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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

    • Young Tableaux in Combinatorics, Invariant Theory, and Algebra

      • 1st Edition
      • May 12, 2014
      • Joseph P.S. Kung
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 2 0 9 5
      • eBook
        9 7 8 1 4 8 3 2 7 2 0 2 3
      Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardso... rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.

    • Artificial Intelligence and Tutoring Systems

      • 1st Edition
      • May 12, 2014
      • Etienne Wenger
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 7 6 8 1
      • eBook
        9 7 8 1 4 8 3 2 2 1 1 1 3
      Artificial Intelligence and Tutoring Systems: Computational and Cognitive Approaches to the Communication of Knowledge focuses on the cognitive approaches, methodologies, principles, and concepts involved in the communication of knowledge. The publication first elaborates on knowledge communication systems, basic issues, and tutorial dialogues. Concerns cover natural reasoning and tutorial dialogues, shift from local strategies to multiple mental models, domain knowledge, pedagogical knowledge, implicit versus explicit encoding of knowledge, knowledge communication, and practical and theoretical implications. The text then examines interactive simulations, existing CAI traditions, and learning environments. The manuscript elaborates on knowledge communication, didactics, and diagnosis. Topics include knowledge presentation and communication, pedagogical contexts, target levels of didactic operations, behavioral and epistemic diagnosis, and aspects of diagnostic experience. The publication is a dependable reference for researchers interested in the computational and cognitive approaches to the communication of knowledge.

    • Multi-Objective Programming in the USSR

      • 1st Edition
      • May 12, 2014
      • Elliot R. Lieberman
      • Gerald J. Lieberman + 1 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 6 5 5 0 6
      Statistical Modeling and Decision Science: Multi-Objective Programming in the USSR provides information pertinent to multi-objective programming that has emerged as an increasingly active area of research in the fields of applied mathematics, operations research, and decision and management science. This book traces and analyzes the development of Soviet multi-objective programming. Organized into 24 chapters, this book begins with an overview of the research institutes most actively involved in multi-objective programming research. This text then presents an analytical framework for grouping and classifying the diverse Soviet methods. Other chapters consider the methods and then evaluated according to the significance and soundness of its basic approach and its kinship to other methods. This book discusses as well some significant Soviet theoretical research and several distinctive approaches proposed by Soviet researchers for comparing the effectiveness of alternative interactive multi-objective programming method. The final chapter deals with distinctive Soviet tendencies in multi-objective research. This book is a valuable resource for economists.

    • Applications of Finite Groups

      • 1st Edition
      • May 12, 2014
      • J. S. Lomont
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 4 5 7 9
      • eBook
        9 7 8 1 4 8 3 2 6 8 9 6 5
      Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

    • Introductory Statistics for Psychology

      • 1st Edition
      • May 12, 2014
      • Gustav Levine
      • English
      • eBook
        9 7 8 1 4 8 3 2 5 7 8 6 0
      Introductory Statistics for Psychology: The Logic and the Methods presents the concepts of experimental design that are carefully interwoven with the statistical material. This book emphasizes the verbalization of conclusions to experiments, which is another means of communicating the reasons for statistical analyses. Organized into 17 chapters, this book begins with an overview of alternative ways of stating the conclusions from a significant interaction. This text then presents the analysis of variance and introduces the summation sign and its use. Other chapters consider frequency distribution as any presentation of data that offers the frequency with which each score occurs. This book discusses as well the differences in and among people, which are a constant source of variability in test scores, and in most other measurements of people. The final chapter deals with the working knowledge of arithmetic and elementary algebra. This book is a valuable resource for students and psychologists.

    • Nonlinear Phenomena in Mathematical Sciences

      • 1st Edition
      • May 12, 2014
      • V. Lakshmikantham
      • English
      • eBook
        9 7 8 1 4 8 3 2 7 2 0 5 4
      Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

    • Entire Functions

      • 1st Edition
      • May 12, 2014
      • A. I. Markushevich
      • English
      • Paperback
        9 7 8 1 4 8 3 2 5 5 0 0 2
      • eBook
        9 7 8 1 4 8 3 2 7 4 9 0 4
      Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.

    • Non-Linear Transformations of Stochastic Processes

      • 1st Edition
      • May 12, 2014
      • P. I. Kuznetsov + 2 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 8 2 6 8 8
      Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

    • The Spectral Analysis of Time Series

      • 1st Edition
      • May 12, 2014
      • L. H. Koopmans
      • Z. W. Birnbaum + 1 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 1 8 5 4 0
      The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

    • Foundations of General Topology

      • 1st Edition
      • May 12, 2014
      • William J. Pervin
      • Ralph P. Boas
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 1 7 2 5
      • eBook
        9 7 8 1 4 8 3 2 2 5 1 5 9
      Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.

Related subjects

Mathematics and applied mathematics

Statistics and probability