Mathematics, its content, methods, and meaning (Record no. 35084)

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020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780486409160
040 ## - CATALOGING SOURCE
Original cataloging agency ICTS-TIFR
050 ## - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA36 .M2913
245 ## - TITLE STATEMENT
Title Mathematics, its content, methods, and meaning
260 ## - PUBLICATION, DISTRIBUTION, ETC.
Place of publication, distribution, etc. Garden City, N.Y. :
Name of publisher, distributor, etc. Dover Publications,
Date of publication, distribution, etc. [c1999]
300 ## - Physical Description
Pages: 3 volumes bound as 1
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note Volume 1. Part 1<br/>Chapter 1. A general view of mathematics (A.D. Aleksandrov)<br/>1. The characteristic features of mathematics<br/>2. Arithmetic<br/>3. Geometry<br/>4. Arithmetic and geometry<br/>5. The age of elementary mathematics<br/>6. Mathematics of variable magnitudes<br/>7. Contemporary mathematics<br/>Suggested reading<br/>Chapter 2. Analysis (M.A. Lavrent'ev and S.M. Nikol'skii)<br/>1. Introduction<br/>2. Function<br/>3. Limits<br/>4. Continuous functions<br/>5. Derivative<br/>6. Rules for differentiation<br/>7. Maximum and minimum investigation of the graphs of functions<br/>8. Increment and differential of a function<br/>9. Taylor's formula<br/>10. Integral<br/>11. Indefinite integrals the technique of integration<br/>12. Functions of several variables<br/>13. Generalizations of the concept of integral<br/>14. Series<br/>Suggested reading<br/>Part 2.<br/>Chapter 3. Analytic Geometry (B. N. Delone)<br/>1. Introduction<br/>2. Descartes' two fundamental concepts<br/>3. Elementary problems<br/>4. Discussion of curves represented by first- and second-degree equations<br/>5. Descartes' method of solving third- and fourth-degree algebraic equations<br/>6. Newton's general theory of diameters<br/>7. Ellipse, hyperbola, and parabola<br/>8. The reduction of the general second-degree equation to canonical form<br/>9. The representation of forces, velocities, and accelerations by triples of numbers theory of vectors<br/>10. Analytic geometry in space equations of a surface in space and equations of a curve<br/>11. Affine and orthogonal transformations<br/>12. Theory of invariants<br/>13. Projective geometry<br/>14. Lorentz transformations<br/>Conclusions Suggested reading<br/>Chapter 4. Algebra: Theory of algebraic equations (B. N. Delone)<br/>1. Introduction<br/>2. Algebraic solution of an equation<br/>3. The fundamental theorem of algebra<br/>4. Investigation of the distribution of the roots of a polynomial on the complex plane<br/>5. Approximate calculation of roots<br/>Suggested reading<br/>Chapter 5. Ordinary differential equations (I. G. Petrovskii)<br/>1. Introduction<br/>2. Linear differential equations with constant coefficients<br/>3. Some general remarks on the formation and solution of differential equations<br/>4. Geometric interpretation of the problem of integrating differential equations generalization of the problem<br/>5. Existence and uniqueness of the solution of a differential equation approximate solution of equations<br/>6. Singular points<br/>7. Qualitative theory of ordinary differential equations<br/>Suggested reading<br/>Volume 2 Part 3<br/>Chapter 6. Partial differential equations (S. L. Sobolev and O. A. Ladyzenskaja)<br/>1. Introduction<br/>2. The simplest equations of mathematical physics<br/>3. Initial-value and boundary-value problems uniqueness of a solution<br/>4. The propagation of waves<br/>5. Methods of constructing solutions<br/>6. Generalized solutions<br/>Suggested reading<br/>Chapter 7. Curves and surfaces (A. D. Aleksandrov)<br/>1. Topics and methods in the theory of curves and surfaces<br/>2. The theory of curves<br/>3. Basic concepts in the theory of surfaces<br/>4. Intrinsic geometry and deformation of surfaces<br/>5. New Developments in the theory of curves and surfaces<br/>Suggested reading<br/>Chapter 8. The calculus of variations (V. I. Krylov)<br/>1. Introduction<br/>2. The differential equations of the calculus of variations<br/>3. Methods of approximate solution of problems in the calculus of variations<br/>Suggested reading<br/>Chapter 9. Functions of a complex variable (M. V. Keldys)<br/>1. Complex numbers and functions of a complex variable<br/>2. The connection between functions of a complex variable and the problems of mathematical physics<br/>3. The connection of functions of a complex variable with geometry<br/>4. The line integral Cauchy's formula and its corollaries<br/>5. Uniqueness properties and analytic continuation<br/>6. Conclusion<br/>Suggested reading<br/>Part 4.