Number theory

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach.

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks.

This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research.

A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm.

The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions.

Professor Kreiger's translation of Sierpinski's earlier work on point-set topology was speedily recognized as the outstanding work on the subject in English.

This book gives a self-contained fundamental study of the subject.

Energy of knots is a theory that was introduced to create a "e;canonical configuration"e; of a knot - a beautiful knot which represents its knot type.

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.

The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered.

This volume contains the expanded versions of the lectures given by the authors at the C.

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.

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.

Linear Algebra and Projective Geometry

Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.

For a long time the techniques of solving linear optimization (LP) problems improved only marginally.

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature.

The Linear Algebra Survival Guide offers a concise introduction to the difficult core topics of linear algebra, guiding you through the powerful graphic displays and visualization of Mathematica that make the most abstract theories seem simple - allowing you to tackle realistic problems using simple mathematical manipulations.

This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics.

Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory.

A self-contained 2010 account of the state of the art in classical complex multiplication.

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics.

This book offers an essential textbook on complex analysis.

Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian.

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition.

From the reviews: "e;This book gives a thorough introduction to several theories that are fundamental to research on modular forms.

This book can be divided into two parts.

PaulErdos ?

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics.

Examines the ancient cosmic science of the female megalithic astronomers*; Describes the shared sacred geometry and astronomy knowledge in the megalithic monuments, temples, and secret calendars of the matrilineal cultures of Malta, Gobekli Tepe, and the Minoans of Crete*; Shows how early Christians helped preserve ancient science by encoding it in the rock-cut churches of the Cappadocia region of Turkey*; Explains how Greek myths reveal the transition from matriarchy to patriarchyLong before Pythagoras and Plato, before arithmetic and Christianity, there existed matrilineal societies around the Mediterranean, led by women with a sophisticated understanding of astronomy and sacred science.

From the review: "e;The present book has as its aim to resolve a discrepancy in the textbook literature and .

This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur.

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes.

Rings That are Nearly Associative

The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications.

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This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory.

The theory of HP spaces has its origins in discoveries made forty or fifty years ago by such mathematicians as G.