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Books > Science & Mathematics > Mathematics > Geometry
The main reason I write this book was just to fullfil my long time
dream to be able to tutor students. Most students do not bring
their text books at home from school. This makes it difficult to
help them. This book may help such students as this can be used as
a reference in understanding Algebra and Geometry.
Dugopolski's Trigonometry, Third Edition gives students the
essential strategies to help them develop the comprehension and
confidence they need to be successful in this course. Students will
find enough carefully placed learning aids and review tools to help
them do the math without getting distracted from their objectives.
Regardless of their goals beyond the course, all students will
benefit from Dugopolski's emphasis on problem solving and critical
thinking, which is enhanced by the addition of nearly 1,000
exercises in this edition. Instructors will also find this book a
pleasure to use, with the support of an Annotated Instructor's
Edition which maps each group of exercises back to each example
within the section; pop quizzes for every section; and answers on
the page for most exercises plus a complete answer section at the
back of the text. An Insider's Guide provides further strategies
for successful teaching with Dugopolski.
If you enjoy beautiful geometry and relish the challenge and excitement of something new, the mathematical art of hinged dissections is for you. Using this book, you can explore ways to create hinged collections of pieces that swing together to form a figure. Swing them another way and then, like magic, they form another figure! The profuse illustrations and lively text will show you how to find a wealth of hinged dissections for all kinds of polygons, stars and crosses, curved and even three-dimensional figures. The author includes careful explanation of ingenious new techniques, as well as puzzles and solutions for readers of all mathematical levels. These novel and original dissections will be a gold mine for math puzzle enthusiasts, for math educators in search of enrichment topics, and for anyone who loves to see beautiful objects in motion.
Voronoi diagrams partition space according to the influence certain
sites exert on their environment. Since the 17th century, such
structures play an important role in many areas like Astronomy,
Physics, Chemistry, Biology, Ecology, Economics, Mathematics and
Computer Science. They help to describe zones of political
influence, to determine the hospital nearest to an accident site,
to compute collision-free paths for mobile robots, to reconstruct
curves and surfaces from sample points, to refine triangular
meshes, and to design location strategies for competing markets.
This unique book offers a state-of-the-art view of Voronoi diagrams
and their structure, and it provides efficient algorithms towards
their computation. Readers with an entry-level background in
algorithms can enjoy a guided tour of gently increasing difficulty
through a fascinating area. Lecturers might find this volume a
welcome source for their courses on computational geometry. Experts
are offered a broader view, including many alternative solutions,
and up-to-date references to the existing literature; they might
benefit in their own research or application development.
The geometry of power exponents includes the Newton polyhedron,
normal cones of its faces, power and logarithmic transformations.
On the basis of the geometry universal algorithms for
simplifications of systems of nonlinear equations (algebraic,
ordinary differential and partial differential) were developed.
The algorithms form a new calculus which allows to make local and
asymptotical analysis of solutions to those systems.
The efficiency of the calculus is demonstrated with regard to
several complicated problems from Robotics, Celestial Mechanics,
Hydrodynamics and Thermodynamics. The calculus also gives classical
results obtained earlier intuitively and is an alternative to
Algebraic Geometry, Differential Algebra, Lie group Analysis and
Nonstandard Analysis.
This book focuses on important mathematical considerations in
describing the synthesis of original mechanisms for generating
curves. The synthesis is manual and not based on the use of
computer tools. Kinematics is applied to confirm the drawing of the
curves, and the closed loop method, and in some cases the distances
method, is applied in this phase. The book provides all the notions
of structure and kinematics that are necessary to calculate the
mechanisms and also analyzes other kinematic possibilities of the
created mechanisms. Offering a concise, yet self-contained guide to
the mathematical fundamentals for mechanisms of curve generation,
together with a useful collection of mechanisms exercises, the book
is intended for students learning about mechanism kinematics, as
well as engineers dealing with mechanism design and analysis. It is
based on the authors' many years of research, which has been
published in different books and journals, mainly, but not
exclusively, in Romanian.
The main topic of the book is amenable groups, i.e., groups on
which there exist invariant finitely additive measures. It was
discovered that the existence or non-existence of amenability is
responsible for many interesting phenomena such as, e.g., the
Banach-Tarski Paradox about breaking a sphere into two spheres of
the same radius. Since then, amenability has been actively studied
and a number of different approaches resulted in many examples of
amenable and non-amenable groups. In the book, the author puts
together main approaches to study amenability. A novel feature of
the book is that the exposition of the material starts with
examples which introduce a method rather than illustrating it. This
allows the reader to quickly move on to meaningful material without
learning and remembering a lot of additional definitions and
preparatory results; those are presented after analyzing the main
examples. The techniques that are used for proving amenability in
this book are mainly a combination of analytic and probabilistic
tools with geometric group theory.
