
Mathematics: Its Content, Methods and Meaning (Dover Books on Mathematics) (Paperback)
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Dispatched in 3 business days When will my order arrive?  DescriptionHailed by "The New York Times Book Review" as "nothing less than a major contribution to the scientific culture of this world," this major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and nonEuclidean geometry, topology, functional analysis, more. 1963 edition.
 Publisher: Dover Publications Inc.
 Published: 28 March 2003
 Format: Paperback 1120 pages
 See: Full bibliographic data
 Categories: Mathematics  Algebra  Calculus  Geometry  Science: General Issues
 ISBN 13: 9780486409160 ISBN 10: 0486409163
 Sales rank: 67,530
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Full bibliographic data for Mathematics
 Title
 Mathematics
 Subtitle
 Its Content, Methods and Meaning
 Authors and contributors
 Physical properties
 Format: Paperback
Number of pages: 1120
Width: 136 mm
Height: 214 mm
Thickness: 54 mm
Weight: 1,134 g  Language
 English
 ISBN
 ISBN 13: 9780486409160
ISBN 10: 0486409163  Classifications
BIC E4L: MAT
Nielsen BookScan Product Class 3: S7.8
B&T Merchandise Category: GEN
B&T Book Type: NF
DC21: 510
DC22: 510
LC subject heading:
BIC subject category V2: PD, PB
B&T General Subject: 710
WarengruppenSystematik des deutschen Buchhandels: 26200
Abridged Dewey: 510
Ingram Subject Code: MA
Libri: IMA
LC subject heading:
BISAC V2.8: MAT005000, MAT012000, MAT002000, MAT000000
LC classification: QA36.M2913, QA36 .M2913 1999
Thema V1.0: PB, PD
 Publisher
 Dover Publications Inc.
 Imprint name
 Dover Publications Inc.
 Publication date
 28 March 2003
 Publication City/Country
 New York
 Table of contents
 Volume 1. Part 1Chapter 1. A general view of mathematics (A.D. Aleksandrov) 1. The characteristic features of mathematics 2. Arithmetic 3. Geometry 4. Arithmetic and geometry 5. The age of elementary mathematics 6. Mathematics of variable magnitudes 7. Contemporary mathematics Suggested readingChapter 2. Analysis (M.A. Lavrent'ev and S.M. Nikol'skii) 1. Introduction 2. Function 3. Limits 4. Continuous functions 5. Derivative 6. Rules for differentiation 7. Maximum and minimum; investigation of the graphs of functions 8. Increment and differential of a function 9. Taylor's formula 10. Integral 11. Indefinite integrals; the technique of integration 12. Functions of several variables 13. Generalizations of the concept of integral 14. Series Suggested reading Part 2.Chapter 3. Analytic Geometry (B. N. Delone) 1. Introduction 2. Descartes' two fundamental concepts 3. Elementary problems 4. Discussion of curves represented by first and seconddegree equations 5. Descartes' method of solving third and fourthdegree algebraic equations 6. Newton's general theory of diameters 7. Ellipse, hyperbola, and parabola 8. The reduction of the general seconddegree equation to canonical form 9. The representation of forces, velocities, and accelerations by triples of numbers; theory of vectors 10. Analytic geometry in space; equations of a surface in space and equations of a curve 11. Affine and orthogonal transformations 12. Theory of invariants 13. Projective geometry 14. Lorentz transformations Conclusions; Suggested readingChapter 4. Algebra: Theory of algebraic equations (B. N. Delone) 1. Introduction 2. Algebraic solution of an equation 3. The fundamental theorem of algebra 4. Investigation of the distribution of the roots of a polynomial on the complex plane 5. Approximate calculation of roots Suggested readingChapter 5. Ordinary differential equations (I. G. Petrovskii) 1. Introduction 2. Linear differential equations with constant coefficients 3. Some general remarks on the formation and solution of differential equations 4. Geometric interpretation of the problem of integrating differential equations; generalization of the problem 5. Existence and uniqueness of the solution of a differential equation; approximate solution of equations 6. Singular points 7. Qualitative theory of ordinary differential equations Suggested readingVolume 2 Part 3Chapter 6. Partial differential equations (S. L. Sobolev