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
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,
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 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
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
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
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
Statistical science as organized in formal academic departments is relatively new. With a few exceptions, most Statistics and Biostatistics departments have been created within the past 60 years. Th
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
"...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,
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 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
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
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as wel
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 of tables provides comparative data from the fields of zoology, botany, microbiology, and human biology. It is a "must" for everyone interested in biology but also of help for all parents to
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
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
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
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are
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
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
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a disti
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a disti
This unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illu
This book presents the history of HIV/AIDS in China, which over the last three decades has been a gripping tale of exclusion and fear, and then, by turns, of involuntary tragedy, cautious experimentat
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
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
Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The bene
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
Enlarged and updated for its second edition, this highly readable book addresses four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is t
From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number the
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
Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatori
