2007, XIII, 263 p., Softcover
ISBN: 978-3-211-73264-9
About this textbook
This book compares the two computer algebra programs, Maple and Mathematica used by students, mathematicians, scientists, and engineers.
Structured by presenting parallel both systems in parallel, Mathematicafs users can learn Maple quickly by finding the Maple equivalent to Mathematica functions, and vice versa.
This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduate mathematical courses (algebra, geometry, calculus, complex functions, special functions, integral transforms, mathematical equations).
Part I describes the foundations of Maple and Mathematica(with equivalent problems and solutions). Part II describes Mathematics with Maple and Mathematica by using equivalent problems.
Written for:
Students, mathematicians, scientists, engineers
Keywords:
Algebra Software
Computer Algebra Systems
Maple
Mathematica
Problem Solving
Table of contents
Preface, Foundations of Maple and Mathematica, Maple, Mathematica, Mathematics: Maple and Mathematica; Graphics,Algebra,Geometry,Calculus, Complex Functions, Special Functions, Integral and Discrete Transforms, Mathematical Equations, Bibliography, Index, Maple Index, Mathematica Index
Series: Surveys and Tutorials in the Applied Mathematical Sciences , Vol. 2
2007, Approx. 210 p., Softcover
ISBN: 978-0-387-73393-7
About this textbook
Expository accessible book, internationally known authors
A combination of the concepts subjective ? or Bayesian ? statistics and scientific computing, the book provides an integrated view across numerical linear algebra and computational statistics. Inverse problems act as the bridge between these two fields where the goal is to estimate an unknown parameter that is not directly observable by using measured data and a mathematical model linking the observed and unknown.
Inverse problems are closely related to statistical inference problems, where the observations are used to infer on an underlying probability distribution. This connection between statistical inference and inverse problems is a central topic of the book. Inverse problems are typically ill-posed: small errors in data may propagate in huge errors in the estimates of the unknowns. To cope with such problems, efficient regularization techniques are developed in the framework of numerical analysis. The counterpart of regularization in the framework of statistical inference is the use prior information. This observation opens the door to a rich interplay between statistics and numerical analysis: the statistical framework provides a rich source of methods that can be used to improve the quality of solutions in numerical analysis, and vice versa, the efficient numerical methods bring computational efficiency to the statistical inference problems.
This book is intended as an easily accessible reader for those who need numerical and statistical methods in applied sciences.
Table of contents
Introduction .- Inverse Problems and Subjective Computing.- Basic Problem of Statistical Inference.-The Praise Of Ignorance: Randomness as Lack of Onformation.- Basic Problem in Numerical Linear Algebra.- Sampling: First Encounter.- Statistically Inspired Preconditioners.- Conditional Gaussian Densities and Predictive Envelopes.- More Applications of the Gaussian Conditioning.- Sampling: The Real Thing.- Wrapping up: Hypermodel, Dynamic Priorconditioners and Bayesian Learning.
Series: Lecture Notes in Mathematics , Vol. 1921
2007, Approx. 220 p., Softcover
ISBN: 978-3-540-74283-8
About this book
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
Written for:
Researchers and graduate students in mathematical biology and algebra
Keywords:
MSC(2000): 08C92, 17D92, 60J10, 92B05, 05C62, 16G99
Markov chains
Mathematical biology
genetic algebras
graph theory
non-associative algebras
Table of contents
Series: Texts in Applied Mathematics , Vol. 53
2008, Approx. 345 p., Hardcover
ISBN: 978-0-387-73828-4
About this textbook
Hot area in applied mathematics
Stuart is one of the leading world experts on multiscale methods
Nice overview of theory and application with example and excercises included.
The book is meant to be an introduction, aimed primarily towards graduate students. Part I of the book (theoretical foundations) and Part III of the book (proving theorems concerning simplified versions of the models that are studied in Part II) are necessarily terse and present the wide range of applications of the ideas, and illustrate their unity.
The subject matter in these set of notes has, for the most part, been known for several decades. However, the particular presentation of the material here is particularly suited to the pedagogical goal of communicating the subject area to the wide range of mathematicians, scientists and engineers who are currently engaged in the use of these tools to tackle the enormous range of applications that require them.
Extensions and generalizations of the results presented in these notes, as well as references to the literature, are given in the Discussion and Bibliography section, at the end of each chapter.
With the exception of Chapter 1, all chapters are supplemented with exercises.
Table of contents
Introduction.- Analysis.- Probability Theory and Stochastic Processes.- Ordinary Differential Equations.- Markov Chains.- Stochastic Differential Equations.- Partial Differential Equations.- Invariant Manifolds for ODEs.- Averaging for Markov Chains.- Averaging for ODEs and SDEs.- Homogenization for ODEs and SDEs.- Homogenization for Elliptic PDEs.- Homogenization for Parabolic PDEs.- Averaging for Linear Transport and Parabolic PDEs.- Invariant Manifolds for ODEs: The Convergence Theorem.- Averaging for Markov Chains: The Convergence Theorem.- Averaging for SDEs: The Convergence Theorem.- Homogenization for SDEs: The Convergence Theorem.- Homogenization for Elliptic PDEs: The Convergence Theorem.- Homogenization for Parabolic PDEs: The Convergence Theorem.- Averaging for Linear Transport and Parabolic PDEs: The Convergence Theorem.
A publication of the Tata Institute of Fundamental Research.
Tata Institute of Fundamental Research
2006; 850 pp; hardcover
ISBN-10: 81-85931-77-1
ISBN-13: 978-81-85931-77-7
M.S. Narasimhan (b. 1932) has made outstanding contributions to diverse areas of mathematics, including algebraic geometry, differential geometry, representation theory of Lie groups, partial differential equations, and mathematical aspects of physics. His famous joint work with Seshadri started a new period in the study of holomorphic vector bundles on projective varieties, and he, along with his collaborators, made pioneering progress in the study of their moduli. His work with Ramanan on universal connections and his work with Okamoto on geometric realization of discrete series are of fundamental importance. In a research career spanning five decades, he has authored about 50 research papers. He is the recipient of several honours and awards, including a Royal Society of London fellowship and the 2006 King Faisal Prize.
This single volume, with about 800 pages, will be of enduring value to mathematicians with diverse interests and backgrounds.
Readership
Graduate students and mathematicians interested in algebra and algebraic geometry.
Table of Contents
Papers of M.S. Narasimhan
Notes
Bibliography