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Topics in Geometry, Coding Theory and Cryptography (Algebra and Applications)
Topics in Geometry, Coding Theory and Cryptography (Algebra and Applications)
The purpose of this reviewarticle is to serve as an introduction and at the same time, as an invitation to the theory of towers of function fields over finite fields. More specifically, we treat here the case of explicit towers; i.e., towers where the function fields are given by explicit equations. The asymptotic behaviour of the genus and of the...
Real Analysis
Real Analysis

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and...

Schaum's Outline Series Theory and Problems of Projective Geometry
Schaum's Outline Series Theory and Problems of Projective Geometry
The purpose of this book is to provide a first course in Projective Geometry for undergraduate majors in mathematics and for prospective teachers of high school geometry. For the former it will furnish an introduction to the important concept of projective spaces; for the latter it will introduce a more general geometry from which,...
Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics, Vol. 23)
Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics, Vol. 23)

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.

Many of the tools used in differential topology are introduced and the
...

Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications)
Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications)
Over the last two or three decades, elliptic curves have been playing an increasingly important role both in number theory and in related fields such as cryptography. For example, in the 1980s, elliptic curves started being used in cryptography and elliptic curve techniques were developed for factorization and primality...
Fourier Analysis (Graduate Studies in Mathematics)
Fourier Analysis (Graduate Studies in Mathematics)

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autónoma de Madrid and incorporates lecture notes from a course taught by José...

The History of Approximation Theory: From Euler to Bernstein
The History of Approximation Theory: From Euler to Bernstein

The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing...

Mathematical Statistics for Economics and Business
Mathematical Statistics for Economics and Business

Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics.  The selection of topics in this textbook is designed to provide students with a...

Advanced Modern Algebra
Advanced Modern Algebra

This book's organizing principle is the interplay between groups and rings, where “rings” includes the ideas of modules. It contains basic definitions, complete and clear theorems (the first with brief sketches of proofs), and gives attention to the topics of algebraic geometry, computers, homology, and...

Elementary Linear Programming with Applications, Second Edition
Elementary Linear Programming with Applications, Second Edition

Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common...

Theory of Linear Operations (North-Holland Mathematical Library)
Theory of Linear Operations (North-Holland Mathematical Library)
The theory of operators, created by V. Volterra, has as its object the study of functions defined on infinite-dimensional spaces. This theory has penetrated several highly important areas of mathematics in an essential way: suffice it to recall that the theory of integral equations and the calculus of variations are included as special cases within...
The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)
The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the...

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