ISBN: 978-0-470-18401-1
Paperback
328 pages
April 2008
Probably Not is intended to be both entertaining and educational in an area that is central to everyday life. The examples provided in the book exemplify how we are living in a statistical world, what we can expect, what we really know based upon the information at hand, and also explains when we only think we know something. The book begins with an introduction needed to further explore the connection between predication and probability, and the subsequent chapters include coverage of: insurance, gambling, and the Precautionary Principle; coin flip games; Central Limit Theorem; binomial distributions and Poisson distributions; medical tests; and more.
Contents
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ISBN: 978-0-470-38342-1
Paperback
760 pages
May 2008
A unique probability guide for computer science
While many computer science curricula include only an introductory course on general probability, there is a recognized need for further study of this mathematical discipline within the specific context of computer science. Probability and Statistics for Computer Science develops introductory topics in probability with this particular emphasis, providing computer science students with an invaluable resource in their continued studies and professional research.
James Johnson's text begins with the basic definitions of probability distributions and random variables and then elaborates their properties and applications. Probability and Statistics for Computer Science treats the most common discrete and continuous distributions, showing how they find use in decision and estimation problems, and constructs computer algorithms for generating observations from the various distributions. This one-of-a-kind resource also:
Includes a thorough and rigorous development of all the necessary supporting mathematics
Provides an opportunity to reconnect applications with the theoretical concepts of distributions introduced in prerequisite courses
Gathers supporting topics in an appendix: set theory, limit processes, real number structure, Riemann-Stieltjes integrals, matrix transformation, and determinants
Uses computer science examples such as client-server performance evaluation and image processing
The author also addresses a variety of supporting topics, such as estimation arguments with limits, properties of power series, and Markov processes. Johnson's text proves an ideal resource for computer science students and practitioners interested in a probability study specific to their field.
ISBN: 978-0-470-22595-0
Hardcover
416 pages
April 2008
"This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds."
?SIAM Review
A practical introduction to nonlinear PDEs and their real-world applications
Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems.
The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include:
Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills
New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases
An expanded bibliography that facilitates further investigation into specialized topics
With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.
Contents
ISBN: 978-0-470-23288-0
Hardcover
416 pages
April 2008
Advanced Calculus highlights the connections between calculus and linear algebra and provides a mathematically sophisticated introduction to functional analytic concepts. The book stresses that proofs must be written down, scrutinized step-by-step and rewritten whenever there is doubt. Unlike the competition, this book approaches the rigorous foundations of calculus in a manner that reorients thinking in the directions taken by modern analysis.
Preface.
Acknowledgments.
Introduction.
PART I. ADVANCED CALCULUS IN ONE VARIABLE.
1. Real Numbers and Limits of Sequences.
2. Continuous Functions.
3. Rieman Integral.
4. The Derivative.
5. Infinite Series.
PART II. ADVANCED TOPICS IN ONE VARIABLE.
6. Fourier Series.
7. The Riemann-Stieltjes Integral.
PART III. ADVANCED CALCULUS IN SEVERAL VARIABLES.
8. Euclidean Space.
9. Continuous Functions on Euclidean Space.
10. The Derivative in Euclidean Space.
11. Riemann Integration in Euclidean Space.
Appendix A. Set Theory.
Problem Solutions.
References.
Index.
ISBN13: 9780195334722
hardback, 320 pages Feb 2008,
Math Applications Series
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 Product Details
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
(hardback) ISBN-13: 978-0-19-857043-1
(paper) ISBN-13: 978-0-19-857042-4
Estimated publication date: June 2008
456 pages, 234x156 mm
Informal and entertaining style, yet mathematically precise and entertaining
Concentrates on developing mathematical thinking and skills rather than accumulating facts
Written by internationally renowned mathematicians with extensive teaching experience
Large collection of exercises and problems
Over 200 drawings and diagrams
New to this edition
New chapters on partially ordered sets and Ramsey's Theorem
New sections on Tuaran's Theorem
Proofs of the Cauchy-Schwarz inequality, Cayley's Formula, and the determinant formula for counting spanning trees
This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals.
The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra. General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.
Readership: Undergraduates and early graduates in mathematics and computer science
Preface to the second edition
Preface to the first edition
1. Introduction and basic concepts
2. Orderings
3. Combinatorial counting
4. Graphs: an introduction
5. Trees
6. Drawing graphs in the plane
7. Double-counting
8. The number of spanning trees
9. Finite projective planes
10. Probability and probabilistic proofs
11. Order from disorder: Ramsey's theorem
12. Generating functions
13. Applications of linear algebra
Appendix
Bibliography
Hints to selected exercises
Index