Monograph In Mathematics
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Convex Polyhedra
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Author : A.D. Alexandrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-10
Convex Polyhedra written by A.D. Alexandrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-10 with Mathematics categories.
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.
Digraphs
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Author : Jorgen Bang-Jensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Digraphs written by Jorgen Bang-Jensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to prac tical problems. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered over the last couple of decades. The theory of graphs can be roughly partitioned into two branches: the areas of undirected graphs and directed graphs (digraphs). Even though both areas have numerous important applications, for various reasons, undirected graphs have been studied much more extensively than directed graphs. One of the reasons is that undirected graphs form in a sense a special class of directed graphs (symmetric digraphs) and hence problems that can be for mulated for both directed and undirected graphs are often easier for the latter. Another reason is that, unlike for the case of undirected graphs, for which there are several important books covering both classical and recent results, no previous book covers more than a small fraction of the results obtained on digraphs within the last 25 years. Typically, digraphs are consid ered only in one chapter or by a few elementary results scattered throughout the book. Despite all this, the theory of directed graphs has developed enormously within the last three decades. There is an extensive literature on digraphs (more than 3000 papers). Many of these papers contain, not only interesting theoretical results, but also important algorithms as well as applications.
The Q Theory Of Finite Semigroups
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Author : John Rhodes
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-05
The Q Theory Of Finite Semigroups written by John Rhodes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-05 with Mathematics categories.
Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader - from the graduate student to the researcher/practitioner – with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: (1) Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; (2) Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; (3) Introduces spectral theory into finite semigroup theory; (4) Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; (5) Presents over 70 research problems, most new, and hundreds of exercises. Additional features: (1) For newcomers, an appendix on elementary finite semigroup theory; (2) Extensive bibliography and index. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory.
Constructivist Views On The Teaching And Learning Of Mathematics
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Author : Robert Benjamin Davis
language : en
Publisher:
Release Date : 1990
Constructivist Views On The Teaching And Learning Of Mathematics written by Robert Benjamin Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Education categories.
Constructivist views on the teaching and learning of mathematics (Journal for research in mathematics education).
Mathematical Techniques For Engineers And Scientists
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Author : Larry C. Andrews
language : en
Publisher: SPIE Press
Release Date : 2003
Mathematical Techniques For Engineers And Scientists written by Larry C. Andrews and has been published by SPIE Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
"This self-study text for practicing engineers and scientists explains the mathematical tools that are required for advanced technological applications, but are often not covered in undergraduate school. The authors (University of Central Florida) describe special functions, matrix methods, vector operations, the transformation laws of tensors, the analytic functions of a complex variable, integral transforms, partial differential equations, probability theory, and random processes. The book could also serve as a supplemental graduate text."--Memento.
Solitons In Field Theory And Nonlinear Analysis
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Author : Yisong Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15
Solitons In Field Theory And Nonlinear Analysis written by Yisong Yang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Mathematics categories.
There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.
Mathematical Topics Between Classical And Quantum Mechanics
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Author : Nicholas P. Landsman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Topics Between Classical And Quantum Mechanics written by Nicholas P. Landsman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper ator algebras, and their state spaces, which is based on this relationship.
Bernoulli Numbers And Zeta Functions
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Author : Tsuneo Arakawa
language : en
Publisher: Springer
Release Date : 2014-07-11
Bernoulli Numbers And Zeta Functions written by Tsuneo Arakawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-11 with Mathematics categories.
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.
Introduction To Singularities And Deformations
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Author : Gert-Martin Greuel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-23
Introduction To Singularities And Deformations written by Gert-Martin Greuel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-23 with Mathematics categories.
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.
Mathematical Thinking How To Develop It In The Classroom
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Author : Shigeo Katagiri
language : en
Publisher: World Scientific
Release Date : 2012-01-27
Mathematical Thinking How To Develop It In The Classroom written by Shigeo Katagiri and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-27 with Mathematics categories.
Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties to develope it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.