A history of mathematics
Bookreader Item Preview
Share or Embed This Item
- Publication date
- 1991
- Topics
- Mathematics -- History
- Publisher
- New York : Wiley
- Contributor
- Internet Archive
- Language
- English
xx, 715 p. : 24 cm
"The initial revision [i.e. 2nd ed.], which appeared two years ago, was designed for classroom use. The exercises found there, and in the original edition, have been dropped in this edition"--P. ix
Includes bibliographical references (p. 665-675) and index
Origins -- Egypt -- Mesopotamia -- Ionia and the Pythagoreans -- Heroic age -- Age of Plato and Aristotle -- Euclid of Alexandria -- Archimedes of Syracuse -- Apollonius of Perga -- Greek trigonometry and mensuration -- Revival and decline of Greek mathematics -- China and India -- Arabic hegemony -- Europe in the Middle Ages -- Renaissance -- Prelude to modern mathematics -- Time of Fermat and Descartes -- Transitional period -- Newton and Leibniz -- Bernoulli era -- Age of Euler -- Mathematicians of the French Revolution -- Time of Gauss and Cauchy -- Geometry -- Analysis -- Algebra -- Poincare and Hilbert -- Aspects of the twentieth century -- References -- General bibliography -- Appendix: Chronological table -- Index
1. Origins -- The concept of number -- Early number bases -- Number language and the origin of counting -- Origin of geometry -- 2. Egypt -- Early records -- Hieroglyphic notation -- Ahmes papyrus -- Unit fractions -- Arithmetic operations -- Algebraic problems -- Geometric problems -- A trigonometric ratio -- Moscow papyrus -- Mathematical weaknesses -- 3. Mesopotamia -- Cuneiform records -- Positional numeration -- Sexagesimal fractions -- Fundamental operations -- Algebraic problems -- Quadratic equations -- Cubic equations -- Pythagorean triads -- Polygonal areas -- Geometry as applied arithmetic -- Mathematical weaknesses -- 4. Ionia and the Pythagoreans -- Greek origins -- Thales of Miletus -- Pythagoras of Samos -- The Pythagorean pentagram -- Number mysticism -- Arithmetic and cosmology -- Figurate numbers -- Proportions -- Attic numeration -- Ionian numeration -- Arithmetic and logistic --
5. The Heroic Age -- Centers of activity -- Anaxagoras as Clazomenae -- Three famous problems -- Quadrature of lunes -- Continued proportions -- Hippias of Elis -- Philolaus and Archytas of Tarentum -- Duplication of the cube -- Incommensurability -- The golden section -- Paradoxes of Zeno -- Deductive reasoning -- Geometric algebra -- Democritus of Abdera -- 6. The age of Plato and Aristotle -- The seven liberal arts -- Socrates -- Platonic solids -- Theodorus of Cyrene -- Platonic arithmetic and geometry -- Origin of analysis -- Eudoxus of Cnidus -- Method of exhaustion -- Mathematical astronomy -- Menaechmus -- Duplication of the cube -- Dinostratus and the squaring of the circle -- Autolycus of Pitane -- Aristotle -- End of the Hellenic period -- 7. Euclid of Alexandria -- Author of the Elements -- Other works -- Purpose of the Elements -- Definitions and postulates -- Scope of Book I -- Geometric algebra -- Books III and IV -- Theory of proportion -- Theory of numbers -- Prime and perfect numbers -- Incommensurability -- Solid geometry -- Apocrypha -- Influence of the Elements --
8. Archimedes of Syracuse -- The siege of Syracuse -- Law of the lever -- The hydrostatic principle -- The Sand-Reckoner -- Measurement of the circle -- Angle trisection -- Area of a parabolic segment -- Volume of a paraboloidal segment -- Segment of a sphere -- On the sphere and cylinder -- Books of Lemmas -- Semiregular solids and trigonometry -- The Method -- Volume of a sphere -- Recovery of The Method -- 9. Apollonius of Perga -- Lost works -- Restoration of lost works -- The problem of Apollonius -- Cycles and epicycles -- The Conics -- Names of the conic sections -- The double-napped cone -- Fundamental properties -- Conjugate diameters -- Tangents and harmonic division -- The three- and four-line locus -- Intersecting conics -- Maxima and minima, tangents and normals -- Similar conics -- Foci of conics -- Use of coordinates -- 10. Greek trigonometry and mensuration -- Early trigonometry -- Aristarchus of Samos -- Eratosthenes of Cyrene -- Hipparchus of Necaea -- Menelaus of Alexandria -- Ptolemy's Almagest -- The 360-degree circle -- Construction of tables -- Ptolemaic astronomy -- Other works by Ptolemy -- Optics and astronomy -- Heron of Alexandria -- Principle of least distance -- Decline of Greek mathematics --
11. Revival and decline of Greek mathematics -- Applied mathematics -- Diophantus of Alexandria -- Nicomachus of Gerasa -- The Arithmetica of Diophantus -- Diophantine problems -- The place of Diophantus in algebra -- Pappus of Alexandria -- The Collection -- Theorems of Pappus -- The Pappus problem -- The Treasury of analysis -- The Pappus-Guldin theorems -- Proclus of Alexandria -- Boethius -- End of the Alexandrian period -- The Greek anthology -- Byzantine mathematicians of the sixth century -- 12. China and India -- The oldest documents -- The Nine chapters -- Magic squares -- Rod numerals -- The abacus and decimal fractions -- Values of pi -- Algebra and Horner's method -- Thirteenth-century mathematicians -- The arithmetic triangle -- Early mathematics in India -- The Sulvasåutras -- The Siddhåantas -- Aryabhata -- Hindu numerals -- The symbol for zero -- Hindu trigonometry -- Hindu multiplication -- Long division -- Brahmagupta -- Brahmagupta's formula -- Indeterminate equations -- Bhaskara -- The Lilavati -- Ramanujan --
