Mathematics - Science & Math: Books: Applied, Pure Mathematics, Geometry & Topology & More

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  • The Mathematics of Logic: A Guide to Completeness Theorems and their Applications

    Sert Kapak
    This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
    104,10  TL306,18  TL
  • Singular Elliptic Problems (Bifurcation and Asymptotic Analysis)

    Sert Kapak
    This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry. One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcation problems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singular phenomena, II BLOW-UP SOLUTIONS ; 2. Blow-up solutions for semilinear elliptic equations ; 3. Entire solutions blowing-up at infinity for elliptic systems ; III ELLIPTIC PROBLEMS WITH SINGULAR NONLINEARITIES ; 4. Sublinear perturbations of singular elliptic problems ; 5. Bifurcation and asymptotic analysis. The monotone case ; 6. Bifurcation and asymptotic analysis. The nonmonotone case ; 7. Superlinear perturbations of singular elliptic problems ; 8. Stability of the solution of a singular problem ; 9. The influence of a nonlinear convection term in singular elliptic problems ; 10. Singular Gierer-Meinhardt systems ; A Spectral theory for differential operators ; B Implicit function theorem ; C Ekeland's variational principle ; D Mountain pass theorem ; References ; Index, Marius Ghergu is Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy. Vicentiu Radulescu is Senior Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy and Full Professor at the University of Craiova.
    22,40  TL224,00  TL
  • Arithmetic and Combinatorics

    Sert Kapak
    This is the only work to provide a historical account of Kant s theory of arithmetic, examining in detail the theories of both his predecessors and his successors.Until his death, Martin was the editor of "Kant-Studien "from 1954, of the general Kant index from 1964, of the Leibniz index from 1968, and coeditor of "Leibnizstudien "from 1969. This background is used to its fullest as he strives to make clear the historical milieu in which Kant s mathematical contributions developed. He uses Leibniz, Wolff, and others whose work was accomplished before Kant was born as well as Lambert, Mendelssohn, and others roughly contemporary with Kant; and when a point requires it, he refers to Gauss, Grassman, Frege, Russell, and Hilbert.In her translation Wubnig has approached the original author with an abiding respect. She makes the translation flow in English while preserving as far as possible the flavor of the original. She has added many bibliographical and biographical details to ease the following up of Martin s allusions and suggestions.", Judy Wubnig teaches in the Department of Philosophy at the University of Waterloo, Ontario, Canada."
    19,04  TL95,20  TL
  • The MATHEMATICA ® Book, Version 3

    The MATHEMATICA ® Book, Version 3

    Karton Kapak
    With over a million users around the world, the Mathematica ® software system created by Stephen Wolfram has defined the direction of technical computing for nearly a decade. With its major new document and computer language technology, the new version, Mathematica 3.0 takes the top-power capabilities of Mathematica and make them accessible to a vastly broader audience. This book presents this revolutionary new version of Mathematica. The Mathematica Book is a must-have purchase for anyone who wants to understand the revolutionary opportunities in science, technology, business and education made possible by Mathematica 3.0. This encompasses a broad audience of scientists and mathematicians; engineers; computer professionals; quantitative financial analysts; medical researchers; and students at high-school, college and graduate levels. Written by the creator of the system, The Mathematica Book includes both a tutorial introduction and complete reference information, and contains a comprehensive description of how to take advantage of Mathematica's ability to solve myriad technical computing problems and its powerful graphical and typesetting capabilities. Like previous editions, the book is sure to be found well-thumbed on the desks of many technical professionals and students around the world.
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  • Analytical Geometry of Three Dimensions (Dover Books on Mathematics)

    Analytical Geometry of Three Dimensions (Dover Books on Mathematics)

    Karton Kapak
    Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.
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  • The Loom of God: Tapestries of Mathematics and Mysticism