This book is a self-contained account of the method based on
Carleman estimates for inverse problems of determining spatially
varying functions of differential equations of the hyperbolic type
by non-overdetermining data of solutions. The formulation is
different from that of Dirichlet-to-Neumann maps and can often
prove the global uniqueness and Lipschitz stability even with a
single measurement. These types of inverse problems include
coefficient inverse problems of determining physical parameters in
inhomogeneous media that appear in many applications related to
electromagnetism, elasticity, and related phenomena. Although the
methodology was created in 1981 by Bukhgeim and Klibanov, its
comprehensive development has been accomplished only recently. In
spite of the wide applicability of the method, there are few
monographs focusing on combined accounts of Carleman estimates and
applications to inverse problems. The aim in this book is to fill
that gap. The basic tool is Carleman estimates, the theory of which
has been established within a very general framework, so that the
method using Carleman estimates for inverse problems is
misunderstood as being very difficult. The main purpose of the book
is to provide an accessible approach to the methodology. To
accomplish that goal, the authors include a direct derivation of
Carleman estimates, the derivation being based essentially on
elementary calculus working flexibly for various equations. Because
the inverse problem depends heavily on respective equations, too
general and abstract an approach may not be balanced. Thus a direct
and concrete means was chosen not only because it is friendly to
readers but also is much more relevant. By practical necessity,
there is surely a wide range of inverse problems and the method
delineated here can solve them. The intention is for readers to
learn that method and then apply it to solving new inverse
problems.
Trigonometry, Tenth Edition, by Lial, Hornsby, Schneider, and
Daniels, engages and supports students in the learning process by
developing both the conceptual understanding and the analytical
skills necessary for success in mathematics. With the Tenth
Edition, the authors recognize that students are learning in new
ways, and that the classroom is evolving. The Lial team is now
offering a new suite of resources to support today's instructors
and students. New co-author Callie Daniels has experience in all
classroom types including traditional, hybrid and online courses,
which has driven the new MyMathLab features. For example, MyNotes
provide structure for student note-taking, and Interactive Chapter
Summaries allow students to quiz themselves in interactive examples
on key vocabulary, symbols and concepts. Daniels' experience,
coupled with the long-time successful approach of the Lial series,
has helped to more tightly integrate the text with online learning
than ever before.
This book covers methods of Mathematical Morphology to model and
simulate random sets and functions (scalar and multivariate). The
introduced models concern many physical situations in heterogeneous
media, where a probabilistic approach is required, like fracture
statistics of materials, scaling up of permeability in porous
media, electron microscopy images (including multispectral images),
rough surfaces, multi-component composites, biological tissues,
textures for image coding and synthesis. The common feature of
these random structures is their domain of definition in n
dimensions, requiring more general models than standard Stochastic
Processes.The main topics of the book cover an introduction to the
theory of random sets, random space tessellations, Boolean random
sets and functions, space-time random sets and functions (Dead
Leaves, Sequential Alternate models, Reaction-Diffusion),
prediction of effective properties of random media, and
probabilistic fracture theories.
This book features a selection of articles based on the XXXV
Bialowieza Workshop on Geometric Methods in Physics, 2016. The
series of Bialowieza workshops, attended by a community of experts
at the crossroads of mathematics and physics, is a major annual
event in the field. The works in this book, based on presentations
given at the workshop, are previously unpublished, at the cutting
edge of current research, typically grounded in geometry and
analysis, and with applications to classical and quantum physics.
In 2016 the special session "Integrability and Geometry" in
particular attracted pioneers and leading specialists in the field.
Traditionally, the Bialowieza Workshop is followed by a School on
Geometry and Physics, for advanced graduate students and
early-career researchers, and the book also includes extended
abstracts of the lecture series.
This monograph focuses on the geometric theory of motivic
integration, which takes its values in the Grothendieck ring of
varieties. This theory is rooted in a groundbreaking idea of
Kontsevich and was further developed by Denef & Loeser and
Sebag. It is presented in the context of formal schemes over a
discrete valuation ring, without any restriction on the residue
characteristic. The text first discusses the main features of the
Grothendieck ring of varieties, arc schemes, and Greenberg schemes.
It then moves on to motivic integration and its applications to
birational geometry and non-Archimedean geometry. Also included in
the work is a prologue on p-adic analytic manifolds, which served
as a model for motivic integration. With its extensive discussion
of preliminaries and applications, this book is an ideal resource
for graduate students of algebraic geometry and researchers of
motivic integration. It will also serve as a motivation for more
recent and sophisticated theories that have been developed since.
