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jdh.hamkins.org | ||
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kpknudson.com
[AI summary] This podcast episode features an engaging conversation with Joel David Hamkins, a mathematician and philosopher at the University of Oxford. The discussion centers on the fundamental theorem of finite games, which asserts that every finite game with perfect information has a winning strategy for one player or a draw strategy for both. Hamkins explores the implications of this theorem in the context of chess, highlighting Zermelo's theorem and its relevance to both finite and infinite chess. He also delves into the mathematical and logical aspects of chess, including the likelihood of random chess positions being legal and the role of logic puzzles in understanding game strategies. The episode touches on Hamkins' work with chess players, the over... |
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micromath.wordpress.com
Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... |
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ecodevoevo.blogspot.com
What is 'philosophy' of science? Does anyone actually need it? When I was an undergraduate, I was a math major and took an unofficial philo... |
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matt.might.net
[AI summary] This text explains how a single perceptron can learn basic Boolean functions like AND, OR, and NOT, but fails to learn the non-linearly separable XOR function. This limitation led to the development of modern artificial neural networks (ANNs). The transition from single perceptrons to ANNs involves three key changes: 1) Adding multiple layers of perceptrons to create Multilayer Perceptron (MLP) networks, enabling modeling of complex non-linear relationships. 2) Introducing non-linear activation functions like sigmoid, tanh, and ReLU to allow networks to learn non-linear functions. 3) Implementing backpropagation and gradient descent algorithms for efficient training of multilayer networks. These changes allow ANNs to overcome the limitations of ... |
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