Paperback,
848 pages; 7-1/2 x 9-1/4; ISBN13: 978-0-19-989049-1
Apr 2012,
With clear explanations and many contemporary examples drawn from popular culture and everyday life, author Paul Herrick untangles the complexities of logical theory in Introduction to Logic. Offering a unique combination of two approaches--the historical and the technical--he presents logic as both a fascinating, evolving story and a body of essential technical information with applications to every area of human thought.
Perfectly suited for use in any introductory logic course, Introduction to Logic is also tailored to the online logic course Philosophy 106, available as part of the Open Course Library at www.opencourselibrary.org. Jointly sponsored by the Washington State Board for Community and Technical Colleges and the Bill & Melinda Gates Foundation, the Open Course Library offers instructors complete, expertly developed online courses in eighty essential college subjects--including the logic class developed by Paul Herrick and his colleague Mark Storey--all available to faculty at no charge.
* An Instructor's Resource CD (978-0-19-989052-1) contains brief chapter summaries, answers to all of the questions in the text, additional questions and exercises to use on quizzes and exams, and a PowerPoint presentation that covers the entire book.
* A Companion Website at www.oup.com/us/herrick provides extra resources for teachers and students, including a Teacher's Manual, Student Manual, and practice quizzes with answers on all key topics.
* An additional online resource at www.manyworldsoflogic.com offers additional practice quizzes, material for extra-credit assignments, and further information on the nature and history of logic.
About the Author(s)
Paul Herrick received his Ph.D in philosophy from the University of Washington. Since 1983 he has taught philosophy at Shoreline Community College in Washington, near Seattle. He is the author of The Many Worlds of Logic, Second Edition (OUP, 2002) and Reason and Worldview: An Introduction to Western Philosophy (1999).
Numerical Mathematics and Scientific Computation
440 pages | 43 b/w line drawings | 234x156mm
978-0-19-965541-0 | Hardback | December 2012 (estimated
Gives researchers and professionals a deeper understanding of the techniques used in Krylov Subspace Methods
Sets Krylov methods in a wider context
Looks at early papers on the work of Krylov and other pioneers in the 1930s
Examines a wide range of mathematical areas and the connections between them
Largely self-contained mathematical exposition
Corrects several persistent misunderstandings and formulates open problems
The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples.
There is an emphasis on the way algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omitted issues and challenges which need to be addressed in future work.
This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as well as benefiting those interested in the history of mathematics.
Readership: Researchers and graduate students in numerical methods, matrix algebra, approximation theory, and engineering. Researchers in the area of Krylov subspace methods and in related areas, including the history of mathematics.
1: Introduction
2: Krylov subspace methods
3: Matching moments and model reduction view
4: Short recurrences for generating orthogonal Krylov subspace bases
5: Cost of computations using Krylov subspace methods
Undergraduate Texts in Mathematics
2012, 2012, XIII, 401 p. 133 illus.
ISBN 978-1-4614-4264-6
.Discusses the multifaceted process of mathematical proof by thoughtful oscillation between what is known and what is to be demonstrated
Presents more than one proof for many results, for instance for the fact that there are infinitely many prime numbers
Shows how the processes of counting and comparing the sizes of finite sets are based in function theory, and how the ideas can be extended to infinite sets via Cantor's theorems
Contains a wide assortment of exercises, ranging from routine checks of a student's grasp of definitions through problems requiring more sophisticated mastery of fundamental ideas
Demonstrates the dual importance of intuition and rigor in the development of mathematical ideas
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor?and the flexible thinking?required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader.
The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers).
-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.
- 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.-
Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index
2013, 2013, XII, 454 p. 104 illus.
Hardcover
ISBN 978-3-642-30231-2
Due: August 31, 2012
.Presents advances in matrix and tensor data processing in the domain of signal, image and information processing
Written by experts in the areas of theoretical mathematics or engineering sciences
Discusses potential applications in sensor and cognitive systems engineering
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Content Level ≫ Research
Keywords ≫ Audio Signal Processing - Covariance matrix - Differential geometry of structured matrix - Fixed-Point SVD Algorithm - Information geometry - Koszul-Vinberg cohomology - Matrix Data Mining - Positive definite matrix - Radar Image Processing
Related subjects ≫ Algebra - Database Management & Information Retrieval - Remote Sensing - Signals & Communication
Book dedication.- Preface.- Part I: State-of-the-art surveys & original matrix theory work.- Part II: Advanced matrix theory for radar processing.- Part III: Matrix-based signal processing applications.- Index of terms
Series: Springer Texts in Statistics, Vol. 75
2nd ed. 2013, 2013, XXV, 650 p. 13 illus.
Hardcover
ISBN 978-1-4614-4707-8
Due: August 31, 2012
Covers probability from a very applied perspective
Many exercises involve mathematical modeling of random phenomena in very practical fields, including insurance/actuarial and the life sciences/biomedicine
Second edition comprehensively updated, including all new exercises
Like its predecessor, Probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including scores of new problems and exercises, as well as new sections in the Inequalities and Random Variables chapters.
Content Level ≫ Graduate
Keywords ≫ Central Limit Theorem - Convergence - Law of Large Numbers - Law of the Iterated Logarithm - Martingales
Related subjects ≫ Probability Theory and Stochastic Processes - Statistical Theory and Methods - Statistics
Preface to the First Edition.- Preface to the Second Edition.- Outline of Contents.- Notation and Symbols.- Introductory Measure Theory.- Random Variables.- Inequalities.- Characteristic Functions.- Convergence.- The Law of Large Numbers.- The Central Limit Theorem.- The Law of the Iterated Logarithm.- Limited Theorems.- Martingales.- Some Useful Mathematics.- References.- Index.