Foundations of Pure Mathematics

By The University of Nottingham

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... more

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FAQs about Foundations of Pure Mathematics:

How many episodes does Foundations of Pure Mathematics have?

The podcast currently has 31 episodes available.

Foundations of Pure Mathematics episodes:

February 18, 2015 Workshop 7 - Foundations of Pure Mathematics - Dr Joel Feinstein
The seventh workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with a variety of questions: questions involving decimal expansions; modular arithmetic: squares and fourth powers modulo 5; finding an example of a function with specified properties.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa 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.
...more
27min
February 18, 2015 Functions and sets - Foundations of Pure Mathematics - Dr Joel Feinstein
The fourteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers set-valued functions. Images and preimages (inverse images) of sets under functions: definitions, notation and example.
Definition and examples of composition of functions. Associativity of function composition.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
45min
February 18, 2015 Functions and their graphs - Foundations of Pure Mathematics - Dr Joel Feinstein
The thirteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers Informal definition of function, along with associated notation and terminology, including domain, codomain, argument, value, and notation.
Definition of the graph of a function, with notation and examples.
Formal definition of function (Bourbaki approach).
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
41min
February 10, 2015 Workshop 6 - Foundations of Pure Mathematics - Dr Joel Feinstein
The sixth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with questions involving relations, equivalence relations, and modular arithmetic. In particular, looking at squares modulo 7, and applying this to show that a certain equation has no integer solutions.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa 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.
...more
29min
February 10, 2015 Decimal expansions and rational numbers - Foundations of Pure Mathematics - Dr Joel Feinstein
The twelfth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers notation for recurring decimal expansions. Real numbers with more than one decimal expansion. Real numbers have recurring/terminating decimal expansions if and only if they are rational.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
50min
February 10, 2015 Equivalence Classes and Modular Arithmetic - Foundations of Pure Mathematics - Dr Joel Feinstein
The eleventh lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers the connection between equivalence relations, equivalence classes and partitions of sets. An introduction to modular arithmetic, especially modulo 2, modulo 9 and modulo 11.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
51min
February 03, 2015 Workshop 5 - Foundations of Pure Mathematics - Dr Joel Feinstein
The fifth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers applications of the Fundamental Theorem of Arithmetic. These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa 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.
...more
32min
February 03, 2015 Unions and Partitions - Foundations of Pure Mathematics - Dr Joel Feinstein
The tenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers sets of subsets of a set. Unions of indexed collections of sets. Definition and examples of partitions of sets.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
42min
February 03, 2015 Equivalence Relations and Equivalence Classes - Foundations of Pure Mathematics - Dr Joel Feinstein
The ninth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers definitions and examples of equivalence relations, especially congruence modulo k.
Brief discussion of equivalence classes (revisited in more detail in Lecture 11)..
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
46min
January 30, 2015 Sets and subsets - Foundations of Pure Mathematics - Dr Joel Feinstein
The seventh lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers sets, subsets and set inclusions. Unions, intersections and differences of sets. De Morgan’s laws.
These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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.
...more
46min

FAQs about Foundations of Pure Mathematics:

How many episodes does Foundations of Pure Mathematics have?

The podcast currently has 31 episodes available.