Математика
Различные книги в жанре МатематикаThe Gentle Art of Mathematics
This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more.
Introduction to Formal Languages
This highly technical introduction to formal languages in computer science covers all areas of mainstream formal language theory, including such topics as operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Geared toward advanced undergraduates and graduate students, the treatment examines mathematical topics related to mathematical logic, set theory, and linguistics. All subjects are integral to the theory of computation.Numerous worked examples appear throughout the book, and end-of-chapter exercises enable readers to apply theory and methods to real-life problems. Elegant mathematical proofs are provided for almost all theorems.
A History of Mathematical Notations
This classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author’s coverage of obsolete notations — and what we can learn from them — is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is presented here in one volume.
Fundamentals of Scientific Mathematics
"For high school seniors or college freshmen with a background in algebra and trigonometry, the book should provide a good introduction to matrices, vector algebra, analytical geometry, and calculus. The work's solid modern mathematical content and its personality recommend consideration as a text or as stimulating supplementary reading." — American Scientist"The book is well written and the presentation throughout achieves clarity of thought with a minimum of computational effort." — Physics TodayThis rewarding text, beautifully illustrated by the author and written with superb clarity, offers undergraduate students a solid mathematical background and functions equally well for independent study.The five-part treatment begins with geometry, defining three-dimensional Euclidean space and its axioms, the coordinate system and coordinate transformation, and matrices. A review of vector algebra covers vector properties, multiplication, the resolution of a vector along a complete set of base vectors, and vector transformations. Topics in analytic geometry introduce loci, straight lines, the plane, two-dimensional curves, and the quadratic form. Functions are defined, as are intervals, along with multiplicity, the slope at a point, continuity, and areas. The concluding chapter, on differential and integral calculus, explains the concept of a limit, the derivative, the integral, differential equations, and applications of the calculus to kinematics.
Mathematical Foundations of Quantum Statistics
A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.
A History of Greek Mathematics, Volume II
"As it is, the book is indispensable; it has, indeed, no serious English rival." — Times Literary Supplement"Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century." — Prof. W. H. Stahl"Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry."The perspective that enabled Sir Thomas Heath to understand the Greek genius — deep intimacy with languages, literatures, philosophy, and all the sciences — brought him perhaps closer to his beloved subjects, and to their own ideal of educated men than is common or even possible today. Heath read the original texts with a critical, scrupulous eye and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English."Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes's proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations.Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.
Functional Analysis
Classic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.
An Introduction to Linear Algebra
"The straight-forward clarity of the writing is admirable." — American Mathematical Monthly.This work provides an elementary and easily readable account of linear algebra, in which the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology. The account is self-contained, and the reader is not assumed to have any previous knowledge of linear algebra. Although its accessibility makes it suitable for non-mathematicians, Professor Mirsky's book is nevertheless a systematic and rigorous development of the subject. Part I deals with determinants, vector spaces, matrices, linear equations, and the representation of linear operators by matrices. Part II begins with the introduction of the characteristic equation and goes on to discuss unitary matrices, linear groups, functions of matrices, and diagonal and triangular canonical forms. Part II is concerned with quadratic forms and related concepts. Applications to geometry are stressed throughout; and such topics as rotation, reduction of quadrics to principal axes, and classification of quadrics are treated in some detail. An account of most of the elementary inequalities arising in the theory of matrices is also included. Among the most valuable features of the book are the numerous examples and problems at the end of each chapter, carefully selected to clarify points made in the text.
The Fourth Dimension Simply Explained
To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable — or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension.This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific American, these essays are so well reasoned and lucidly written that they were judged to merit publication in book form. Their easily understood explanations cover such topics as how the fourth dimension may be studied, the relationship of non-Euclidean geometry to the fourth dimension, analogues to three-dimensional space, some four-dimensional absurdities and curiosities, possible measurements and forms in the fourth dimension, and extensive considerations of four-dimensional space's simpler properties.Since each essay is independently conceived, all of the writers offer fresh viewpoints and original examples. Because of this, some of the most important principles relating to the fourth dimension are viewed from several different angles at once — an invaluable aid to visualizing these abstruse but fascinating ideas. New Introduction by Thomas F. Banchoff, Brown University. 82 figures.
Integral, Measure and Derivative
This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. «The exposition is fresh and sophisticated,» declared Sci-Tech Book News, «and will engage the interest of accomplished mathematicians.» Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the «classical» Lebesgue integral in n space. Part two constructs the Lebesgue-Stieltjes integral through the Daniell scheme using the Reimann-Stieltjes integral as the elementary integral. Part three develops theory of measure with the general Daniell scheme, and the final part is devoted to the theory of the derivative.