    The Loom of God: Tapestries of Mathematics and Mysticism

    Karton Kapak
    From the mysterious cult of Pythagoras to the awesome mechanics of Stonehenge to the “gargoyles” and fractals on today’s computers, mathematics has always been a powerful, even divine force in the world. In a lively, intelligent synthesis of math, mysticism, and science fiction, Clifford Pickover explains the eternal magic of numbers. Taking a uniquely humorous approach, he appoints readers “Chief Historian” of an intergalactic museum and sends them, along with a quirky cast of characters, hurtling through the ages to explore how individuals used numbers for such purposes as predicting the end of the world, finding love, and winning wars.
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  • Invitation to Geometry (Dover Books on Mathematics)

    Invitation to Geometry (Dover Books on Mathematics)

    Karton Kapak
    Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra.This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.
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  • Mathematical Methods for Neural Network Analysis and Design

    Mathematical Methods for Neural Network Analysis and Design

    Sert Kapak
    This graduate-level text teaches students how to use a small number of powerful mathematical tools for analyzing and designing a wide variety of artificial neural network (ANN) systems, including their own customized neural networks.Mathematical Methods for Neural Network Analysis and Design offers an original, broad, and integrated approach that explains each tool in a manner that is independent of specific ANN systems. Although most of the methods presented are familiar, their systematic application to neural networks is new. Included are helpful chapter summaries and detailed solutions to over 100 ANN system analysis and design problems. For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.This text is unique in several ways. It is organized according to categories of mathematical tools -- for investigating the behavior of an ANN system, for comparing (and improving) the efficiency of system computations, and for evaluating its computational goals -- that correspond respectively to David Marr's implementational, algorithmic, and computational levels of description. And instead of devoting separate chapters to different types of ANN systems, it analyzes the same group of ANN systems from the perspective of different mathematical methodologies.
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  • Interpolation and Approximation with Splines and Fractals

    Interpolation and Approximation with Splines and Fractals

    Sert Kapak
    This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces., This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material., 1. The General Interpolation and Approximation Problem ; 2. Splines ; 3. Interpolation in Rs, s > 1 ; 4. Fractals ; 5. Fractal Functions ; 6. Fractal Surfaces ; 7. Superfractals ; 8. Superfractal Functions, "A very valuable addition to the existing literature on the subject and the exposition takes the reader to very recent topics as Besov or Triebel-Lizorkin spaces, as well as their use in the theory of splines and fractals. Highly recommended for students or researchers working in applied fields who need to refresh their tools with current ones."--Libertas Mathematica"A useful book, well-written, and covering interesting areas of research in numerical analysis...A comprehensive volume. It is sufficiently introductory to be well readable for the non-expert while at the same time giving many interesting and useful results for the connaisseur."--ZentralblattMath"There are several attractive features: historical footnotes sprinkled throughout the book, lots of beautifully designed figures, many well-chosen and easy-to-follow examples, and suggested student projects. The author does a great job in making available to students a set of fundamental topics at the crossroads of numerical analysis, functional analysis, fractals, and numerical harmonic analysis." -- Palle E. T. Jorgensen, MathSciNet, Peter Massopust holds a Master of Science in physics and a Ph.D. in applied mathematics. Dr. Massopust is best known for his work in fractal geometry, in particular fractal functions and fractal surfaces, and wavelet theory. His current research interests focus on complex splines and wavelets, and their applications to signal and image processing. He is currently a Senior Research Scientist on the Marie Curie Excellence in Research Team MAMEBIA.
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  • The Factorization Method for Inverse Problems

    The Factorization Method for Inverse Problems

    Sert Kapak
    The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples., The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method)., Preface ; 1. The Simplest Cases: Dirichlet and Neumann Boundary Conditions ; 2. The Factorization Method for Other Types of Inverse Obstacle Scattering Problems ; 3. The Mixed Boundary Value Problem ; 4. The MUSIC Algorithm and Scattering by an Inhomogenous Medium ; 5. The Factorization method for Maxwell's Equations ; 6. The Factorization Method in Impedance Tomography ; 7. Alternative Sampling and Probe Methods ; Bibliography, "This is a nice collection of results on the factorization method for a variety of scattering applications. It provides beginning researchers with a good survey of the basic theoretical approach, and for more experienced researchers working with factorization techniques it is a good reference source. I await the second edition with great anticipation."--SIAM Review
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