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Exceptional Lie Algebras (Lecture Notes in Pure and Applied Mathematics #1)

This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, � 6 's, and � 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in general-especially thoseinterested in the classification of Lie algebras or groups-and for theoretical physicists.

A History of Pi

The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

Introduction to Probability Theory

Random Walks and Poisson Processes Combinatorial Analysis Discrete Random Variables Expectation of Discrete Random Variables Continuous Random Variables Jointly Distributed Random Variables Expectations and the Central Limit Theorem Moment Generating Functions and Characteristic Functions Probability Spaces

Iterative Solution of Large Linear Systems

This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR method for consistently ordered matrices; nonstationary methods; generalizations of SOR theory and variants of method; second-degree methods, alternating direction-implicit methods, and a comparison of methods. 1971 edition.

Linear Models

This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

Moja Means One: A Swahili Counting Book

A counting book that portrays the life and culture of Swahili-speaking Africa, with a brief text and dramatic illustrations. The numbers one through ten in Swahili accompany two-page illustrations of various aspects of East African life.

Necessary Conditions for an Extremum

This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.

Number Theory: The Theory Of Partitions (Dover Books on Mathematics #Vol. 2)

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

Probability: Elements of the Mathematical Theory

Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.

Problems in Thermodynamics and Statistical Physics (Dover Books on Physics)

Well respected and widely used, this volume presents problems and full solutions related to a wide range of topics in thermodynamics, statistical physics, and statistical mechanics. The text is intended for instructors, undergraduates, and graduate students of mathematics, physics, chemistry, and engineering. Twenty-eight chapters, each prepared by an expert, proceed from simpler to more difficult subjects. Similarly, the early chapters are easier than the later ones, making the book ideal for independent study.Subjects begin with the laws of thermodynamics and statistical theory of information and of ensembles, advancing to the ideal classical gases of polyatomic molecules, non-electrolyte liquids and solutions, and surfaces. Subsequent chapters explore imperfect classical and quantum gas, phase transitions, cooperative phenomena, Green function methods, the plasma, transport in gases and metals, Nyquist's theorem and its generalizations, stochastic methods, and many other topics.

Regular Algebra and Finite Machines

World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular algebra, axiomatic questions, the strength of classical axioms, and logical problems. Complete solutions to problems appear at the end.

الأخلاق والسير في مداواة النفوس

قد جمعت في كتابي هذا معان كثيرة أفادنيها واهب التمييز تعالى بمرور الأيام وتعاقب الأحوال بما منحني عز وجل من التهمم بتصاريف الزمان والإشراف على أحواله حتى أنفقت في ذلك أكثر عمري وآثرت تقييد ذلك بالمطالعة له والفكرة فيه على جميع اللذات التي تميل إليها أكثر النفوس وعلى الازدياد من فضول المال ورقمت كل ما سبرت من ذلك بهذا الكتاب لينفع الله تعالى به من شاء من عباده ممن يصل إليه ما أتعبت فيه نفسي واجهدتها فيه واطلت فيه فكري فيأخذه عفوا وأهديته إليه هنيئا فيكون ذلك أفضل له من كنوز المال وعقد الأملاك إذا تدبره ويسره الله تعلي لاستعماله. وانا راج في ذلك من الله تعالي أعظم الأجر لنيتي في نفع عباده وإصلاح ما فسد من أخلاقهم ومداواة علل نفوسهم وبالله تعالى استعين وحسبنا الله ونعم الوكيل

The 32nd Mersenne Prime

ABC's of Science

This books is about alpha, beta, and gamma. These are the first three letters of the Greek alphabet. <P> <P> This alphabet was the major method of written communication in ancient times, and is of course still used today. The Greek letters are also the most commonly used symbols in science. In all branches of science, we use symbols to represent ideas and definitions. Symbols serve to simplify communication and calculations—once you get used to them, that is.

Accessibility Tests Mathematics

Math Recommendation for EPUB. This is a test book from epubtest.org.

Analytical Geometry of Three Dimensions: Second Revised Version

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.

Applications of Tensor Analysis (Dover Books on Mathematics)

This standard work applies tensorial methods to subjects within the realm of advanced college mathematics. In its four main divisions, it explains the fundamental ideas and the notation of tensor theory; covers the geometrical treatment of tensor algebra; introduces the theory of the differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity, and hydrodynamics.Partial contents: algebraic preliminaries (notation, definitions, determinants, tensor analysis); algebraic geometry (rectilinear coordinates, the plane, the straight line, the quadric cone and the conic, systems of cones and conics, central quadrics, the general quadric, affine transformations); differential geometry (curvilinear coordinates, covariant differentiation, curves in a space, intrinsic geometry of a surface, fundamental formulae of a surface, curves on a surface); applied mathematics (dynamics of a particles, dynamics of rigid bodies, electricity and magnetism, mechanics of continuous media, special theory of relativity).

