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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.

  • Functional Analysis, Holomorphy and Approximation Theory

    • 1st Edition
    • Volume 71
    • J.A. Barroso
    • English

  • Analytic Sets in Locally Convex Spaces

    • 1st Edition
    • Volume 89
    • P. Mazet
    • English

  • Families of Curves and the Origins of Partial Differentiation

    • 1st Edition
    • Volume 93
    • S.B. Engelsman
    • English
    This book provides a detailed description of the main episodes in the emergence of partial differentiation during the period 1690-1740. It argues that the development of this concept - to a considerable degree of perfection - took place almost exclusively in problems concerning families of curves. Thus, the book shows the origins of the ideas and techniques which paved the way for the sudden introduction of partial differential equations in 1750. The main methodological characteristic of the book is its emphasis on a full understanding of the motives, problems and goals of the mathematicians of that time.

  • Introduction to Hilbert Spaces with Applications

    • 3rd Edition
    • Lokenath Debnath + 1 more
    • English
    Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.

  • Lie Algebras: Theory and Algorithms

    • 1st Edition
    • Volume 56
    • W.A. de Graaf
    • English
    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.

  • Elsevier's Dictionary of Mathematics

    In English, German, French and Russian
    • 1st Edition
    • K. Peeva + 3 more
    • English
    Elsevier's Dictionary of Mathematics contains 11,652 entries with more than 4,750 cross-references. Selection of the terms was based either on their significance or on their frequency of use according to authoritative encyclopedias, dictionaries and textbooks. Included are both modern developments and contemporary changes in terminology as well as recently established terms.The terminology covers all the major branches from elementary to advanced subjects: arithmetic, algebra, geometry, set theory, discrete mathematics, logic, Boolean algebra, linear algebra, matrix algebra, calculus, differential equations, vector algebra, field theory, probability theory and statistics, optimization, numerical methods, mathematical programming, modern algebra, algebraic structures, computer algebra, category theory, applied mathematics, theory of automata and formal languages, theory of games, theory of graphs, as well as some commonly used entries in computer architecture, hardware, communications, system and application software, microprogramming, etc.This work will provide readers, writers and translators with a guide of the most widely used terms and collections in the area, and will prove to be a useful tool for all professionals exploring the multilingual scientific terminology.

  • Handbook of Differential Geometry, Volume 1

    • 1st Edition
    • F.J.E. Dillen + 1 more
    • English
    In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

  • Handbook of Computational Geometry

    • 1st Edition
    • J.R. Sack + 1 more
    • English
    Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

  • Probability and Measure Theory

    • 2nd Edition
    • Robert B. Ash + 1 more
    • English
    Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

  • Biomathematics

    Mathematics of Biostructures and Biodynamics
    • 1st Edition
    • S. Andersson + 3 more
    • English
    This book presents new mathematics for the description of structure and dynamics in molecular and cellular biology. On an exponential scale it is possible to combine functions describing inner organisation, including finite periodicity, with functions for outside morphology into a complete definition of structure. This mathematics is particularly fruitful to apply at molecular and atomic distances. The structure descriptions can then be related to atomic and molecular forces and provide information on structural mechanisms. The calculations have been focussed on lipid membranes forming the surface layers of cell organelles. Calculated surfaces represent the mid-surface of the lipid bilayer. Membrane dynamics such as vesicle transport are described in this new language. Periodic membrane assemblies exhibit conformations based on the standing wave oscillations of the bilayer, considered to reflect the true dynamic nature of periodic membrane structures. As an illustration the structure of an endoplasmatic reticulum has been calculated. The transformation of such cell membrane assemblies into cubosomes seems to reflect a transition into vegetative states. The organisation of the lipid bilayer of nerve cells is analyzed, taking into account an earlier observed lipid bilayer phase transition associated with the depolarisation of the membrane. Evidence is given for a new structure of the alveolar surface, relating the mathematical surface defining the bilayer organisation to new experimental data. The surface layer is proposed to consist of a coherent phase, consisting of a lipid-protein bilayer curved according to a classical surface - the CLP surface. Without employing this new mathematics it would not be possible to give an analytical description of this structure and its deformation during the respiration cycle. In more general terms this mathematics is applied to the description of the structure and dynamic properties of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled. This mathematical description of biological structure and dynamics, biomathematics, also provides significant new information in order to understand the mechanisms governing shape of living organisms.

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