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31 results for "combinatorics"
The solution of a combinatorial problem By Giacomo Lorenzoni
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Is exposed a procedure for determine the solution of a combinatorial problem. The data of the problem are a natural N and a positive real Δ. The solution of the problem are N positive real... More > numbers such that all the sums, that have for addends the elements of a theirs combination without repetitions, can be ordered as an arithmetic progression whose common difference is Δ.< Less
Combinatorial properties of ladders, generalised Pont-Neuf and caterpillar diagrams in the space of coloured open Jacobi diagrams By Frank Ditsche
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This doctoral thesis is a contribution to the analysis of the combinatorics of arbitrarily coloured open Jacobi diagrams and their relationship to Vassiliev invariants. We examine J.~Kneissler's five... More > ladder relations and state them in a much more precise way. We also analyse their role in the space of colored open Jacobi diagrams. Then, we establish a sort of machinery - a language together with a toolbox of lemmata, theorems and definitions to build, manipulate and analyse coloured open Jacobi diagrams. With this, we examine the role of generalised Pont-Neuf diagrams and caterpillar diagrams. Lastly we transfer this to the uncolored case, which allows us to show that the space of open Jacobi diagrams up to first Betti number five is already contained in the module of caterpillar diagrams, considered as a module of a certain subset of Vogels' algebra. This means that Vassiliev invariants associated to these degrees do not detect knot orientation.< Less
DissertationB&W By Jay Cummings
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Jay Cummings' PhD dissertation studies the math of juggling and edge flipping in the complete graph, as well as some related problems. This edition is in color.
Applied Discrete Structures - Part 1: Fundamentals By Ken Levasseur & Al Doerr
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This is Part 1 of Applied Discrete Structures, containing the fundamental concepts taught in a one semester course in discrete mathematics. It corresponds with the content of Discrete Structures I at... More > UMass Lowell, which is a required course for students in Computer Science, Mathematics and Information Technology. Part II - Applied Abstract Algebra would normally be used in a second semester course such as Discrete Structures II at UMass Lowell. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http://www.aimath.org/textbooks/. This version was created using Mathbook XML (https://mathbook.pugetsound.edu/) Version 3.5 - May 2018< Less
G.A.M.E. Games Autonomy Motivation & Education By Menno Deen
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This thesis reviews and utilizes concepts from cognitive psychology, developmental psychology and game design to bring forth a number of design principles for educational games that may improve... More > students’ motivation to learn. Its main contribution is a novel approach to serious game design, namely envisioning play and learning as a restructuring practice. This change of perspective, from a formal game design approach (focused on rules and regulations) towards a more activity-centered approach (focused on process and style), may help designers to leverage the motivational potential of games, in order to make education more engaging to students.< Less
Essays in Online Mathematics Interaction By Gerry Stahl
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This collection of case studies from VMT data includes teams working on problems of combinatorics. In particular, two teams that interacted on the same problems during 2006 provide a variety of... More > insights into the nature of CSCL. These papers were written with close colleagues.< Less
Essays in Online Mathematics Interaction By Gerry Stahl
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These are case studies of student teams using VMT to work on problems in the mathematical domain of combinatorics. The version of VMT used here included a generic whiteboard for sketching graphical... More > representations. Data from these sessions was analyzed by a number of researchers in addition to the VMT project members.The essays in this volume were co-authored with close colleagues.< Less
Large Scale Methods to Enumerate Extreme Rays and Elementary Modes (b/w print) By Marco Terzer
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A major challenge in systems biology is to improve the understanding of complex metabolic networks. Here, we focus on structural analysis since it requires mainly reaction stoichiometries, in... More > contrary to detailed dynamic methods that are often limited by insufficient knowledge on mechanisms and parameters. Thermodynamic reaction constraints and the steady state assumption reduce the solution space for valid reaction fluxes to a convex polyhedral cone. Pathway analysis methods aim at finding a unique generating set for the flux cone---called extreme rays or elementary modes. We describe critical aspects for an efficient implementation of the double description method for large scale application. The efficiency of introduced techniques is demonstrated with large application examples from combinatorics and systems biology.< Less
Large Scale Methods to Enumerate Extreme Rays and Elementary Modes (color print) By Marco Terzer
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A major challenge in systems biology is to improve the understanding of complex metabolic networks. Here, we focus on structural analysis since it requires mainly reaction stoichiometries, in... More > contrary to detailed dynamic methods that are often limited by insufficient knowledge on mechanisms and parameters. Thermodynamic reaction constraints and the steady state assumption reduce the solution space for valid reaction fluxes to a convex polyhedral cone. Pathway analysis methods aim at finding a unique generating set for the flux cone---called extreme rays or elementary modes. We describe critical aspects for an efficient implementation of the double description method for large scale application. The efficiency of introduced techniques is demonstrated with large application examples from combinatorics and systems biology.< Less
Large Scale Methods to Enumerate Extreme Rays and Elementary Modes (color print) By Marco Terzer
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A major challenge in systems biology is to improve the understanding of complex metabolic networks. Here, we focus on structural analysis since it requires mainly reaction stoichiometries, in... More > contrary to detailed dynamic methods that are often limited by insufficient knowledge on mechanisms and parameters. Thermodynamic reaction constraints and the steady state assumption reduce the solution space for valid reaction fluxes to a convex polyhedral cone. Pathway analysis methods aim at finding a unique generating set for the flux cone---called extreme rays or elementary modes. We describe critical aspects for an efficient implementation of the double description method for large scale application. The efficiency of introduced techniques is demonstrated with large application examples from combinatorics and systems biology.< Less

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