Applied Probability Models with Optimization Applications

"A clarity of style and a conciseness of treatment which students will find most welcome. The material is valuable and well organized ... an excellent introduction to applied probability." -- Journal of the American Statistical Association. This book offers a concise introduction to some of the stochastic processes that frequently arise in applied probability. Emphasis is on optimization models and methods, particularly in the area of decision processes. After reviewing some basic notions of probability theory and stochastic processes, the author presents a useful treatment of the Poisson process, including compound and nonhomogeneous Poisson processes. Subsequent chapters deal with such topics as renewal theory and Markov chains; semi-Markov, Markov renewal, and regenerative processes; inventory theory; and Brownian motion and continuous time optimization models.Each chapter is followed by a section of useful problems that illustrate and complement the text. There is also a short list of relevant references at the end of every chapter. Students will find this a largely self-contained text that requires little previous knowledge of the subject. It is especially suited for a one-year course in applied probability at the advanced undergraduate or beginning postgraduate level. 1970 edition.

Arithmetic Optimization Techniques for Hardware and Software Design

Obtain better system performance, lower energy consumption, and avoid hand-coding arithmetic functions with this concise guide to automated optimization techniques for hardware and software design. High-level compiler optimizations and high-speed architectures for implementing FIR filters are covered, which can improve performance in communications, signal processing, computer graphics, and cryptography. Clearly explained algorithms and illustrative examples throughout make it easy to understand the techniques and write software for their implementation. Background information on the synthesis of arithmetic expressions and computer arithmetic is also included, making the book ideal for new-comers to the subject. This is an invaluable resource for researchers, professionals, and graduate students working in system level design and automation, compilers, and VLSI CAD.

Calculus of Variations

This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems.Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features numerous illustrative problems, and solutions appear at the end.

The Cambridge Dictionary of Statistics

If you work with data and need easy access to clear, reliable definitions and explanations of modern statistical and statistics-related concepts, then look no further than this dictionary. Nearly 4000 terms are defined, covering medical, survey, theoretical, and applied statistics, including computational and graphical aspects. Entries are provided for standard and specialized statistical software. In addition, short biographies of over 100 important statisticians are given. Definitions provide enough mathematical detail to clarify concepts and give standard formula when these are helpful. The majority of definitions then give a reference to a book or article where the user can seek further or more specialized information, and many are accompanied by graphical material to aid understanding.

Cartesian Tensors: An Introduction (Dover Books on Mathematics)

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of tensors in orthogonal curvilinear coordinates. Numerous examples illustrate the general theory and indicate certain extensions and applications. 1960 edition.

CK-12 Advanced Probability and Statistics

CK-12 Foundation's Advanced Probability and Statistics FlexBook covers the following chapters: An Introduction to Analyzing Statistical Data - Students learn definitions of statistical terminology, and review data, measures of center, and measures of spread. Visualizations of Data - histograms and frequency distributions, common graphs and data plots, and box-and-whisker plots. An Introduction to Probability - events, sample spaces, probability, compound events, the complement of an event, conditional probability, and basic counting rules. Discrete Probability Distribution - random variables, probability distribution for a discrete random variable, mean and standard deviation of discrete random variables and the Binomial Probability Distribution. Normal Distribution - standard normal probability distribution, the density curve of the normal distribution, and applications of the normal distribution. Planning and Conducting an Experiment or Study - surveys, sampling and experimental design. Sampling Distributions and Estimations - sampling distributions and the Central Limit Theorem. Hypothesis Testing - The P-value, testing a proportion hypothesis, testing a mean hypothesis, and testing a hypothesis for dependent and independent samples. Regression and Correlation - scatterplots and linear correlation, Least-Squares regression, inferences about regression, and an introduction to multiple regression. Chi-Square- the Goodness-of-Fit test, test of independence, and testing one variance. Analysis of Variance and the F-Distribution - the F-Distribution and testing two variances, the One-Way ANOVA test, and the Two-Way ANOVA test. Non Parametric Statistics - nonparametric statistics, the rank sum test and rank Correlation, and the Kruskal-Wallis test.

CK-12 Advanced Probability and Statistics Second Edition Volume 1

An open source textbook.

CK-12 Algebra I

CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.