Login

iTunes U albums

Album: Foundations of Pure Mathematics

32 tracks

Mathematics-fpm14

Description: 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 first-year honours mathematics university students. However, pre-university 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/

Keywords: pure mathematics, relations, functions, countable and uncountable sets, set theory, binomial coefficients Category: Mathematics Subcategory: Mathematics

Copyright: Copyright (c) University of Nottingham Language: en Explicit: no

Author: The University of Nottingham Owner: The University of Nottingham Owneremail: itunesu@nottingham.ac.uk

Web page: http://www.nottingham.ac.uk/mathematics

Image: http://itunesu.nottingham.ac.uk/media/Mathematics/FoundationsofPureMathematics/images/mathematics-FPM14.jpg

Thumbnail: http://itunesu.nottingham.ac.uk/media/Mathematics/FoundationsofPureMathematics/images/mathematics-FPM14.jpg

Feed URLs: RSS: http://itunesu.nottingham.ac.uk/albums/125.rss, Atom: http://itunesu.nottingham.ac.uk/albums/125.atom

Back to albums

Tracks

Mathematics-fpm14 Introduction to Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Sets and Numbers - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 1: About this module - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Definitions and Direct Proofs - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Rational numbers, irrational numbers and indirect proofs - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 2 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Rational numbers and irrational numbers: further results- Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Bezout's Lemma and Prime Factorization - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 3 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Sets and subsets - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Cartesian Products and Relations - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 4 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Equivalence Relations and Equivalence Classes - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Unions and Partitions - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 5 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Equivalence Classes and Modular Arithmetic - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Decimal expansions and rational numbers - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 6 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Functions and their graphs - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Functions and sets - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 7 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Properties of functions - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Finite sets and cardinality - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 8 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Permutations of finite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Permutations continued - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 9 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Cardinality for infinite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Conclusion of Cardinality for infinite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Countability and uncountability - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Workshop 10 - Foundations of Pure Mathematics - Dr Joel Feinstein
Mathematics-fpm14 Discussions of Class Test 2 - Foundations of Pure Mathematics - Dr Joel Feinstein