This volume consists of ten articles which provide an in-depth and
reader-friendly survey of some of the foundational aspects of
singularity theory. Authored by world experts, the various
contributions deal with both classical material and modern
developments, covering a wide range of topics which are linked to
each other in fundamental ways. Singularities are ubiquitous in
mathematics and science in general. Singularity theory interacts
energetically with the rest of mathematics, acting as a crucible
where different types of mathematical problems interact, surprising
connections are born and simple questions lead to ideas which
resonate in other parts of the subject. This is the first volume in
a series which aims to provide an accessible account of the
state-of-the-art of the subject, its frontiers, and its
interactions with other areas of research. The book is addressed to
graduate students and newcomers to the theory, as well as to
specialists who can use it as a guidebook.
This self-contained book is an exposition of the fundamental ideas
of model theory. It presents the necessary background from logic,
set theory and other topics of mathematics. Only some degree of
mathematical maturity and willingness to assimilate ideas from
diverse areas are required. The book can be used for both teaching
and self-study, ideally over two semesters. It is primarily aimed
at graduate students in mathematical logic who want to specialise
in model theory. However, the first two chapters constitute the
first introduction to the subject and can be covered in
one-semester course to senior undergraduate students in
mathematical logic. The book is also suitable for researchers who
wish to use model theory in their work.
This elegant little book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries. Many famous mathematicians have worked on the problem, but the proof eluded fomulation until the 1950s, when it was finally cracked with a brute-force approach using a computer. The book begins by discussing the history of the problem, and then goes into the mathematics, both pleasantly enough that anyone with an elementary knowledge of geometry can follow it, and still with enough rigor that a mathematician can also read it with pleasure. The authors discuss the mathematics as well as the philosophical debate that ensued when the proof was announced: Just what is a mathematical proof, if it takes a computer to provide one -- and is such a thing a proof at all?
0 Basic Facts.- 1 Hey's Theorem and Consequences.- 2 Siegel-Weyl
Reduction Theory.- 3 The Tamagawa Number and the Volume of
G(?)/G(?).- 3.1 Statement of the main result.- 3.2 Proof of 3.1.-
3.3 The volume of G(?)/G(?).- 4 The Size of ?.- 4.1 Statement of
results.- 4.2 Proofs.- 5 Margulis' Finiteness Theorem.- 5.1 The
Result.- 5.2 Amenable groups.- 5.3 Kazhdan's property (T).- 5.4
Proof of 5.1; beginning.- 5.5 Interlude: parabolics and their
opposites.- 5.6 Continuation of the proof.- 5.7 Contracting
automorphisms and the Moore Ergodicity theorem.- 5.8 End of proof.-
5.9 Appendix on measure theory.- 6 A Zariski Dense and a Free
Subgroup of ?.- 7 An Example.- 8 Problems.- 8.1 Generators.- 8.2
The congruence problem.- 8.3 Betti numbers.- References.
This volume contains a collection of research papers and useful
surveys by experts in the field which provide a representative
picture of the current status of this fascinating area. Based on
contributions from the VIII International Meeting on Lorentzian
Geometry, held at the University of Malaga, Spain, this volume
covers topics such as distinguished (maximal, trapped, null,
spacelike, constant mean curvature, umbilical...) submanifolds,
causal completion of spacetimes, stationary regions and horizons in
spacetimes, solitons in semi-Riemannian manifolds, relation between
Lorentzian and Finslerian geometries and the oscillator spacetime.
In the last decades Lorentzian geometry has experienced a
significant impulse, which has transformed it from just a
mathematical tool for general relativity to a consolidated branch
of differential geometry, interesting in and of itself. Nowadays,
this field provides a framework where many different mathematical
techniques arise with applications to multiple parts of mathematics
and physics. This book is addressed to differential geometers,
mathematical physicists and relativists, and graduate students
interested in the field.
While it is well known that the Delian problems are impossible to
solve with a straightedge and compass - for example, it is
impossible to construct a segment whose length is cube root of 2
with these instruments - the discovery of the Italian mathematician
Margherita Beloch Piazzolla in 1934 that one can in fact construct
a segment of length cube root of 2 with a single paper fold was
completely ignored (till the end of the 1980s). This comes as no
surprise, since with few exceptions paper folding was seldom
considered as a mathematical practice, let alone as a mathematical
procedure of inference or proof that could prompt novel
mathematical discoveries. A few questions immediately arise: Why
did paper folding become a non-instrument? What caused the
marginalisation of this technique? And how was the mathematical
knowledge, which was nevertheless transmitted and prompted by paper
folding, later treated and conceptualised? Aiming to answer these
questions, this volume provides, for the first time, an extensive
historical study on the history of folding in mathematics, spanning
from the 16th century to the 20th century, and offers a general
study on the ways mathematical knowledge is marginalised,
disappears, is ignored or becomes obsolete. In doing so, it makes a
valuable contribution to the field of history and philosophy of
science, particularly the history and philosophy of mathematics and
is highly recommended for anyone interested in these topics.
