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MERLOT MaterialsCopyright (C) 2018 MERLOT Some Rights ReservedTue, 10 Feb 2015 22:13:46 GMTMERLOThttps://www.merlot.org/merlot/images/merlot_column.png
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-1-1Diamond Theory
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Symmetry properties of the 4x4 array. The invariance of symmetry displayed in the author's Diamond 16 Puzzle (online) suggests insights into finite geometry, group theory, and combinatorics.Wed, 17 Apr 2002 07:00:00 GMTSteven CullinaneMudd Math Fun Facts
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This archive is designed as a resource for enriching your courses with mathematical Fun Facts! It is designed to pique the interest of students in different areas of mathematics. The fun facts were originally conceived as five minute warm ups at the beginning of lectures so that non mathematics majors would not think math was just calculus. Presentation suggestions are also given.Tue, 02 Aug 2005 07:00:00 GMTFrancis Edward Su Department of Mathematics, Harvey Mudd CollegeThe Diamond 16 Puzzle
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In solving this puzzle, you permute rows, columns, and quadrants in a 4x4 array of 2-color tiles to make a variety of symmetric designs. A link to underlying theory is provided.Thu, 21 Feb 2002 08:00:00 GMTSteven CullinaneMathPages
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This site contains several hundred articles concerned with mathematics and physics. General topics include Number Theory, Combinatorics, Geometry, Algebra, Calculus & Differential Equations, Probability & Statistics, Set Theory & Foundations, Reflections on Relativity, History, and Physics. The articles under each general heading are highly varied, many are quite advanced, and there is no apparent organizational scheme. For example, under Calculus & Differential Equations there is a proof that pi is irrational, a examination of the Limit Paradox, a discussion of Ptolemy's Orbit, and an historical review of the cycloid among many other articles. Visitors can browse by topics or search by keyword. (Anyone with information on the identity of the site author please contact the MERLOT submitter.)Tue, 08 Mar 2005 08:00:00 GMTUnknownCombinatorial Math: How to Count Without Counting
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A collection of JavaScript for computing permutations and combinations counting with or without repetitions.Thu, 06 Jan 2005 08:00:00 GMTBarbra Bied Sperling CSU, Office of the ChancellorMi tarea
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This is an exceptional site for locating all types of content material in creating modules. The are links to the following disciplines: Sciences, History, Art and Culture, Humanities, and general resources. On several of the links, one can find audio files, e.g., Christmas carols. While this site is designed for native speakers in middle school or a secondary level, it is quite appropriate for Spanish language students having an intermediate language proficiency or higher in secondary or college courses.Sat, 03 Feb 2001 08:00:00 GMTAntonia Rodriguez Mi tareaApplied Discrete Structures
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<p><strong>Applied Discrete Structures</strong> by <a href="http://faculty.uml.edu/math/faculty/doerr.htm" target="_new">Al Doerr</a> and <a href="http://faculty.uml.edu/klevasseur/" target="_new">Ken Levasseur</a> is a <em>free</em> open content textbook in discrete mathematics. Originally published in 1984 & 1989 by Pearson, the book has been updated to include references to Mathematica and Sage, the open source computer algebra system. </p><p><strong>Contents:</strong></p><p>Front Matter: Contents and Introduction</p><p><span>Chapter 1: Set Theory I</span><span> </span></p><p><span>Chapter 2: Combinatorics</span><span> </span></p><p><span>Chapter 3: Logic</span><span> </span></p><p><span>Chapter 4: More on Sets</span><span> </span></p><p><span>Chapter 5: Introduction to Matrix Algebra</span><span> </span></p><p><span>Chapter 6: Relations and Graphs</span><span> </span></p><p><span>Chapter 7: Functions</span><span> </span></p><p><span>Chapter 8: Recursion and Recurrence Relations</span><span> </span></p><p><span>Chapter 9: Graph Theory</span><span> </span></p><p><span>Chapter 10: Trees</span><span> </span></p><p><span>Chapter 11: Algebraic Systems</span><span> </span></p><p><span>Chapter 12: More Matrix Algebra</span><span> </span></p><p><span>Chapter 13: Boolean Algebra</span><span> </span></p><p><span>Chapter 14: Monoids and Automata</span><span> </span></p><p><span>Chapter 15: Group Theory and Applications</span><span> </span></p><p><span>Chapter 16: An Introduction to Rings and Fields</span><span> </span></p><p><span>Solutions to Odd-Numbered Exercises</span><span> </span></p>Thu, 14 Mar 2013 16:17:19 GMTKen Levasseur; Alan Doerr UMass LowellPolyforms
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Background and description of polyform sets as a new puzzle genre.Sat, 30 Nov 2002 08:00:00 GMTKate JonesErdös-Ko-Rado theorems
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This video was recorded at 6th Slovenian International Conference on Graph Theory, Bled 2007. I will show that this theorem has a natural proof using linear algebra, and that this approach also applies to situations where sets are replaced by objects such as subspaces, permutations or partitions.Tue, 10 Feb 2015 22:13:46 GMTChris Godsil Combinatorics and Optimization Department, University of WaterlooMinimax Policies for Combinatorial Prediction Games
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This video was recorded at 24th Annual Conference on Learning Theory (COLT), Budapest 2011. We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the partial information models of the so-called "semi-bandit", and "bandit" problems. We consider both L∞-, and L2-type of restrictions for the losses assigned by the adversary. We formulate a general strategy using Bregman projections on top of a potential-based gradient descent, which generalizes the ones studied in the series of papers György et al. (2007), Dani et al. (2008), Abernethy et al. (2008), Cesa-Bianchi and Lugosi (2009), Helmbold and Warmuth (2009), Koolen et al. (2010), Uchiya et al. (2010), Kale et al. (2010) and Audibert and Bubeck (2010). We provide simple proofs that recover most of the previous results. We propose new upper bounds for the semi-bandit game. Moreover we derive lower bounds for all three feedback assumptions. With the only exception of the bandit game, the upper and lower bounds are tight, up to a constant factor. Finally, we answer a question asked by Koolen et al. (2010) by showing that the exponentially weighted average forecaster is suboptimal against L∞ adversaries.Mon, 09 Feb 2015 04:56:08 GMTSébastien Bubeck Department of Operations Research and Financial Engineering, Princeton University