Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life.This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ...

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other end, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, it clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while...

This book constitutes the thoroughly refereed proceedings of the 5th International Conference on Mathematics and Computation in Music, MCM 2015, held in London, UK, in June 2015. The 24 full papers and 14 short papers presented were carefully reviewed and selected from 64 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on notation and representation, mus...

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic serie...

This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice.Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for ach...

This book constitutes the refereed proceedings of the 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, held in Ensenada, Mexico, in April 2016.The 52 papers presented together with 5 abstracts were carefully reviewed and selected from 131 submissions. The papers address a variety of topics in theoretical computer science with a certain focus on algorithms (approximation, online, randomized, algorithmic game theory, etc.), analytic combinatorics and analysis of a...

This book constitutes the thoroughly refereed post-conference proceedings of the 40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014, held in Nouan-le-Fuzelier, France, in June 2014.The 32 revised full papers presented were carefully reviewed and selected from 80 submissions. The book also includes two invited papers. The papers cover a wide range of topics in graph theory related to computer science, such as design and analysis of sequential, paral...

The cryptosystems based on the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP) and the Elliptic Curve Discrete Logarithm Problem (ECDLP) are essentially the only three types of practical public-key cryptosystems in use. The security of these cryptosystems relies heavily on these three infeasible problems, as no polynomial-time algorithms exist for them so far. However, polynomial-time quantum algorithms for IFP, DLP and ECDLP do exist, provided that a practical qu...

This book constitutes the proceedings of the 10th International Workshop on Algorithms and Computation, WALCOM 2016, held in Kathmandu, Nepal, in March 2016.The 27 full papers presented together with 4 invited talks were carefully reviewed and selected from 68 submissions. The papers cover a wide range of topics such as approximation algorithms, computational complexity, computational geometry, data structures, graph algorithms, graph coloring, graph exploration, and online algorit...

The two-volume set LNCS 10627 and 10628 constitutes the refereed proceedings of the 11th International Conference on Combinatorial Optimization and Applications, COCOA 2017, held in Shanghai, China, in December 2017.The 59 full papers and 19 short papers presented were carefully reviewed and selected from 145 submissions. The papers cover most aspects of theoretical computer science and combinatorics related to computing, including classic combinatorial optimization, geometric opti...

The two volume-set, LNCS 9215 and LNCS 9216, constitutes the refereed proceedings of the 35th Annual International Cryptology Conference, CRYPTO 2015, held in Santa Barbara, CA, USA, in August 2015. The 74 revised full papers presented were carefully reviewed and selected from 266 submissions. The papers are organized in the following topical sections: lattice-based cryptography; cryptanalytic insights; modes and constructions; multilinear maps and IO; pseudorandomness; block cipher crypta...

This book constitutes the refereed proceedings of the 16th European Conference on Evolutionary Computation in Combinatorial Optimization, EvoCOP 2016, held in Porto, Portugal, in March/April 2016, co-located with the Evo*2015 events EuroGP, EvoMUSART and EvoApplications.The 17 revised full papers presented were carefully reviewed and selected from 44 submissions. The papers cover methodology, applications and theoretical studies. The methods included evolutionary and memetic algorit...