides a foundation for all subsequent modules in Pure Mathematics. All of Pure Mathematics is written in the language of sets, functions and relations, and a large part of the module is devoted to gaining familiarity with both reading and writing this language.There will be an introduction to some basic counting principles, and the most important number systems will be introduced. Along the way, a variety of useful and interesting facts will be discussed. The module will include formal proofs and students will be given practice in writing proofs themselves. Topics to be covered will include:
• counting problems, binomial coefficients;
• the language of set theory;
• relations and functions;
• countable and uncountable sets.
This module is aimed at firstyear honours mathematics university students. However, preuniversity students (including keen GCSE students) may find that much of the material is accessible.
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. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.
See also Dr Feinstein's blog http://explainingmaths.wordpress.com/

 video
Introduction to Foundations of Pure Mathematics  Dr Joel Feinstein
Motivation for pure mathematical thinking (definitions, proofs and examples) illustrated by looking at
some introductory puzzles, with voting.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. 
 video
Sets and Numbers  Foundations of Pure Mathematics  Dr Joel Feinstein
The second class in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers Sets and their elements. Number systems. Elementary reasoning using examples and counterexamples.Various ways to specify sets, and simplifying their descriptions. Intervals and number line sketches.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. 
 video
Workshop 1: About this module  Foundations of Pure Mathematics  Dr Joel Feinstein
The first workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module is a detailed look at some extracts from the Module Information Document including:
Module aims and learning outcomes.
The importance of understanding and being able to demonstrate. understanding of the material.
Likely style of exam questions.
The importance of looking at the feedback on student performances in the last two years' exams.
What you need to do if you want to do well in this module, rather than just passing it.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. 
 video
Definitions and Direct Proofs  Foundations of Pure Mathematics  Dr Joel Feinstein
The third lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers an introduction to formal definitions and direct proofs, with discussion, motivation and examples. The dangers of backwards logic.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. 
 video
Rational numbers, irrational numbers and indirect proofs  Foundations of Pure Mathematics  Dr Joel Feinstein
The fourth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers Highest Common Factor (HCF, also known as Greatest Common Divisor, GCD) for integers, and lowest terms for rational numbers.
How and why indirect proof (proof by contradiction) works. Examples of indirect proofs, including the proof that the square root of two is irrational.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. 
 video
Workshop 2  Foundations of Pure Mathematics  Dr Joel Feinstein
The second workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet based on working with definitions. Questions involving sums of subsets of the real line, set inclusions and set equalities. These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_kBzsKBqQHEqD6WVLIHSNuXa
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.