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Applied Abstract Algebra
Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
Finite Fields
This book is devoted entirely to the theory of finite fields.
Cryptographic Hardware and Embedded Systems - CHES 2001
These are the proceedings of CHES 2001, the third Workshop on Cryptographic Hardware and Embedded Systems. The ?rst two CHES Workshops were held in Massachusetts, and this was the ?rst Workshop to be held in Europe. There was a large number of submissions this year, and in response the technical program was extended to 2 1/2 days. As is evident by the papers in these proceedings, many excellent submissions were made. Selecting the papers for this year’s CHES was not an easy task, and weregretthatwehadtorejectseveralveryinterstingpapersduetotheac l kof time. There were 66 submitted contributions this year, of which 31, or 47%, were selected for presentation. If we look at the number of subm...
Topics in Finite Fields
This volume contains the proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11), held July 22-26, 2013, in Magdeburg, Germany. Finite Fields are fundamental structures in mathematics. They lead to interesting deep problems in number theory, play a major role in combinatorics and finite geometry, and have a vast amount of applications in computer science. Papers in this volume cover these aspects of finite fields as well as applications in coding theory and cryptography.
Histories of Computing
Computer technology is pervasive in the modern world, its role ever more important as it becomes embedded in a myriad of physical systems and disciplinary ways of thinking. The late Michael Sean Mahoney was a pioneer scholar of the history of computing, one of the first established historians of science to take seriously the challenges and opportunities posed by information technology to our understanding of the twentieth century. MahoneyÕs work ranged widely, from logic and the theory of computation to the development of software and applications as craft-work. But it was always informed by a unique perspective derived from his distinguished work on the history of medieval mathematics and ...
Model Theory
Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
Bijective Combinatorics
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
Finite Fields and Applications
This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.
Computation and Automata
In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography.
Mathematical Foundations of Computer Science 1998
This book constitutes the refereed proceedings of the 23rd International Symposium on the Mathematical Foundations of Computer Science, MFCS'98, held in Brno, Czech Republic, in August 1998. The 71 revised full papers presented were carefully reviewed and selected from a total of 168 submissions. Also included are 11 full invited surveys by prominent leaders in the area. The papers are organized in topical sections on problem complexity; logic, semantics, and automata; rewriting; automata and transducers; typing; concurrency, semantics, and logic; circuit complexity; programming; structural complexity; formal languages; graphs; Turing complexity and logic; binary decision diagrams, etc..
