A History Of Mathematics, Third Edition 9780470525487 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

　　The updated new edition of the classic and comprehensive guide

to the history of mathematics

For more than forty years, A History of Mathematics has been the

reference of choice for those looking to learn about the

fascinating history of humankind’s relationship with numbers,

shapes, and patterns. This revised edition features up-to-date

coverage of topics such as Fermat’s Last Theorem and the Poincaré

Conjecture, in addition to recent advances in areas such as finite

group theory and computer-aided proofs.

Distills thousands of years of mathematics into a single,

approachable volume

Covers mathematical discoveries, concepts, and thinkers, from

Ancient Egypt to the present

Includes up-to-date references and an extensive chronological

table of mathematical and general historical developments.

Whether you're interested in the age of Plato and Aristotle or

Poincaré and Hilbert, whether you want to know more about 　　the

Pythagorean theorem or the golden mean, A History of Mathematics is

an essential reference that will help you explore 　　the incredible

history of mathematics and the men and women who created it.

Foreword by Isaac Asimov.

Preface to the Third Edition.

Preface to the Second Edition.

Preface to the First Edition.

1 Traces.

Concepts and Relationships.

Early Number Bases.

Number Language and Counting.

Spatial Relationships.

2 Ancient Egypt.

The Era and the Sources.

Numbers and Fractions.

Arithmetic Operations.

"Heap" Problems.

Geometric Problems.

Slope Problems.

Arithmetic Pragmatism.

3 Mesopotamia.

The Era and the Sources.

Cuneiform Writing.

Numbers and Fractions; Sexagesimals.

Positional Numeration.

Sexagesimal Fractions.

Approximations.

Tables.

Equations.

Measurements: Pythagorean Triads.

Polygonal Areas.

Geometry as Applied Arithmetic.

4 Hellenic Traditions.

The Era and the Sources.

Thales and Pythagoras.

Numeration.

Arithmetic and Logistic.

Fifth Century Athens.

Three Classical Problems.

Incommensurability.

Paradoxes of Zeno.

Deductive Reasoning.

Democritus of Abdera.

Mathematics and the Liberal Arts.

The Academy.

Aristotle.

5 Euclid of Alexandria.

Alexandria.

Lost Works.

Extant Works.

The Elements.

6 Archimedes of Syracuse.

The Siege of Syracuse.

On the Equilibriums of Planes.

On Floating Bodies.

The Sand-Reckoner.

Measurement of the Circle.

On Spirals.

Quadrature of the Parabola.

On Conoids and Spheroids.

On the Sphere and Cylinder.

Book of Lemmas.

Semiregular Solids and Trigonometry.

The Method.

7 Apollonius of Perge.

Works and Tradition.

Lost Works.

Cycles and Epicycles.

The Conics.

8 Cross-Currents.

Changing Trends.

Eratosthenes.

Angles and Chords.

Ptolemy's Almagest.

Heron of Alexandria.

Decline of Greek Mathematics.

Nichomachus of Gerasa.

Diophantus of Alexandria.

Pappus of Alexandria.

The End of Alexandrian Dominance.

Proclus of Alexandria.

Boethius.

Athenian Fragments.

Byzantine Mathematicians.

9 Ancient and Medieval China.

The Oldest Known Texts.

The Nine Chapters .

Rod Numerals.

The Abacus and Decimal Fractions.

Values of Pi.

Thirteenth-Century Mathematics.

10 Ancient and Medieval India.

Early Mathematics in India.

The Sulbasutras.

The Siddhantas.

Aryabhata.

Numerals.

Trigonometry.

Multiplication.

Long Division.

Brahmagupta.

Indeterminate Equations.

Bhaskara.

Madhava and the Keralese School.

11 The Islamic Hegemony.

Arabic Conquests.

The House of Wisdom.

Al-Khwarizmi.

‘Abd Al-Hamid ibn-Turk.

Thabit ibn-Qurra.

Numerals.

Trigonometry.

Abu’l-Wefa and Al-Karkhi.

Al-Biruni and Alhazen.

Omar Khayyam.

The Parallel Postulate.

Nasir al-Din al-Tusi.

Al-Kashi.

12 The Latin West.

Introduction.

Compendia of the Dark Ages.

Gerbert.

The Century of Translation.

Abacists and Algorists.

Fibonacci.

Jordanus Nemorarius.

Campanus of Novara.

Learning in the Thirteenth Century.

Archimedes Revived.

Medieval Kinematics.

Thomas Bradwardine.

Nicole Oresme.

The Latitude of Forms.

Infinite Series.

Levi ben Gerson.

Nicholas of Cusa.

Decline of Medieval Learning.

13 The European Renaissance.

Overview.

Regiomontanus.

Nicolas Chuquet’s Triparty.

Luca Pacioli's Summa.

German Algebras and Arithmetics.

Cardan’s Ars Magna.

Rafael Bombelli.

Robert Recorde.

