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Highlights of Calculus

Highlights of Calculus
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College Open Textbooks - College Open Textbooks Lecture 1: The geometry of linear equations | Video Lectures | Linear Algebra | Mathematics Front Page | OpenSpires Statistics course for PhD students Lectures topic list Cheat sheet / notes Lecture 1 : basic descriptive statistics Lecture 1 - slides [pdf] Lecture 1 - slides [keynote] Lecture 1 - problem set Lecture 2 : searching for correlations Lecture 2 - slides [pdf] Lecture 2 - slides [keynote] Lecture 2 - problem set Lecture 2 - Lemaitre (1927) dataset Lecture 2 - Hubble (1929) dataset Lecture 2 - Two distribution dataset Lecture 3 : hypothesis testing and model-fitting Lecture 3 - slides [pdf] Lecture 3 - slides [keynote] Lecture 3 - problem set Lecture 3 - Model-fitting example dataset Lecture 4 : Bayesian inference Lecture 4 - slides [pdf] Lecture 4 - slides [keynote] Lecture 4 - problem set Other resources Useful textbooks: Wall & Jenkins, "Practical Statistics for Astronomers", 2nd edition Press et al., "Numerical Recipes"

openMaterials Neural networks and deep learning The human visual system is one of the wonders of the world. Consider the following sequence of handwritten digits: Most people effortlessly recognize those digits as 504192. That ease is deceptive. The difficulty of visual pattern recognition becomes apparent if you attempt to write a computer program to recognize digits like those above. Neural networks approach the problem in a different way. and then develop a system which can learn from those training examples. In this chapter we'll write a computer program implementing a neural network that learns to recognize handwritten digits. We're focusing on handwriting recognition because it's an excellent prototype problem for learning about neural networks in general. Of course, if the point of the chapter was only to write a computer program to recognize handwritten digits, then the chapter would be much shorter! Perceptrons What is a neural network? So how do perceptrons work? That's the basic mathematical model. Is the weather good?

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How Stockfish Works: An Evaluation of the Databases Behind the Top Open-Source Chess Engine | math is art Playing chess has been on the forefront of AI research since Alan Turing and his students proposed chess playing machines. The game of chess is a domain of human thought where very limited sets of rules yield inexhaustible depths, challenges, frustration and beauty. The playing strategies of AI and human players have diverged proportional to the increase of available computing power, namely speed and storage space. Human players recognize and aim to achieve particular patterns; typically, they perform a deep search weighted towards moves that lead to such desired patterns, transferring past knowledge and adapting it to their present situation. AI chess is mostly played by parsing through a huge database, with broad search algorithms used to search for the next optimal move. Keywords: Chess, AI Chess, Search Techniques, Chess algorithms, Databases, Alpha-Beta Pruning, Stockfish, Stockfish 2.3.1 Application Domain Design and Schema A move search in Stockfish consists of 21 steps. Step 1. H.