and O. A. Ladyzenskaja) 1. Introduction 2. The simplest equations of mathematical physics 3. Initialvalue and boundaryvalue problems; uniqueness of a solution 4. The propagation of waves 5. Methods of constructing solutions 6. Generalized solutions Suggested readingChapter 7. Curves and surfaces (A. D. Aleksandrov) 1. Topics and methods in the theory of curves and surfaces 2. The theory of curves 3. Basic concepts in the theory of surfaces 4. Intrinsic geometry and deformation of surfaces 5. New Developments in the theory of curves and surfaces Suggested readingChapter 8. The calculus of variations (V. I. Krylov) 1. Introduction 2. The differential equations of the calculus of variations 3. Methods of approximate solution of problems in the calculus of variations Suggested readingChapter 9. Functions of a complex variable (M. V. Keldys) 1. Complex numbers and functions of a complex variable 2. The connection between functions of a complex variable and the problems of mathematical physics 3. The connection of functions of a complex variable with geometry 4. The line integral; Cauchy's formula and its corollaries 5. Uniqueness properties and analytic continuation 6. Conclusion Suggested reading Part 4.Chapter 10. Prime numbers (K. K. Mardzanisvili and A. B. Postnikov) 1. The study of the theory of numbers 2. The investigation of problems concerning prime numbers 3. Chebyshev's method 4. Vinogradov's method 5. Decomposition of integers into the sum of two squares; complex integers Suggested readingChapter 11. The theory of probability (A. N. Kolmogorov) 1. The laws of probability 2. The axioms and basic formulas of the elementary theory of probability 3. The law of large numbers and limit theorems 4. Further remarks on the basic concepts of the theory of probability 5. Deterministic and random processes 6. Random processes of Markov type Suggested readingChapter 12. Approximations of functions (S. M. Nikol'skii) 1. Introduction 2. Interpolation polynomials 3. Approximation of definite integrals 4. The Chebyshev concept of best uniform approximation 5. The Chebyshev polynomials deviating least from zero 6. The theorem of Weierstrass; the best approximation to a function as related to its properties of differentiability 7. Fourier series 8. Approximation in the sense of the mean square Suggested readingChapter 13. Approximation methods and computing techniques (V. I. Krylov) 1. Approximation and numerical methods 2. The simplest auxiliary means of computation Suggested readingChapter 14. Electronic computing machines (S. A. Lebedev and L. V. Kantorovich) 1. Purposes and basic principles of the operation of electronic computers 2. Programming and coding for highspeed electronic machines 3. Technical principles of the various units of a highspeed computing machine 4. Prospects for the development and use of electronic computing machines Suggested readingVolume 3. Part 5.Chapter 15. Theory of functions of a real variable (S. B. Stechkin) 1. Introduction 2. Sets 3. Real Numbers 4. Point sets 5. Measure of sets 6. The Lebesque integral Suggested readingChapter 16. Linear algebra (D. K. Faddeev) 1. The scope of linear algebra and its apparatus 2. Linear spaces 3. Systems of linear equations 4. Linear transformations 5. Quadratic forms 6. Functions of matrices and some of their applications Suggested readingChapter 17. NonEuclidean geometry (A. D. Aleksandrov) 1. History of Euclid's postulate 2. The solution of Lobachevskii 3. Lobachevskii geometry 4. The real meaning of Lobachevskii geometry 5. The axioms of geometry; their verification in the present case 6. Separation of independent geometric theories from Euclidean geometry 7. Manydimensional spaces 8. Generalization of the scope of geometry 9. Riemannian geometry 10. Abstract geometry and the real space Suggested reading Part 6.Chapter 18. Topology (P. S. Aleksandrov) 1. The object of topology 2. Surfaces 3. Manifolds 4. The combinatorial method 5. Vector fields 6. The development of topology 7. Metric and topological space Suggested readingChapter 19. Functional analysis (I. M. Gelfand) 1. ndimensional space 2. Hilbert space (Infinitedimensional space)