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 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
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 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
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
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
The challenge of population aging requires innovative approaches to meet the needs of increasing numbers of older people. Emerging information and communication technologies (ICTs), such as pervasive
At the Mogao Grottoes, a World Heritage site near Dunhuang city in Gansu Province, visitor numbers have increased inexorably since 1979 when the site opened. A national policy that identifies tourism
Smallpox, measles, diphtheria, polio: vaccines have diminished their power, and in some cases, eradicated these dreaded diseases. Yet this century has seen growing numbers of parents refusing vaccinat
This delicious new book reveals the fascinating science behind some of our favorite candies. If you’ve ever wondered how candy corn is made or whether Baby Ruth bars really float, as in the movie Cadd
This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion
Alzheimer’s disease (AD) is a devastating and dehumanizing illness affecting increasingly large numbers of elderly and even middle-aged persons in a worldwide epidemic. Alzheimer’s Disease: A Physicia
"Infection in the Compromised Host" has become a classic chapter in textbooks devoted to infectious diseases and internal medicine. The numbers of compromised hosts are increasing in
Rising numbers of young children diagnosed with autism spectrum disorders means more students with ASD entering pre-school and the elementary grades. For these young learners, individualized instructi
This book starts with the basic concepts of Fuzzy Logic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers
Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in alge
The raw numbers of high-energy-density physics are amazing: shock waves at hundreds of km/s (approaching a million km per hour), temperatures of millions of degrees, and pressures that exceed 100 mill
Production planning in fresh food industries is a challenging task. Although modern Advanced Planning and Scheduling (APS) systems could provide significant support, APS implementation numbers in thes
TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly con
This text attempts to present the whole range of quantum mechanics, from the fundamental assumptions to the experimental numbers. The author presents a unified theoretical formulation and includes exa
This lively and practical introduction to the mathematics of money invites us to take a fresh look at the numbers that underpin our financial decisions. Morton D. Davis talks about strategies to use w
This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot b
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classi
In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been include
The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty
All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until
"...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART,