Trigonometry.

Geometry.

Renaissance Trends.

Fran?ois Viète.

14 Early Modern Problem Solvers.

Accessibility of Computation.

Decimal Fractions.

Notation.

Logarithms.

Mathematical Instruments.

15 Analysis, Synthesis, the Infinite, and Numbers.

Galileo’s Two New Sciences.

Bonaventura Cavalieri.

Evangelista Torricelli.

Mersenne’s Communicants.

Rene? Descartes.

Fermat’s Loci.

Gregory of St. Vincent.

The Theory of Numbers.

Gilles Persone de Roberval.

Girard Desargues and Projective Geometry.

Blaise Pascal.

Philippe de Lahire.

Georg Mohr.

Pietro Mengoli.

Frans van Schooten.

Jan de Witt.

Johann Hudde.

René Fran?ois de Sluse.

Christiaan Huygens.

16 British Techniques and Continental Methods.

John Wallis.

James Gregory.

Nicolaus Mercator and William Brouncker.

Barrow’s Method of Tangents.

Newton.

Abraham De Moivre.

Roger Cotes.

James Stirling.

Colin Maclaurin.

Textbooks.

Rigor and Progress.

Leibniz.

The Bernoulli Family.

Tschirnhaus Transformations.

Solid Analytic Geometry.

Michel Rolle and Pierre Varignon.

The Clairauts.

Mathematics in Italy.

The Parallel Postulate.

Divergent Series.

17 Euler.

The Life of Euler.

Notation.

Foundation of Analysis.

Logarithms and the Euler Identities.

Differential Equations.

Probability.

The Theory of Numbers.

Textbooks.

Analytic Geometry.

The Parallel Postulate: Lambert

18 Pre- to Postrevolutionary France.

Men and Institutions.

The Committee on Weights and Measures.

D'Alembert.

Bézout.

Condorcet.

Lagrange.

Monge.

Carnot.

Laplace.

Legendre.

Aspects of Abstraction.

Paris in the 1820s.

Fourier.

Cauchy.

Diffusion.

19 Gauss.

Nineteenth-Century Overview.

Gauss: Early Work.

Number Theory.

Reception of the Disquisitiones Arithmeticae.

Astronomy.

Gauss's Middle Years.

Differential Geometry.

Gauss's Later Work.

Gauss’s Influence.

20 Geometry.

The School of Monge.

Projective Geometry: Poncelet and Chasles.

Synthetic Metric Geometry: Steiner.

Synthetic Nonmetric Geometry: von Staudt.

Analytic Geometry.

Non-Euclidean Geometry.

Riemannian Geometry.

Spaces of Higher Dimensions.

Felix Klein.

Post-Riemannian Algebraic Geometry.

21 Algebra.

Introduction.

British Algebra and the Operational Calculus of Functions.

Boole and the Algebra of Logic.

Augustus De Morgan.

William Rowan Hamilton.

Grassmann and Ausdehnungslehre.

Cayley and Sylvester.

Linear Associative Algebras.

Algebraic Geometry.

Algebraic and Arithmetic Integers.

Axioms of Arithmetic.

22 Analysis.

Berlin and G?ttingen at Mid-Century.

Riemann in G?ttingen.

Mathematical Physics in Germany.

Mathematical Physics in English-Speaking Countries.

Weierstrass and Students.

The Arithmetization of Analysis.

Dedekind.

Cantor and Kronecker.

Analysis in France.

23 Twentieth Century Legacies.

Henri Poincare.

David Hilbert.

Integration and Measure.

Functional Analysis and General Topology.

Algebra.

Differential Geometry and Tensor Analysis.

Probability.

Bounds and Approximations.

The 1930s and World War II.

Nicolas Bourbaki.

Homological Algebra and Category Theory.

Algebraic Geometry.

Logic and Computing.

The Fields Medals.

24 Recent Trends.

Overview.

The Four-Color Conjecture.

Classification of Finite Simple Groups.

Fermat’s Last Theorem.

Poincaré's Query.

Future Outlook.

References.

eneral Bibliography.

Index.

　　Uta C. Merzbach is Curator Emeritus of Mathematics at the

Smithsonian Institution and Director of the LHM Institute

　　The late Carl B. Boyer was a professor of Mathematics at Brooklyn

College and the author of several classic works on the history of

mathematics.

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数学意识的基础：辨别数字、大小、顺序和形状。

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对数字的认知，最终变得足够广泛、足够清晰，这样一来人们觉得有必要以某种方式表达这种属性。

表示数字观念的单词，形成得却很缓慢。数字记号很可能要早于数字单词，因为，要标识一个数字，在木棒上划刻痕总比创立一个音调和谐的短语更容易。

语言的发展总是从具体走向抽象。

在某些神话仪式中，按照特定的顺序召唤参加者上场是必不可少的，没准，发明计算，就是为了处理这个问题。

书籍介绍

The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture , in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.