Mathematical Thought From Ancient to Modern Times, Volume 1, Volum 1Oxford University Press, 1. mars 1990 - 432 sider This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study. |
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... produce a freshman text that departed from the traditional dry-as-dust mathematics textbook. Later, I wrote a calculus text with the same end in view. While I was directing a research group in electromagnetic theory and doing research ...
... produce a freshman text that departed from the traditional dry-as-dust mathematics textbook. Later, I wrote a calculus text with the same end in view. While I was directing a research group in electromagnetic theory and doing research ...
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... produced wedge-shaped impressions that could be oriented in different ways. From cuneus, the Latin word for “wedge,” the script became known as cuneiform. The most highly developed arithmetic of the Babylonian civilization is the ...
... produced wedge-shaped impressions that could be oriented in different ways. From cuneus, the Latin word for “wedge,” the script became known as cuneiform. The most highly developed arithmetic of the Babylonian civilization is the ...
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... produced an element in the universe which denied the Pythagorean doctrine that all phenomena in the universe can be reduced to whole numbers or their ratios. The proof that is incommensurable with 1 was given by the Pythagoreans ...
... produced an element in the universe which denied the Pythagorean doctrine that all phenomena in the universe can be reduced to whole numbers or their ratios. The proof that is incommensurable with 1 was given by the Pythagoreans ...
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... produced the strong Pythagorean inuence in the entire Platonic school. Theodorus is noted for having proved that the ratios that represent incommensurable with a unit. Archytas introduced the idea of regarding a curve as generated by a ...
... produced the strong Pythagorean inuence in the entire Platonic school. Theodorus is noted for having proved that the ratios that represent incommensurable with a unit. Archytas introduced the idea of regarding a curve as generated by a ...
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... producing correct laws of mathematical reasoning the Greeks had laid the groundwork for logic, but it took Aristotle to codify and systematize these laws into a separate discipline. Aristotle's writings make it abundantly clear that he ...
... producing correct laws of mathematical reasoning the Greeks had laid the groundwork for logic, but it took Aristotle to codify and systematize these laws into a separate discipline. Aristotle's writings make it abundantly clear that he ...
Innhold
Euclid and Apollonius | |
The Work of Desargues | 4-3 |
The Work of Pascal and La Hire | 4-4 |
The Emergence of New Principles | 4-5 |
Progress inMathematics Proper | 4-7 |
The Status of the Number System and Arithmetic | 4-250 |
Symbolism | 4-262 |
The Solution of Third and Fourth Degree Equations | 4-267 |
The Theory of Equations | 4-276 |
The Binomial Theorem and Allied Topics | 4-280 |
The Theory of Numbers | 4-282 |
The Relationship of Algebra to Geometry | 4-288 |
The Beginnings of Projective Geometry | 4-298 |
The Merits and Defects of the Elements | 4-10 |
Coordinate Geometry | 4-15 |
The Reemergence of Arithmetic | 4-78 |
The Demise of the Greek World | 4-135 |
The Mathematics of the Hindus and Arabs | 4-152 |
The Medieval Period in Europe | 4-177 |
Progress in Physical Science | 4-193 |
Summary | 4-196 |
The Renaissance 1 Revolutionary Inuences in Europe | 4-199 |
The New Intellectual Outlook | 4-202 |
The Spread of Learning | 4-205 |
Humanistic Activity in Mathematics | 4-206 |
The Clamor for the Reform of Science | 4-210 |
The Rise of Empiricism | 4-215 |
Mathematical Contributions in the Renaissance 1 Perspective | 4-221 |
Geometry Proper | 4-225 |
Algebra | 4-228 |
Trigonometry | 4-230 |
The Major Scientific Progress in the Renaissance 6 Remarks on the Renaissance | 4-244 |
and Algebra | 4-249 |
The Rebirth of Geometry | 14-1 |
The Problems Raised by the Work on Perspective | 14-2 |
René Descartes | 14-3 |
Descartess Work in Coordinate Geometry | 14-4 |
SeventeenthCentury Extensions | 14-5 |
The Importance of Coordinate Geometry Coordinate | 14-21 |
The Mathematization of Science 1 Introduction | 14-54 |
Descartess Concept of Science | 14-55 |
Galileos Approach to Science | 14-57 |
The Function Concept | 14-69 |
The Creation of the Calculus 1 The Motivation for the Calculus | 14-78 |
Early SeventeenthCentury Work on the Calculus | 14-80 |
The Work of Newton | 14-98 |
The Work of Leibniz | 14-118 |
A Comparison of the Work of Newton and Leibniz | 14-130 |
The Controversy over Priority | 14-132 |
Some Immediate Additions to the Calculus | 14-133 |
The Soundness of the Calculus 383 | 14-136 |
List of Abbreviations Index | 24 |
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Mathematical Thought From Ancient to Modern Times, Volum 1 Morris Kline Ingen forhåndsvisning tilgjengelig - 1990 |
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