Counting on Frameworks

Mathematics to Aid the Design of Rigid Structures

Author: Jack E. Graver

Publisher: Cambridge University Press

ISBN: 9780883853313

Category: Mathematics

Page: 180

View: 5429

DOWNLOAD NOW »
Consider a scaffolding that is constructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to support the workers and their equipment. This is the problem that motivates the area of mathematics known as rigidity theory. The purpose of this book is to develop a mathematical model for the rigidity of structures. In fact the author develops three distinct models in which the structure under consideration is modelled as a framework. These models are the degrees of freedom model and two models based on quadratic equations and linear equations respectively. The author shows that all three of these models agree except for a very small class of specially constructed frameworks. This is a theory with significant practical applications and will be of interest to a wide range of people including those studying graph theory or mathematical modelling.

Cooperative Control

A Post-Workshop Volume, 2003 Block Island Workshop on Cooperative Control

Author: Vijay Kumar,Naomi Leonard,A. Stephen Morse

Publisher: Springer Science & Business Media

ISBN: 9783540228615

Category: Technology & Engineering

Page: 291

View: 9949

DOWNLOAD NOW »
Are there universal principles of coordinated group motion and if so what might they be? This carefully edited book presents how natural groupings such as fish schools, bird flocks, deer herds etc. coordinate themselves and move so flawlessly, often without an apparent leader or any form of centralized control. It shows how the underlying principles of cooperative control may be used for groups of mobile autonomous agents to help enable a large group of autonomous robotic vehicles in the air, on land or sea or underwater, to collectively accomplish useful tasks such as distributed, adaptive scientific data gathering, search and rescue, or reconnaissance.

Automated Deduction in Geometry

4th International Workshop, ADG 2002, Hagenberg Castle, Austria, September 4-6, 2002, Revised Papers

Author: Franz Winkler

Publisher: Springer

ISBN: 3540246169

Category: Mathematics

Page: 229

View: 2675

DOWNLOAD NOW »
This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.

Automated Deduction in Geometry

4th International Workshop, ADG 2002, Hagenberg Castle, Austria, September 4-6, 2002, Revised Papers

Author: Franz Winkler

Publisher: Springer Science & Business Media

ISBN: 3540209271

Category: Computers

Page: 229

View: 6658

DOWNLOAD NOW »
This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.

Biscuits of Number Theory

Author: Arthur T. Benjamin,Ezra Brown

Publisher: MAA

ISBN: 9780883853405

Category: Mathematics

Page: 311

View: 8587

DOWNLOAD NOW »
An anthology of articles designed to supplement a first course in number theory.

Combinatorics with Emphasis on the Theory of Graphs

Author: J. E. Graver,M. E. Watkins

Publisher: Springer Science & Business Media

ISBN: 1461299144

Category: Mathematics

Page: 352

View: 5055

DOWNLOAD NOW »
Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of unformulated or unrecognized general theorems. The body of knowledge has now reached a stage where approaches toward unification are overdue. To paraphrase Professor Gian-Carlo Rota (Toronto, 1967), "Combinatorics needs fewer theorems and more theory. " In this book we are doing two things at the same time: A. We are presenting a unified treatment of much of combinatorics and graph theory. We have constructed a concise algebraically based, but otherwise self-contained theory, which at one time embraces the basic theorems that one normally wishes to prove while giving a common terminology and framework for the develop ment of further more specialized results. B. We are writing a textbook whereby a student of mathematics or a mathematician with another specialty can learn combinatorics and graph theory. We want this learning to be done in a much more unified way than has generally been possible from the existing literature. Our most difficult problem in the course of writing this book has been to keep A and B in balance. On the one hand, this book would be useless as a textbook if certain intuitively appealing, classical combinatorial results were either overlooked or were treated only at a level of abstraction rendering them beyond all recognition.

Lectures on Sphere Arrangements – the Discrete Geometric Side

Author: Károly Bezdek

Publisher: Springer Science & Business Media

ISBN: 146148118X

Category: Mathematics

Page: 175

View: 7007

DOWNLOAD NOW »
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.

Rigidity and Symmetry

Author: Robert Connelly,Asia Ivić Weiss,Walter Whiteley

Publisher: Springer

ISBN: 1493907816

Category: Mathematics

Page: 374

View: 7396

DOWNLOAD NOW »
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Algorithmic Problem Solving

Author: Roland Backhouse

Publisher: John Wiley & Sons

ISBN: 0470684534

Category: Computers

Page: 432

View: 3682

DOWNLOAD NOW »
An entertaining and captivating way to learn the fundamentals of using algorithms to solve problems The algorithmic approach to solving problems in computer technology is an essential tool. With this unique book, algorithm guru Roland Backhouse shares his four decades of experience to teach the fundamental principles of using algorithms to solve problems. Using fun and well-known puzzles to gradually introduce different aspects of algorithms in mathematics and computing. Backhouse presents you with a readable, entertaining, and energetic book that will motivate and challenge you to open your mind to the algorithmic nature of problem solving. Provides a novel approach to the mathematics of problem solving focusing on the algorithmic nature of problem solving Uses popular and entertaining puzzles to teach you different aspects of using algorithms to solve mathematical and computing challenges Features a theory section that supports each of the puzzles presented throughout the book Assumes only an elementary understanding of mathematics Let Roland Backhouse and his four decades of experience show you how you can solve challenging problems with algorithms!

