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Algorithmic Algebra and Number Theory
This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing ...
An Invitation to Computational Homotopy
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifyi...
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to creat...
Groups and Computation III
This volume contains contributions by the participants of the conference "Groups and Computation", which took place at The Ohio State University in Columbus, Ohio, in June 1999. This conference was the successor of two workshops on "Groups and Computation" held at DIMACS in 1991 and 1995. There are papers on permutation group algorithms, finitely presented groups, polycyclic groups, and parallel computation, providing a representative sample of the breadth of Computational Group Theory. On the other hand, more than one third of the papers deal with computations in matrix groups, giving an in-depth treatment of the currently most active area of the field. The points of view of the papers range from explicit computations to group-theoretic algorithms to group-theoretic theorems needed for algorithm development.
Computational and Combinatorial Group Theory and Cryptography
This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York. Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.
Groups and Computation
Consists of papers presented at the workshop on Groups and Computation held at DIMACS.
Introduction to Combinatorial Designs, Second Edition
This new edition presents a comprehensive look at combinatorial designs. It coversclassical designs such as Latin squares, balanced incomplete block designs, and finite projective and affine planes as well as more contemporary designs that include one-factorizations, Room squares, tournament designs, and nested designs. The book featuresapplications in cryptography, computer science, experimental design, communications theory, and more. With every topic, it includes instructive examples and theorems. The text also provides exercises in each section, select answers in the back of the book, and more complete solutions on the author's website.
