elementary probability
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We first play and then analyze wars of attrition; the games that afflict trench warfare, strikes, and businesses in some competitive settings. We find long and damaging fights can occur in class in these games even when the prizes are small in relation to the accumulated costs. These could be caused by irrationality or by players' having other goals like pride or reputation. But we argue that long, costly fights should be expected in these...more
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The Tree of Life must be discovered through rigorous analysis. Genetic information is crucial because appearances can be deceiving, and species that look similar can prove to be genetically very dissimilar and not share recent common ancestors. Two criteria, used to determine what the "correct" Tree is, are simplicity and whether the tree maximizes the probability of observing what we actually see.
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April 6, 2009 - Leonard Susskind overviews elementary mathematics to define a method for understanding statistical mechanics.
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Probability functions.
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Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a p...more
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Outcomes, sample, space, events, and probability functions.
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Note: This course is being offered this summer by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. To...more
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March 30, 2009 - Leonard Susskind discusses the study of statistical analysis as calculating the probability of things subject to the constraints of a conserved quantity. Susskind introduces energy, entropy, temperature, and phase states as they relate directly to statistical mechanics.
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Conditional probability.
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Note: This course is offered by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learnin...more
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Professor Sylvia Ceyer focuses on p-orbitals, describing nodal planes, angular nodes, and radial probability distributions. The conversation continues forward to wavefunctions for multielectron atoms, beginning with an explanation of electron configuration. The Pauli and spin exclusion principle is covered, and the lecture concludes with a discussion of one electron wavefunctions for multielectron atoms.
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This is a math course aimed at students with life science majors covering elementary probability, probability distributions, random variables, and limit theorems.
