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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Computable Structures and the Hyperarithmetical Hierarchy

      • 1st Edition
      • Volume 144
      • June 16, 2000
      • C.J. Ash + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 0 7 2 4
      • eBook
        9 7 8 0 0 8 0 5 2 9 5 2 3
      This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).

    • Set Theory

      • 1st Edition
      • Volume 76
      • April 1, 2000
      • Lev D. Beklemishev
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 4 8 6 8

    • Lie Algebras: Theory and Algorithms

      • 1st Edition
      • Volume 56
      • February 4, 2000
      • W.A. de Graaf
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 1 1 6 5
      • Paperback
        9 7 8 0 4 4 4 5 5 1 7 4 0
      • eBook
        9 7 8 0 0 8 0 5 3 5 4 5 6
      The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Wi... theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

    • Introduction to Global Variational Geometry

      • 1st Edition
      • Volume 10
      • April 1, 2000
      • Demeter Krupka
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 4 1 8 9
      This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

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