Definitions, proofs and examples
By Dr Joel Feinstein
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These sessions are intended to reinforce material from lectures, while also providing more opportunities for students to hone their skills in a number of areas, including the following: working with formal definitions; making deductions from information given; writing relatively routine proofs; investigating the properties of examples; thinking up examples with specified combinations of properties. 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.
|1||CleanVideoWhy do we do proofs?||This is the first of three sessions by Dr Joel Feinstein on how and why we do proofs. Dr Feinstein's blog is available at http://explainingmaths.wordpress.com/ The aim of this session is to motivate students to understand why we might want to do proofs,||16 11 2011||Free||View in iTunes|
|2||CleanVideoHow do we do proofs? (Part I)||This is the first of two sessions on how to do proofs. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ The aim of these sessions on how we do proofs is to help students with some of the relatively routine aspects of doing proofs. I||16 11 2011||Free||View in iTunes|
|3||CleanVideoHow do we do proofs? (Part II)||How do we do proofs? (Part II)||16 11 2011||Free||View in iTunes|
|4||CleanVideoDefinitions, Proofs and Examples 1||Discussion of questions relating to: set inclusions and set equalities; sums of subsets of the real line; examples showing the difference between sum and union. Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein||1 11 2011||Free||View in iTunes|
|5||CleanVideoDefinitions, Proofs and Examples 2||Discussion of questions relating to: Cartesian products, set differences and set inclusions; bounded sets and unbounded sets; open sets and sets which are not open; continuous functions, divergent sequences and convergent sequences. Dr Feinstein's blog||1 11 2011||Free||View in iTunes|
|6||CleanVideoDefinitions, Proofs and Examples 3||Discussion of questions relating to: unions of finite sets, bounded sets and closed sets; convergence of sequences, and the related (non-standard) concept of absorption of sequences by sets. Dr Feinstein's blog may be viewed at: http://explainingmaths.w||11 11 2011||Free||View in iTunes|
|7||CleanVideoDefinitions, Proofs and Examples 4||A close look at sequences of real numbers which tend to plus or minus infinity, and connections with the (non)-existence of bounded subsequences and/or convergent subsequences. Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com D||21 11 2011||Free||View in iTunes|
|8||CleanVideoDefinitions, Proofs and Examples 5||An easy proof by contradiction concerning sets absorbing sequences; a proof that various statements about convergence of sequences in a non-empty set are equivalent to the set having exactly one point; various examples relating to (non) sequential compa||2 12 2011||Free||View in iTunes|
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- Category: Higher Education
- Language: English
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