Mathematics: Its Content, Methods and MeaningCourier Corporation, 7 de maig 2012 - 1120 pàgines ". . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book Review This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels." Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems. Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference. "This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science |
Continguts
6 Conclusion 194 | 194 |
2 The Investigation of Problems Concerning Prime | 204 |
3 Cebyševs Method | 213 |
5 Decomposition of Integers into the Sum of | 225 |
APPROXIMATIONS OF FUNCTIONS 265 | 265 |
3 Approximation of Definite Integrals 276 | 276 |
4 The Cebysey Concept of Best Uniform | 282 |
6 The Theorem of Weierstrass the Best Approximation | 288 |
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6 Rules for Differentiation | 101 |
7 Maximum and Minimum Investigation of the Graphs of Functions | 108 |
8 Increment and Differential of a Function | 117 |
9 Taylors Formula | 125 |
10 Integral | 128 |
11 Indefinite Integrals the Technique of Integration | 137 |
Functions of Several Variables | 142 |
13 Generalizations of the Concept of Integral | 158 |
Series | 166 |
Suggested Reading | 180 |
ANALYTIC GEOMETRY | 183 |
5 Descartes Method of Solving Third and FourthDegree | 190 |
8 The Reduction of the General SecondDegree | 207 |
9 The Representation of Forces Velocities | 213 |
11 Affine and Orthogonal Transformations | 227 |
12 Theory of Invariants | 238 |
14 Lorentz Transformations | 249 |
THEORY OF ALGEBRAIC | 261 |
5 Approximate Calculation of Roots | 302 |
ORDINARY DIFFERENTIAL | 311 |
3 Some General Remarks on the Formation and Solution | 330 |
6 Singular Points | 343 |
6 Fundamental Concepts of the General Theory | 6 |
FUNCTIONS OF A COMPLEX | 139 |
8 Approximation in the Sense of the Mean | 298 |
2 The Simplest Auxiliary Means of Computation 3 19 | 319 |
ELECTRONIC COMPUTING MACHINES 331 | 331 |
3 Technical Principles of the Various Units of | 350 |
4 Prospects for the Development and Use of Electronic | 365 |
1 Introduction 3 II | 3 |
LINEAR ALGEBRA 37 | 37 |
NONEUCLIDEAN GEOMETRY 97 | 97 |
TOPOLOGY 193 | 193 |
3 Manifolds 202 | 202 |
5 Vector Fields 212 | 212 |
6 The Development of Topology 218 | 218 |
FUNCTIONAL ANALYSIS 227 | 227 |
3 Expansion by Orthogonal Systems | 237 |
4 Integral Equations 245 | 245 |
5 Linear Operators and Further Developments | 252 |
GROUPS AND OTHER ALGEBRAIC | 263 |
3 Groups of Transformations 273 | 273 |
4 Fedorov Groups Crystallographic Groups 285 | 285 |
5 Galois Groups 293 | 293 |
Groups 297 | 297 |
7 Continuous Groups 305 | 305 |
8 Fundamental Groups 308 | 308 |
9 Representations and Characters of Groups 3 14 | 314 |
Hypercomplex Numbers 320 | 320 |
2 Linear Differential Equations with Constant | 323 |
Associative Algebras 330 | 330 |
13 Lie Algebras 339 | 339 |
Rings 342 | 342 |
Lattices 347 | 347 |
Other Algebraic Systems 349 | 349 |
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Altres edicions - Mostra-ho tot
Mathematics: Its Content, Methods and Meaning Aleksandr Danilovich Aleksandrov,Andre? Nikolaevich Kolmogorov,M. A. Lavrent'ev Previsualització limitada - 1999 |
Mathematics, Its Content, Methods, and Meaning, Volum 1 Matematicheskiĭ institut im. V.A. Steklova Visualització de fragments - 1964 |
Mathematics: Its Content, Methods, and Meaning Matematicheskiĭ institut im. V.A. Steklova Visualització de fragments - 1990 |
Frases i termes més freqüents
abstract affine transformations algebra analysis analytic application approaches approximation arbitrary arithmetic assume axes body calculation called century Chapter closed coefficients completely computation concept connected consider consists constant construction continuous convergent coordinates corresponding curve defined definition dependence derivative determine differential differential equations direction distance domain elements equal equation example exists expressed fact figure formula function geometry give given important increase independent integral interval laws length limit linear machines magnitude mathematics means measure method motion namely natural necessary obtain operations origin particular physics plane polynomial positive possible practical problem properties proved question ratio relation represented respect result roots satisfy segment side solution solved space square sufficient surface tangent theorem theory transformation unit variable various vector whole zero