www.mathtube.org - Logic and Foundations
http://www.mathtube.org/taxonomy/term/115/0
enUnivalence as a New Principle of Logic
http://www.mathtube.org/lecture/video/univalence-new-principle-logic
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Speaker: </div>
Steve Awodey </div>
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Date: </div>
<span class="date-display-single">Thu, Oct 2, 2014</span> </div>
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Location: </div>
PIMS, University of Calgary </div>
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Conference: </div>
The Calgary Mathematics & Philosophy Lectures </div>
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<p>It is often convenient or useful in mathematics to treat isomorphic structures as the same. The Univalence Axiom for the foundations of mathematics elevates this idea to a foundational principle in the setting of Homotopy Type Theory. It states, roughly, that isomorphic structures can be identified. In his talk, Prof. Awodey will explain this principle and how it can be taken as an axiom, and explore the motivations and consequences, both mathematical and philosophical, of making such an assumption.</p> </div>
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ScientificMathematicsLogic and FoundationsWed, 15 Oct 2014 23:16:54 +0000root485 at http://www.mathtube.orgAlan Turing and Enigma
http://www.mathtube.org/lecture/video/alan-turing-and-enigma
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Speaker: </div>
John R. Ferris </div>
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Date: </div>
<span class="date-display-single">Tue, Mar 27, 2012</span> </div>
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Location: </div>
PIMS, University of Calgary </div>
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Conference: </div>
Alan Turing Year </div>
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Central to Alan Turing's posthumous reputation is his work with British codebreaking during the Second World War. This relationship is not well understood, largely because it stands on the intersection of two technical fields, mathematics and cryptology, the second of which also has been shrouded by secrecy. This lecture will assess this relationship from an historical cryptological perspective. It treats the mathematization and mechanization of cryptology between 1920-50 as international phenomena. It assesses Turing's role in one important phase of this process, British work at Bletchley Park in developing cryptanalytical machines for use against Enigma in 1940-41. It focuses on also his interest in and work with cryptographic machines between 1942-46, and concludes that work with them served as a seed bed for the development of his thinking about computers.
<h3>Turing 2012 - Calgary</h3>
This talk is part of a <a href="http://www.ucalgary.ca/turing">series celebrating the Alan Turing Centenary</a> in Calgary. The following mathtube videos are part of this series
<ol>
<li><a href="/lecture/video/alan-turing-and-decision-problem">Alan Turing and the Decision Problem</a>, <em>Richard Zach</em>.</li>
<li><a href="/lecture/video/turings-real-machines">Turing's Real Machine</a>, <em>Michael R. Williams</em>.</li>
<li>Alan Turing and Enigma, John R. Ferris.</li>
</ol> </div>
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ScientificMathematicsComputational ComplexityDiscrete MathematicsInformation Theory and CryptographyLogic and FoundationsComputer ScienceWed, 11 Apr 2012 05:46:48 +0000root162 at http://www.mathtube.orgTuring's Real Machines
http://www.mathtube.org/lecture/video/turings-real-machines
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Speaker: </div>
Michael R. Williams </div>
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Date: </div>
<span class="date-display-single">Tue, Feb 28, 2012</span> </div>
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Location: </div>
PIMS, University of Calgary </div>
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Conference: </div>
Alan Turing Year </div>
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While Turing is best known for his abstract concept of a "Turing Machine," he did design (but not build) several other machines - particularly ones involved with code breaking and early computers. While Turing was a fine mathematician, he could not be trusted to actually try and construct the machines he designed - he would almost always break some delicate piece of equipment if he tried to do anything practical.
The early code-breaking machines (known as "bombes" - the Polish word for bomb, because of their loud ticking noise) were not designed by Turing but he had a hand in several later machines known as "Robinsons" and eventually the Colossus machines.
After the War he worked on an electronic computer design for the National Physical Laboratory - an innovative design unlike the other computing machines being considered at the time. He left the NPL before the machine was operational but made other contributions to early computers such as those being constructed at Manchester University.
This talk will describe some of his ideas behind these machines.
