Fibonacci Numbers -- Homogeneous Linear Recurrence Relations -- Finite Difference Equations -- Generating Functions -- Nonnegative Difference Equations -- Leslie’s Population Matrix Model -- Matrix Difference Equations -- Modular Recurrences -- Computational Complexity -- Some Nonlinear Recurrences.Difference equations are models of the world around us. From clocks to computers to chromosomes…
Foreword -- Introduction -- The Homogeneous Case -- Hilbert Functions -- Further Applications -- A. The ABC of CoCoA 5 -- B. Suggestions for Further Reading -- C. Hints for Selected Exercises -- Bibliography.Computational Commutative Algebra 2 is the natural continuation of Computational Commutative Algebra 1 with some twists, starting with the differently coloured cover graphics. The first vol…
Complex Numbers in Algebraic Form -- Complex Numbers in Trigonometric Form -- Complex Numbers and Geometry -- More on Complex Numbers and Geometry -- Olympiad-Caliber Problems -- Answers, Hints and Solutions to Proposed Problems.It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from t…
Monomial Ideals -- Squarefree monomial ideals -- Borel-fixed monomial ideals -- Three-dimensional staircases -- Cellular resolutions -- Alexander duality -- Generic monomial ideals -- Toric Algebra -- Semigroup rings -- Multigraded polynomial rings -- Syzygies of lattice ideals -- Toric varieties -- Irreducible and injective resolutions -- Ehrhart polynomials -- Local cohomology -- Determinants…
The Main Theorem: Cyclic Algebras -- The Paper: Dedication to Hensel -- The Local-Global Principle -- From the Local-Global Principle to the Main Theorem -- The Brauer Group and Class Field Theory -- The Team: Noether, Brauer and Hasse -- The American Connection: Albert -- Epilogue: Käte Hey.The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept…
Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (espec…
Basic Matrix Theory and Linear Algebra -- Multivariate Distributions -- Distribution Expansions -- Multivariate Linear Models.The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The b…
Preliminaries -- Preliminaries -- Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- T…
Genesis and Theory of Computer Viruses -- The Formalization Foundations: from Turing to von Neumann (1936 – 1967) -- F. Cohen and L. Adleman’s Formalization (1984 – 1989) -- Taxonomy, Techniques and Tools -- Fighting Against Viruses -- Learning Computer Viruses by Programming -- Computer Viruses in Interpreted Programming Language -- Companion Viruses -- Worms -- Computer Viruses and Appl…
On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems -- Computing the Betti Numbers of Arrangements in Practice -- A MAPLE Symbolic-Numeric Program for Solving the 2D-Eigenvalue Problem by a Self-consistent Basis Method -- RelView – An OBDD-Based Computer Algebra System for Relations -- On the Use of Gröbner Bases for Computing the Structure of Finite Abelian Groups -…