Böcker utgivna av Birkhauser Boston Inc

A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra.

It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions.

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations.

The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups.

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory.

Covers such topics as: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.

The Collected Papers of Raoul Bott are contained in five volumes, with each volume covering a different subject and each representing approximately a decade of Bott's work.

Examines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques.

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and t-motives.

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions.The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. Thereare four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.¿

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. No knowledge of measure theory is presumed.

* Uses a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn* Self-contained and standalone text that may be used in the classroom, for an online course, for self-study, as a reference* Using MAPLE allows the reader to easily and quickly change the models and parameters

This book is an outgrowth of the Workshop on "Regulators in Analysis, Geom etry and Number Theory" held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996.

Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way.

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students.

Exploring the use of cellular automata in modeling pattern formation in biological systems, the 2nd edition describes mathematical modeling approaches using cellular automata that can be used to study the dynamics of interacting cell systems in simulation and in practice. New chapters cover cell migration, tissue development, and cancer dynamics.

Various imperfections in existing market systems prevent the free market from serving as a truly efficient allocation mechanism, but optimization of economic activities provides an effective remedial measure.

* Presents a comprehensive treatment with a global view of the subject* Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics.

This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable.

Consists of articles from the Encyclopedia of neuroscience / edited by George Adelman. 1987.