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<h3>Turing 2012 - Calgary</h3>
This talk is part of a series celebrating <a href="http://www.ucalgary.ca/turing">The Alan Turing Centenary in Calgary</a>. The following mathtube videos are also part of this series
<ol>
<li><a href="/lecture/video/alan-turing-and-decision-problem">Alan Turing and the Decision Problem</a>, <em>Richard Zach</em>.</li>
<li>Turing's Real Machine, <em>Michael R. Williams</em>.</li>
<li><a href="/lecture/video/alan-turing-and-enigma">Alan Turing and Enigma</a>, <em>John R. Ferris</em>.</li>
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ScientificMathematicsComputational ComplexityDiscrete MathematicsInformation Theory and CryptographyLogic and FoundationsComputer ScienceWed, 14 Mar 2012 00:33:33 +0000root161 at http://www.mathtube.orgAlan Turing and the Decision Problem
http://www.mathtube.org/lecture/video/alan-turing-and-decision-problem
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Speaker: </div>
Richard Zach </div>
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Date: </div>
<span class="date-display-single">Tue, Jan 24, 2012</span> </div>
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Location: </div>
PIMS, University of Calgary </div>
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Conference: </div>
Alan Turing Year </div>
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Many scientific questions are considered solved to the best possible degree when we have a method for computing a solution. This is especially true in mathematics and those areas of science in which phenomena can be described mathematically: one only has to think of the methods of symbolic algebra in order to solve equations, or laws of physics which allow one to calculate unknown quantities from known measurements. The crowning achievement of mathematics would thus be a systematic way to compute the solution to any mathematical problem. The hope that this was possible was perhaps first articulated by the 18th century mathematician-philosopher G. W. Leibniz. Advances in the foundations of mathematics in the early 20th century made it possible in the 1920s to first formulate the question of whether there is such a systematic way to find a solution to every mathematical problem. This became known as the decision problem, and it was considered a major open problem in the 1920s and 1930s. Alan Turing solved it in his first, groundbreaking paper "On computable numbers" (1936). In order to show that there cannot be a systematic computational procedure that solves every mathematical question, Turing had to provide a convincing analysis of what a computational procedure is. His abstract, mathematical model of computability is that of a Turing Machine. He showed that no Turing machine, and hence no computational procedure at all, could solve the Entscheidungsproblem.
<h3>Turing 2012 - Calgary</h3>
This talk is part of a <a href="http://www.ucalgary.ca/turing">series celebrating the Alan Turing Centenary</a> in Calgary. The following mathtube videos are also part of this series
<ol>
<li>Alan Turing and the Decision Problem, <em>Richard Zach</em>.</li>
<li><a href="/lecture/video/turings-real-machines">Turing's Real Machine</a>, <em>Michael R. Williams</em>.</li>
<li><a href="/lecture/video/alan-turing-and-enigma">Alan Turing and Enigma</a>, <em>John R. Ferris</em>.</li>
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ScientificMathematicsComputational ComplexityDiscrete MathematicsInformation Theory and CryptographyLogic and FoundationsComputer ScienceFri, 09 Mar 2012 23:16:55 +0000root159 at http://www.mathtube.orgOn the Chromatic Number of Graphs and Set Systems
http://www.mathtube.org/lecture/notes/chromatic-number-graphs-and-set-systems
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András Hajnal </div>
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<span class="date-display-single">Wed, Sep 1, 2004</span> </div>
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University of Calgary, Calgary, Canada </div>
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PIMS Distinguished Chair Lectures </div>
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During this series of lectures, we are talking about infinite graphs and set systems, so this will be infinite combinatorics. This subject was initiated by Paul Erdös in the late 1940’s.
I will try to show in these lectures how it becomes an important part of modern set theory, first serving as a test case for modern tools, but also influencing their developments.
In the first few of the lectures, I will pretend that I am talking about a joint work of István Juhász, Saharon Shelah and myself [23].
The actual highly technical result of this paper that appeared in the <strong>Fundamenta</strong> in 2000 will only be stated in the second or the third part of these lectures. Meanwhile I will introduce the main concepts and state—--and sometimes prove—--simple results about them. </div>
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<div class="filefield-file"><img class="filefield-icon field-icon-application-pdf" alt="application/pdf icon" src="http://www.mathtube.org/sites/all/modules/icontheme/icons/application-pdf.png" /><a href="http://www.mathtube.org/sites/default/files/lecture-notes/Hajnal.pdf" type="application/pdf; length=213181">Hajnal.pdf</a></div> </div>
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ScientificDiscrete MathematicsLogic and FoundationsMon, 18 Apr 2011 18:26:16 +0000Gotay20 at http://www.mathtube.org