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 32 episodes available.

Foundations of Pure Mathematics episodes:

March 30, 2015 Discussions of Class Test 2 - Foundations of Pure Mathematics - Dr Joel Feinstein
Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module: discussions of Class Test 2.
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
59min
March 19, 2015 Workshop 10 - Foundations of Pure Mathematics - Dr Joel Feinstein
The tenth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module Worksheet on functions and countability: one-sided inverses (left inverses and right inverses), injective, surjective and bijective functions, and countability.
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
28min
March 19, 2015 Countability and uncountability - Foundations of Pure Mathematics - Dr Joel Feinstein
The twentieth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers countability in terms of injections and surjections. The Cartesian product of two countable sets is countable. The set of rational numbers is countable. A countable union of countable sets is countable.
Intervals of real numbers: the interval (0, 1) is uncountable (proved using Cantor’s diagonal argument), and it follows that every non-degenerate interval is uncountable.
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
48min
March 12, 2015 Conclusion of Cardinality for infinite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
The conclusion of the nineteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a brief discussion of sequences using up sets. Proof that the union of two countable sets is countable.
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
7min
March 12, 2015 Cardinality for infinite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
The nineteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a brief discussion of different sizes of infinity. (The video “Beyond Infinity” may also be helpful here.)
Sets with the same cardinality. Countable sets and uncountable sets defined. Connections between functions and sequences.
Countability in terms of sequences. The union of two countable sets is countable. (Proved at the start of next class.)
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
March 05, 2015 Workshop 9 - Foundations of Pure Mathematics - Dr Joel Feinstein
The ninth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with a variety of questions: Cartesian products and set inclusions; Ssts, characteristic functions and congruence modulo 2; symmetric differences 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
31min
March 05, 2015 Permutations continued - Foundations of Pure Mathematics - Dr Joel Feinstein
The eighteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers disjoint permutations, especially disjoint cycles. Writing permutations as products of disjoint cycles.
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
March 05, 2015 Permutations of finite sets - Foundations of Pure Mathematics - Dr Joel Feinstein
The seventeenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers permutations of sets, especially finite sets. The two-line form for permutations. Inverses for permutations and the identity permutation. Multiplication of permutations using 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
44min
February 24, 2015 Workshop 8 - Foundations of Pure Mathematics - Dr Joel Feinstein
The eighth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a worksheet with a variety of questions: an application of the Binomial Theorem; working with sets and their characteristic functions, and the connection with the Inclusion-Exclusion Principle.
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
25min
February 24, 2015 Finite sets and cardinality - Foundations of Pure Mathematics - Dr Joel Feinstein
The sixteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers cardinality of finite sets: n-sets and k-subsets of sets. Discussion of injections, surjections and bijections between finite sets, including the Pigeonhole Principle. Contrast with infinite sets.
Cardinalities of unions of sets: the Inclusion-Exclusion Principle (see Workshop 8 for more details). Binomial coefficients and the Binomial Theorem.
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
43min

FAQs about Foundations of Pure Mathematics:

How many episodes does Foundations of Pure Mathematics have?

The podcast currently has 32 episodes available.