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Computational Methods for Representations of Groups and Algebras
I Introductory Articles.- 1 Classification Problems in the Representation Theory of Finite-Dimensional Algebras.- 2 Noncommutative Gröbner Bases, and Projective Resolutions.- 3 Construction of Finite Matrix Groups.- II Keynote Articles.- 4 Derived Tubularity: a Computational Approach.- 5 Problems in the Calculation of Group Cohomology.- 6 On a Tensor Category for the Exceptional Lie Groups.- 7 Non-Commutative Gröbner Bases and Anick's Resolution.- 8 A new Existence Proof of Janko's Simple Group J4.- 9 The Normalization: a new Algorithm, Implementation and Comparisons.- 10 A Computer Algebra Approach to sheaves over Weighted Projective Lines.- 11 Open Problems in the Theory of Kazhdan-Lusztig polynomials.- 12 Relative Trace Ideals and Cohen Macaulay Quotients.- 13 On Sims' Presentation for Lyons' Simple Group.- 14 A Presentation for the Lyons Simple Group.- 15 Reduction of Weakly Definite Unit Forms.- 16 Decision Problems in Finitely Presented Groups.- 17 Some Algorithms in Invariant Theory of Finite Groups.- 18 Coxeter Transformations associated with Finite Dimensional Algebras.- 19 The 2-Modular Decomposition Numbers of Co2.- 20 Bimodule and Matrix Problems.
Commutative Algebra, Singularities and Computer Algebra
Proceedings of the NATO Advanced Research Workshop, held in Sinaia, Romania, 17-22 September 2002
Mathematics Under the Microscope
The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, th...
Symbolic Rewriting Techniques
Symbolic rewriting techniques are methods for deriving consequences from systems of equations, and are of great use when investigating the structure of the solutions. Such techniques appear in many important areas of research within computer algebra: • the Knuth-Bendix completion for groups, monoids and general term-rewriting systems, • the Buchberger algorithm for Gröbner bases, • the Ritt-Wu characteristic set method for ordinary differential equations, and • the Riquier-Janet method for partial differential equations. This volume contains invited and contributed papers to the Symbolic Rewriting Techniques workshop, which was held at the Centro Stefano Franscini in Ascona, Switzerland, from April 30 to May 4, 1995. That workshop brought together 40 researchers from various areas of rewriting techniques, the main goal being the investigation of common threads and methods. Following the workshops, each contribution was formally refereed and 14 papers were selected for publication.
50th IMO - 50 Years of International Mathematical Olympiads
In July 2009 Germany hosted the 50th International Mathematical Olympiad (IMO). For the very first time the number of participating countries exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO age group and all those who have interest in this worldwide leading competition for highschool students.
Computer Algebra Handbook
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
Computational Algebra
Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.
Plain Plane Geometry
The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads. Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of "play" in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.
Mathematical Buffet
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