Combinatorial Rigidity

Author: Jack E. Graver,Brigitte Servatius,Herman Servatius

Publisher: American Mathematical Soc.

ISBN: 0821838016

Category: Mathematics

Page: 172

View: 2721

DOWNLOAD NOW »
This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. The book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibiolography with over 150 entries. The book is aimed at graduate students and researchers in graph theory and combinatorics or in fields which apply the structural aspects of these subjects in architecture and engineering. Accessible to those who have had an introduction to graph theory at the senior or graduate level, the book would be suitable for a graduate course in graph theory.

When Less is More

Visualizing Basic Inequalities

Author: Claudi Alsina,Roger B. Nelsen

Publisher: MAA

ISBN: 9780883853429

Category: Mathematics

Page: 181

View: 9848

DOWNLOAD NOW »
Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

An Invitation to Mathematics

From Competitions to Research

Author: Dierk Schleicher,Malte Lackmann

Publisher: Springer Science & Business Media

ISBN: 9783642195334

Category: Mathematics

Page: 220

View: 3341

DOWNLOAD NOW »
This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.

Fascinating Mathematical People

Interviews and Memoirs

Author: Donald J. Albers,Gerald L. Alexanderson

Publisher: Princeton University Press

ISBN: 9781400839551

Category: Mathematics

Page: 352

View: 8521

DOWNLOAD NOW »
Fascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics. Featured here--in their own words--are major research mathematicians whose cutting-edge discoveries have advanced the frontiers of the field, such as Lars Ahlfors, Mary Cartwright, Dusa McDuff, and Atle Selberg. Others are leading mathematicians who have also been highly influential as teachers and mentors, like Tom Apostol and Jean Taylor. Fern Hunt describes what it was like to be among the first black women to earn a PhD in mathematics. Harold Bacon made trips to Alcatraz to help a prisoner learn calculus. Thomas Banchoff, who first became interested in the fourth dimension while reading a Captain Marvel comic, relates his fascinating friendship with Salvador Dalí and their shared passion for art, mathematics, and the profound connection between the two. Other mathematical people found here are Leon Bankoff, who was also a Beverly Hills dentist; Arthur Benjamin, a part-time professional magician; and Joseph Gallian, a legendary mentor of future mathematicians, but also a world-renowned expert on the Beatles. This beautifully illustrated collection includes many photographs never before published, concise introductions by the editors to each person, and a foreword by Philip J. Davis. Some images inside the book are unavailable due to digital copyright restrictions.

Mathematical People

Profiles and Interviews

Author: Donald Albers,Gerald L. Alexanderson

Publisher: CRC Press

ISBN: 1439865175

Category: Mathematics

Page: 416

View: 3421

DOWNLOAD NOW »
This unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introduction by Philip J. Davis.

On Evaluating Curricular Effectiveness:

Judging the Quality of K-12 Mathematics Evaluations

Author: Committee for a Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials,Mathematical Sciences Education Board,Center for Education,Division of Behavioral and Social Sciences and Education,National Research Council

Publisher: National Academies Press

ISBN: 0309092426

Category: Education

Page: 288

View: 9455

DOWNLOAD NOW »
This book reviews the evaluation research literature that has accumulated around 19 K-12 mathematics curricula and breaks new ground in framing an ambitious and rigorous approach to curriculum evaluation that has relevance beyond mathematics. The committee that produced this book consisted of mathematicians, mathematics educators, and methodologists who began with the following charge: Evaluate the quality of the evaluations of the thirteen National Science Foundation (NSF)-supported and six commercially generated mathematics curriculum materials; Determine whether the available data are sufficient for evaluating the efficacy of these materials, and if not; Develop recommendations about the design of a project that could result in the generation of more reliable and valid data for evaluating such materials. The committee collected, reviewed, and classified almost 700 studies, solicited expert testimony during two workshops, developed an evaluation framework, established dimensions/criteria for three methodologies (content analyses, comparative studies, and case studies), drew conclusions on the corpus of studies, and made recommendations for future research.

Teaching Formal Methods

Second International Conference, TFM 2009, Eindhoven, The Netherlands, November 2-6, 2009, Proceedings

Author: Jeremy Gibbons,Jose Nuno Oliveira

Publisher: Springer Science & Business Media

ISBN: 3642049117

Category: Computers

Page: 175

View: 1103

DOWNLOAD NOW »
This book constitutes the refereed proceedings of the TFM 2009, held in Eindhoven, The Netherlands in November 2009. The 10 revised full papers presented together with an abstracts of invited talk were carefully reviewed and selected from 19 submissions. The papers presented explore the experiences of teaching FMs, both successful and unsuccessful, educational resources including the use of books, case studies and the internet, the education of weak and mathphobic students, the integration, or otherwise, of FMs into the curriculum, including, contributions to the definition of a Formal Methods Body of Knowledge (FMBOK), the advantages of FM-trained graduates in the workplace, changing attitudes towards FMs in students, academic staff and practitioners and the necessary mathematical background.