Series: Sources and Studies in the History of Mathematics and Physical Sciences,
2011, X, 144 p. 64 illus.
Hardcover, ISBN 978-1-4614-0145-2
Due: October 28, 2011
Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, four of which have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII.
Motivated by such questions as what role did Halley's reconstruction play in the mathematical world of the late 17th and early 18th century? and what did Halley see himself learning from engaging with mathematicians such as Apollonius?, Michael Fried’s work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. The volume also contains an introduction discussing aspects of Apollonius’s Conics, an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and appendices giving brief accounts of Apollonius’s approach to conic sections and his mathematical techniques.
This book will be of great interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period.
I. Introduction.- 1. Edmond Halley: Ancient and Modern.- 2. Apollonius’s Conics.- 3. The Path to Halley.- 4. Halley's General Strategy for Reconstructing Conics, Book VIII.- 5. Halley’s Dialogue with the Past.-6. A Note on the Translation-II. Apollonius of Perga’s On Conics: Book Eight Restored.- III.Synopsis and Appendices.-Synopsis of the Contents of Halley's Conics, Book VIII.-Appendix 1: Terminology and Notions from Greek Mathematics.-Appendix 2: Hippocrates' First Quadrature of a Lune.-References.-Index.
Series: Universitext
12012, XIV, 288 p. 170 illus.
Softcover, ISBN 978-1-4614-0796-6
Due: September 29, 2011
This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics.
Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories. Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.
The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences.
Preface.- 1 Graphs.- 2 Bipartite Graphs.- 3 Cubes.- 4 Cubical Graphs.- 5 Partial Cubes.- 6 Lattice Embeddings.- 7 Hyperplane Arrangements.- 8 Token Systems.- Notation.- References.- Index
Series: Springer Briefs in Mathematics
2011, VI, 89 p.
Softcover, ISBN 978-1-4614-0588-7
Due: September 28, 2011
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables.
Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level.
-1. Uniform Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications, References). -2. Approximation by General Multivariate Singular Integral Operators(Introduction, Main Results, Applications, References). -3. Global Smoothness Preservation and Simultaneous Approximation by Multivariate General Singular Integrals(Introduction, Main Results, Applications, References). -4. Multivariate Voronovskaya Asymptotic Expansions for General Singular Integrals (Introduction, Main Results, Applications, References).-5. Simultaneous Approximation by Multivariate Complex General Singular Integrals (Introduction, Main Results, Applications, References). -6. Approximation of Functions of Two Variables via Almost Convergence of Double Sequences (Introduction and Preliminaries, Korovkin type approximation theorem, Some consequences, References).
Series: Springer Texts in Statistics
2011, DCCCVIII, 4 p. 214 illus., 160 in color.
Hardcover, ISBN 978-1-4614-0390-6
Due: October 28, 2011
An extensive range of applications that will appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and business, economics, and quantitative social science students
Nearly 1,500 exercises to help students master the material and better understand sophisticated concepts and arguments
An emphasis on the importance of statistical software, including output from the statistical software packages Minitab, R, and SAS.
Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without much attention paid to how statistics is actually used.. In contrast, Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data.
The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics. Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters. The remainder of the book explores the use of this methodology in a variety of more complex settings.
This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature.
Overview and Descriptive Statistics.- Probability.- Discrete Random Variables and Probability Distributions.- Continuous Random Variables and Probability Distributions.- Joint Probability Distributions.- Statistics and Sampling Distributions.- Point Estimation.- Statistical Intervals Based on a Single Sample.- Tests of Hypotheses Based on a Single Sample.- Inferences Based on Two Samples.- The Analysis of Variance.- Regression and Correlation.- Goodness-of-Fit Tests and Categorical Data Analysis.- Alternative Approaches to Inference.- Appendix Tables.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
A Series of Modern Surveys in Mathematics, Vol. 56
011, 487 p. 28 illus.
Hardcover, ISBN 978-3-642-22249-8
Due: September 30, 2011
Keywords ≫ Holomorphic approximation - Oka manifolds - Stein manifolds - Stein spaces
Related subjects ≫ Analysis
Preliminaries. - Stein Manifolds. - Stein Neighborhoods and Holomorphic Approximation. - Automorphisms of Complex Euclidean Spaces. - Oka Manifolds. - Elliptic Complex Geometry and Oka Principle. - Applications. - Embeddings, Immersions and Submersions.- Topological Methods in Stein Geometry. - References. - Index.