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Algorithms and Computation in Mathematics

Algorithms and Computation in Mathematics
34 Jahrgänge | 1997 - 2020


With this forward-thinking series Springer recognizes that the prevailing trend in mathematical research towards algorithmic and constructive processes is one of long-term importance. This series is intended to further the development of computational and algorithmic mathematics. In particular, Algorithms and Computation in Mathematics emphasizes the computational aspects of algebraic geometry, number theory, combinatorics, commutative, non-commutative and differential algebra, geometric and algebraic topology, group theory, optimization, dynamical systems and Lie theory.

Alle Bücher der Reihe Algorithms and Computation in Mathematics

2020 | Buch

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective …

2020 | Buch

Topics in Galois Fields

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive …

2018 | Buch

The Gröbner Cover

This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Gröbner Cover, the most accurate algebraic method for discussing parametric polynomial systems. It also …

2013 | Buch

Graphs, Networks and Algorithms

From the reviews of the previous editions

".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this a

2013 | Buch

Geometry of Continued Fractions

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generali

2010 | Buch


The Formal Theory of Differential Equations and its Applications in Computer Algebra

2010 | Buch


Structures for Algorithms and Applications

2009 | Buch

Computability of Julia Sets

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content.

Computational hardness of

2008 | Buch

Graphs, Networks and Algorithms

From the reviews of the 2nd edition

The substantial development effort of this text clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applicatio

2008 | Buch

Rational Algebraic Curves

A Computer Algebra Approach

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-cor

2008 | Buch

Combinatorial Algebraic Topology

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitu

2007 | Buch

Algorithmic Topology and Classification of 3-Manifolds

From the reviews of the 1st edition:

"This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-

2007 | Buch

Binary Quadratic Forms

An Algorithmic Approach

This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerabl

2006 | Buch

Classification Algorithms for Codes and Designs

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings,

2006 | Buch

Computing in Algebraic Geometry

A Quick Start using SINGULAR

2006 | Buch

Self-Dual Codes and Invariant Theory

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers writt

2006 | Buch

Error-Correcting Linear Codes

Classification by Isometry and Applications

The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. - ing an applied discipl

2006 | Buch

Algorithms in Real Algebraic Geometry

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connec

2006 | Buch

Discovering Mathematics with Magma

Reducing the Abstract to the Concrete

The appearance of this volume celebrates the ?rst decade of Magma, a new computeralgebrasystemlaunchedattheFirstMagmaConferenceonCom- tational Algebra held at Queen Mary and West?eld College, London, August 1993. This book introduces the reader to th

2005 | Buch

Symbolic Integration I

Transcendental Functions

Symbolic Integration I is destined to become the standard reference work in the field. Manuel Bronstein is a leading expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail