Workshop 4 - Foundations of Pure Mathematics - Dr Joel Feinstein
The fourth workshop in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers a proof of Bézout’s Lemma.These videos are also available for download on iTunes U at: https://itunes.apple.com/us/itunes-u/...Dr Feinstein's blog may be......
Introduction to Foundations of Pure Mathematics - Dr Joel Feinstein
The first class in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers motivation for pure mathematical thinking (definitions, proofs and examples) illustrated by looking at some introductory puzzles with voting.These videos are......
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 abl......
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 descript......
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 for download on iTunes......
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 Pigeon......
Cartesian Products and Relations - Foundations of Pure Mathematics - Dr Joel Feinstein
The eighth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers definitions and examples of Cartesian products and (binary) relations, including order relations and congruence modulo k.These videos are also available f......
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 set......
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 Lect......
Bezout's Lemma and Prime Factorization - Foundations of Pure Mathematics - Dr Joel Feinstein
The sixth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers the statement of Bézout’s Lemma (see Workshop 4 for a proof). Application of Bézout’s Lemma to divisibility by primes. The statement of the Fundamental The......
ACET exam Foundations of Mathematics
ACET(Actuarial Science Common Entrance Test) training on Mathematics at pacegurus by Vamsidhar Ambatipudi(IIMI, PRM, completed 14 papers of Institute of Actuaries of India)...
Part 3. Foundations of Mathematics
Part 3 of "Brief Introduction to the Foundations of Mathematics"Foundations of MathematicsFor more than 2,000 years, the Axioms of Euclidean Geometry served as the foundation for the development of Mathematics. However, a series of discoveries during......
The Foundations of Mathematics - YouTube
Topic 3 of "Brief Introduction to the Foundations of Mathematics" lecture.-----------------------------------In this video we will talk very briefly about the evolution of The Foundations of Mathematics.We will also stress the fact that the foundatio......
The Baire Category Theorem - Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional Analysis. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the associated blog post at http://wp.me/posHB-7y In this screencast, Dr Feins......
The Uniform Boundedness Principle - Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional Analysis.See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB-8vIn this s......
Using a tablet PC and screencasts when teaching mathematics - Dr. Joel Feinstein - Camtasia edition
This is one of two recordings of a session given by Dr Joel Feinstein (Nottingham) in Loughborough on November 18 2009 as part of the seminar series "How We Teach" running at the Mathematics Education Centre, Loughborough University. See also Dr Fein......
Univalent Foundations: New Foundations of Mathematics | Vladimir Voevodsky
Univalent Foundations: New Foundations of MathematicsVladimir Voevodsky, Professor, School of Mathematicshttp://www.ias.edu/people/faculty-and...March 26, 2014In Voevodsky’s experience, the work of a mathematician is 5% creative insight and 95% self-......