<br/>Chapter 10. Prime numbers (K. K. Mardzanisvili and A. B. Postnikov)<br/>1. The study of the theory of numbers<br/>2. The investigation of problems concerning prime numbers<br/>3. Chebyshev's method<br/>4. Vinogradov's method<br/>5. Decomposition of integers into the sum of two squares complex integers<br/>Suggested reading<br/>Chapter 11. The theory of probability (A. N. Kolmogorov)<br/>1. The laws of probability<br/>2. The axioms and basic formulas of the elementary theory of probability<br/>3. The law of large numbers and limit theorems<br/>4. Further remarks on the basic concepts of the theory of probability<br/>5. Deterministic and random processes<br/>6. Random processes of Markov type<br/>Suggested reading<br/>Chapter 12. Approximations of functions (S. M. Nikol'skii)<br/>1. Introduction<br/>2. Interpolation polynomials<br/>3. Approximation of definite integrals<br/>4. The Chebyshev concept of best uniform approximation<br/>5. The Chebyshev polynomials deviating least from zero<br/>6. The theorem of Weierstrass the best approximation to a function as related to its properties of differentiability<br/>7. Fourier series<br/>8. Approximation in the sense of the mean square<br/>Suggested reading<br/>Chapter 13. Approximation methods and computing techniques (V. I. Krylov)<br/>1. Approximation and numerical methods<br/>2. The simplest auxiliary means of computation<br/>Suggested reading<br/>Chapter 14. Electronic computing machines (S. A. Lebedev and L. V. Kantorovich)<br/>1. Purposes and basic principles of the operation of electronic computers<br/>2. Programming and coding for high-speed electronic machines<br/>3. Technical principles of the various units of a high-speed computing machine<br/>4. Prospects for the development and use of electronic computing machines<br/>Suggested reading<br/>Volume 3. Part 5.<br/>Chapter 15. Theory of functions of a real variable (S. B. Stechkin)<br/>1. Introduction<br/>2. Sets<br/>3. Real Numbers<br/>4. Point sets<br/>5. Measure of sets<br/>6. The Lebesque integral<br/>Suggested reading<br/>Chapter 16. Linear algebra (D. K. Faddeev)<br/>1. The scope of linear algebra and its apparatus<br/>2. Linear spaces<br/>3. Systems of linear equations<br/>4. Linear transformations<br/>5. Quadratic forms<br/>6. Functions of matrices and some of their applications<br/>Suggested reading<br/>Chapter 17. Non-Euclidean geometry (A. D. Aleksandrov)<br/>1. History of Euclid's postulate<br/>2. The solution of Lobachevskii<br/>3. Lobachevskii geometry<br/>4. The real meaning of Lobachevskii geometry<br/>5. The axioms of geometry their verification in the present case<br/>6. Separation of independent geometric theories from Euclidean geometry<br/>7. Many-dimensional spaces<br/>8. Generalization of the scope of geometry<br/>9. Riemannian geometry<br/>10. Abstract geometry and the real space<br/>Suggested reading<br/>Part 6.<br/>Chapter 18. Topology (P. S. Aleksandrov)<br/>1. The object of topology<br/>2. Surfaces<br/>3. Manifolds<br/>4. The combinatorial method<br/>5. Vector fields<br/>6. The development of topology<br/>7. Metric and topological space<br/>Suggested reading<br/>Chapter 19. Functional analysis (I. M. Gelfand)<br/>1. n-dimensional space<br/>2. Hilbert space (Infinite-dimensional space)<br/>3. Expansion by orthogonal systems of functions<br/>4. Integral equations<br/>5. Linear operators and further developments of functional analysis<br/>Suggested reading<br/>Chapter 20. Groups and other algebraic systems (A. I. Malcev)<br/>1. Introduction<br/>2. Symmetry and transformations<br/>3. Groups of transformations<br/>4. Fedorov groups (crystallographic groups)<br/>5. Galois groups<br/>6. Fundamental concepts of the general theory of groups<br/>7. Continuous groups<br/>8. Fundamental groups<br/>9. Representations and characters of groups<br/>10. The general theory of groups<br/>11. Hypercomplex numbers<br/>12. Associative algebras<br/>13. Lie algebras<br/>14. Rings<br/>15. Lattices<br/>16. Other algebraic systems<br/>Suggested reading<br/>Index
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name edited by Aleksandrov, A. D. (Aleksandr Danilovich)
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Personal name Kolmogorov, A. N. (Andreĭ Nikolaevich)
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Personal name Lavrentʹev, M. A. (Mikhail Alekseevich)
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name translation edited by S.H. Gould.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
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        Mathematics ICTS Rack No 3 04/03/2024 QA36 .M2913 02809 Book