This book provides a comprehensive account of the theory of moduli
spaces of elliptic curves (over integer rings) and its application
to modular forms. The construction of Galois representations, which
play a fundamental role in Wiles' proof of the Shimura-Taniyama
conjecture, is given. In addition, the book presents an outline of
the proof of diverse modularity results of two-dimensional Galois
representations (including that of Wiles), as well as some of the
author's new results in that direction.In this new second edition,
a detailed description of Barsotti-Tate groups (including formal
Lie groups) is added to Chapter 1. As an application, a
down-to-earth description of formal deformation theory of elliptic
curves is incorporated at the end of Chapter 2 (in order to make
the proof of regularity of the moduli of elliptic curve more
conceptual), and in Chapter 4, though limited to ordinary cases,
newly incorporated are Ribet's theorem of full image of modular
p-adic Galois representation and its generalization to 'big' -adic
Galois representations under mild assumptions (a new result of the
author). Though some of the striking developments described above
is out of the scope of this introductory book, the author gives a
taste of present day research in the area of Number Theory at the
very end of the book (giving a good account of modularity theory of
abelian -varieties and -curves).
The book provides an introduction of very recent results about the
tensors and mainly focuses on the authors' work and perspective. A
systematic description about how to extend the numerical linear
algebra to the numerical multi-linear algebra is also delivered in
this book. The authors design the neural network model for the
computation of the rank-one approximation of real tensors, a
normalization algorithm to convert some nonnegative tensors to
plane stochastic tensors and a probabilistic algorithm for locating
a positive diagonal in a nonnegative tensors, adaptive randomized
algorithms for computing the approximate tensor decompositions, and
the QR type method for computing U-eigenpairs of complex tensors.
This book could be used for the Graduate course, such as
Introduction to Tensor. Researchers may also find it helpful as a
reference in tensor research.
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Geometry, Algebra, Number Theory, and Their Information Technology Applications
- Toronto, Canada, June, 2016, and Kozhikode, India, August, 2016
(Hardcover, 1st ed. 2018)
Amir Akbary, Sanoli Gun
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R4,434
Discovery Miles 44 340
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Ships in 12 - 17 working days
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This volume contains proceedings of two conferences held in Toronto
(Canada) and Kozhikode (India) in 2016 in honor of the 60th
birthday of Professor Kumar Murty. The meetings were focused on
several aspects of number theory: The theory of automorphic forms
and their associated L-functions Arithmetic geometry, with special
emphasis on algebraic cycles, Shimura varieties, and explicit
methods in the theory of abelian varieties The emerging
applications of number theory in information technology Kumar Murty
has been a substantial influence in these topics, and the two
conferences were aimed at honoring his many contributions to number
theory, arithmetic geometry, and information technology.
This collection of contributions originates from the
well-established conference series "Fractal Geometry and
Stochastics" which brings together researchers from different
fields using concepts and methods from fractal geometry. Carefully
selected papers from keynote and invited speakers are included,
both discussing exciting new trends and results and giving a gentle
introduction to some recent developments. The topics covered
include Assouad dimensions and their connection to analysis,
multifractal properties of functions and measures, renewal theorems
in dynamics, dimensions and topology of random discrete structures,
self-similar trees, p-hyperbolicity, phase transitions from
continuous to discrete scale invariance, scaling limits of
stochastic processes, stemi-stable distributions and fractional
differential equations, and diffusion limited aggregation.
Representing a rich source of ideas and a good starting point for
more advanced topics in fractal geometry, the volume will appeal to
both established experts and newcomers.
According to Grothendieck, the notion of topos is "the bed or deep
river where come to be married geometry and algebra, topology and
arithmetic, mathematical logic and category theory, the world of
the continuous and that of discontinuous or discrete structures".
It is what he had "conceived of most broad to perceive with
finesse, by the same language rich of geometric resonances, an
"essence" which is common to situations most distant from each
other, coming from one region or another of the vast universe of
mathematical things". The aim of this book is to present a theory
and a number of techniques which allow to give substance to
Grothendieck's vision by building on the notion of classifying
topos educed by categorical logicians. Mathematical theories
(formalized within first-order logic) give rise to geometric
objects called sites; the passage from sites to their associated
toposes embodies the passage from the logical presentation of
theories to their mathematical content, i.e. from syntax to
semantics. The essential ambiguity given by the fact that any topos
is associated in general with an infinite number of theories or
different sites allows to study the relations between different
theories, and hence the theories themselves, by using toposes as
'bridges' between these different presentations. The expression or
calculation of invariants of toposes in terms of the theories
associated with them or their sites of definition generates a great
number of results and notions varying according to the different
types of presentation, giving rise to a veritable mathematical
morphogenesis.
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