This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, a
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view,
This book brings together selected lectures given by eminent educationalists in memory of Ruth Wong, an influential figure in the field of education. The lectures represent the powerful ideas seeded b
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by compu
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 form
This book deals with various systems of "numbers" that can be constructed by adding "imaginary units" to the real numbers. The complex numbers are a classical example of such a system. One of the most
Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from
Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough backg
Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experiment
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, includin
Everyone talks about the beauty of mathematics, but almost no one observes that this beauty is largely a result of the symmetries that emerge from simple combinations of natural numbers. One sees this
By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques o
This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-functi
Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Auth
The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will
The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deep
The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather
This monograph covers the theory of finite and infinite matrices, over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their re
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient l
The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as di
The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather
This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physi
This text plugs a gap in the standard curriculum by linking set theory with analysis. It features a distinctive, detailed treatment of the real numbers system, and combines an introduction to set theo
Refugees and migration are not a new story in the history of humankind, but in the last few years, against a backdrop of huge numbers of migrants, especially from war-torn countries, they have again b
This book discusses the ethical dilemmas of migration in the era of globalization. Centered on the recent influx of large numbers of migrants and refugees to the United States and Europe and viewed th
The book offers an in-depth study of the translation of vote counts into seat numbers in proportional representation systems – an approach guided by practical needs. It also provides plenty of empiri
Women are entering medical school in equal numbers as men, yet still face unique challenges in a profession where, overall, male physicians outnumber female physicians 3 to 1. Women in medicine also f
This book presents the topology optimization theory for laminar flows with low and moderate Reynolds numbers, based on the density method and level-set method, respectively. The density-method-based t
This unique volume presents an ecocultural and embodied perspective on understanding numbers and their history in indigenous communities. The book focuses on research carried out in Papua New Guinea
With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers a
Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) net
* Hepatocellular carcinoma (HCC) used to be regarded as a rare disease. However, the increasing numbers of chronic HCC carriers in the U.S. and subsequent increased incidences of HCC seen in most larg
Presenting a multidisciplinary approach to the prevention and management of injuries to young tennis players, this unique book considers multiple factors contributing to the increasing numbers of such
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the em
This book describes the exciting discovery of every isotope observed on earth to date, which currently numbers some 3000. For each isotope a short essay highlights the authors of the first publication
This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asympt
This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asympt
In this book the authors explain what computability means for data more complex than natural numbers and similar discrete data. In particular, they show how to develop a good theory of computability i
