
Lecture Description
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 for download on iTunes U at: itunes.apple.com/us/itunes-u/foundations-pure-mathematics/id950755120
Dr Feinstein's blog may be viewed at: explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.
Course Index
- Introduction to Pure Mathematics
- Sets and Numbers
- Workshop 1: About this module
- Definitions and Direct Proofs
- Rational and Irrational Numbers
- Workshop 2
- More on Rational and Irrational Numbers
- Bezout's Lemma and Prime Factorization
- Workshop 3
- Sets and Subsets
- Cartesian Products and Relations
- Workshop 4
- Equivalence Relations and Equivalence Classes
- Unions and Partitions
- Workshop 5
- Equivalence Classes and Modular Arithmetic
- Decimal expansions and rational numbers
- Workshop 6
- Functions and their graphs
- Functions and sets
- Workshop 7
- Properties of functions
- Finite sets and cardinality
- Workshop 8
- Permutations of finite sets
- Permutations continued
- Workshop 9
- Cardinality for infinite sets
- Conclusion of Cardinality for infinite sets
Course Description
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