Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particularattention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.

Geometry. --- Euclidean algorithm. --- Geometria euclidiana

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o

Fourier series. --- Euclidean algorithm. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Fourier series --- Euclidean algorithm --- Mathematical models.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.

NP-Completeness --- protocol compiler --- post-quantum cryptography --- Reed–Solomon codes --- key equation --- euclidean algorithm --- permutation group --- t-modified self-shrinking generator --- ideal cipher model --- algorithms in groups --- lightweight cryptography --- generalized self-shrinking generator --- numerical semigroup --- pseudo-random number generator --- symmetry --- pseudorandom permutation --- Berlekamp–Massey algorithm --- semigroup ideal --- algebraic-geometry code --- non-commutative cryptography --- provable security --- Engel words --- block cipher --- cryptography --- beyond birthday bound --- Weierstrass semigroup --- group theory --- braid groups --- statistical randomness tests --- group-based cryptography --- alternating group --- WalnutDSA --- Sugiyama et al. algorithm --- cryptanalysis --- digital signatures --- one-way functions --- key agreement protocol --- error-correcting code --- group key establishment

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

Cryptography -- Mathematics. --- Euclidean algorithm. --- Integer programming. --- Lattice theory. --- Cryptography --- Lattice theory --- Integer programming --- Euclidean algorithm --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Algorithms. --- Mathematics. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Algorism --- Computer science. --- Data structures (Computer science). --- Data encryption (Computer science). --- Computer science --- Computer Science. --- Data Structures. --- Data Encryption. --- Mathematics of Computing. --- Data Structures, Cryptology and Information Theory. --- Algorithm Analysis and Problem Complexity. --- Algebra --- Arithmetic --- Foundations --- Algorithms --- Number theory --- Programming (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data structures (Computer scienc. --- Computer software. --- Cryptology. --- Data Structures and Information Theory. --- Informatics --- Science --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Artificial intelligence --- Cryptography. --- Information theory. --- Data Science. --- Data processing. --- Communication theory --- Communication --- Cybernetics --- Computer mathematics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The Euclidean shortest path (ESP) problem asks the question: what is the path of minimum length connecting two points in a 2- or 3-dimensional space? Variants of this industrially-significant computational geometry problem also require the path to pass through specified areas and avoid defined obstacles. This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Suitable for a second- or third-year university algorithms course, the text enables readers to understand not only the algorithms and their pseudocodes, but also the correctness proofs, the analysis of time complexities, and other related topics. Topics and features: Provides theoretical and programming exercises at the end of each chapter Presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms Discusses algorithms for calculating exact or approximate ESPs in the plane Examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves Describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems Includes lists of symbols and abbreviations, in addition to other appendices This hands-on guide will be of interest to undergraduate students in computer science, IT, mathematics, and engineering. Programmers, mathematicians, and engineers dealing with shortest-path problems in practical applications will also find the book a useful resource. Dr. Fajie Li is at Huaqiao University, Xiamen, Fujian, China. Prof. Dr. Reinhard Klette is at the Tamaki Innovation Campus of The University of Auckland.

Computational complexity. --- Computer aided design. --- Computer science. --- Computer science -- Mathematics. --- Computer software. --- Electronic data processing. --- Euclidean algorithm. --- Optical pattern recognition. --- Graph algorithms --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Computer Science --- Mathematical analysis. --- Algebraic spaces. --- Spaces, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms. --- Numerical analysis. --- Computer science --- Pattern recognition. --- Computer-aided engineering. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Numeric Computing. --- Pattern Recognition. --- Discrete Mathematics in Computer Science. --- Math Applications in Computer Science. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Mathematics. --- Geometry, Algebraic --- Algorithms --- Number theory --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Informatics --- Science --- Complexity, Computational --- Electronic data processing --- Machine theory --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Software, Computer --- Computer systems --- Automation --- Computer science—Mathematics. --- CAE --- Engineering --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Algorism --- Arithmetic --- Foundations