13. The Arabic hegemony -- Arabic conquests -- The House of Wisdom -- Al-jabr -- Quadratic equations -- The father of algebra -- Geometric foundation -- Algebraic problems -- A problem from Heron -- 'Abd al-Hamid ibn-Turk -- Thabit ibn-Qurra -- Arabic numerals -- Arabic trigonometry -- Abu'l-Wefa and al-Karkhi -- Al-Biruni and Alhazen -- Omar Khayyam -- The parallel postulate -- Nasir Eddin -- Al-Kashi -- 14. Europe in the Middle Ages -- From Asia to Europe -- Byzantine mathematics -- The Dark Ages -- Alcuin and Gerbert -- The century of translation -- The spread of Hindu-Arabic numerals -- The Liber abaci -- The Fibonacci sequence -- A solution of a cubic equation -- Theory of numbers and geometry -- Jordanus Nemorarius -- Campanus of Novara -- Learning in the thirteenth century -- Medieval kinematics -- Thomas Bradwardine -- Nicole Oresme -- The latitute of forms -- Infinite series -- Decline of medieval learning --
15. The Renaissance -- Humanism -- Nicholas of Cusa -- Regiomontanus -- Application of algebra to geometry -- A transitional figure -- Nicolas Chuquet's Triparty -- Luca Pacioli's Summa -- Leonardo da Vinci -- Germanic algebras -- Cardan's Ars magna -- Solution of the cubic equation -- Ferrari's solution of the quartic equation -- Irreducible cubics and complex numbers -- Robert Recorde -- Nicholas Copernicus -- Georg Joachim Rheticus -- Pierre de la Ramâee -- Bombelli's Algebra -- Johannes Werner -- Theory of perspective -- Cartography -- 16. Prelude to modern mathematics -- Franðcois Viáete -- Concept of a parameter -- The analytic art -- Relations between roots and coefficients -- Thomas Harriot and William Oughtred -- Horner's method again -- Trigonometry and prosthaphaeresis -- Trigonometric solution of equations -- John Napier -- Invention of logarithms -- Henry Briggs -- Jobst Bèurgi -- Applied mathematics and decimal fractions -- Algebraic notations -- Galileo Galilei -- Values of pi -- Reconstruction of Apollonius' On Tangencies -- Infinitesimal analysis -- Johannes Kepler -- Galileo's Two new sciences -- Galileo and the infinite -- Bonaventure Cavalieri -- The spiral the and parabola --
17. The time of Fermat and Descartes -- Leading mathematicians of the time -- The Discours de la mâethode -- Invention of analytic geometry -- Arithmetization of geometry -- Geometric algebra -- Classification of curves -- Rectification of curves -- Identification of conics -- Normals and tangents -- Descartes' geometric concepts -- Fermat's loci -- Higher-dimensional analytic geometry -- Fermat's differentiations -- Fermat's integrations -- Gregory of St. Vincent -- Theory of numbers -- Theorems of Fermat -- Gilles Persone de Roberval -- Evangelista Torricelli -- New curves -- Girard Desargues -- Projective geometry -- Blaise Pascal -- Probability -- The cycloid -- 18. A transitional period -- Philippe de Lahire -- Georg Mohr -- Pietro Mengoli -- Frans van Schooten -- Jan De Witt -- Johann Hudde -- Renâe Franðcois de Sluse -- The pendulum clock -- Involutes and evolutes -- John Wallis -- On conic sections -- Arithmetica infinitorum -- Christopher Wren -- Wallis' formulas -- James Gregory -- Gregory's series -- Nicolaus Mercator and William Brouncker -- Barrow's method of tangents --
19. Newton and Leibniz -- Newton's early work -- The binomial theorem -- Infinite series -- The Method of fluxions -- The Principia -- Leibniz and the harmonic triangle -- The differential triangle and infinite series -- The differential calculus -- Determinants, notations, and imaginary numbers -- The algebra of logic -- The inverse square law -- Theorems on conics -- Optics and curves -- Polar and other coordinates -- Newton's method and Newton's parallelogram -- The Arithmetica universalis -- Later years -- 20. The Bernoulli era -- The Bernoulli family -- The logarithmic spiral -- Probability and infinite series -- L'Hospital's rule -- Exponential calculus -- Logarithms of negative numbers -- Petersburg paradox -- Abraham De Moivre -- De Moivre's theorem -- Roger Cotes -- James Stirling -- Colin Maclaurin -- Taylor's series -- The Analyst controversy -- Cramer's rule -- Tschirnhaus transformations -- Solid analytic geometry -- Michel Rolle and Pierre Varignon -- Mathematics in Italy -- The parallel postulate -- Divergent series --
21. The age of Euler -- Life of Euler -- Notation -- Foundation of analysis -- Infinite series -- Convergent and divergent series -- Life of d'Alembert -- The Euler identities -- D'Alembert and limits -- Differential equations -- The Clairauts -- The Riccatis -- Probability -- Theory of numbers -- Textbooks -- Synthetic geometry -- Solid analytic geometry -- Lambert and the parallel postulate -- Bâezout and elimination -- 22. Mathematicians of the French Revolution -- The age of revolutions -- Leading mathematicians -- Publications before 1789 -- Lagrange and determinants -- Committee on Weights and Measures -- Condorcet on education -- Monge as administrator and teacher -- Descriptive geometry and analytic geometry -- Textbooks -- Lacroix on analytic geometry -- The organizer of victory -- Metaphysics of the calculus and geometry -- Gâeomâetrie de position -- Transversals -- Legendre's Geometry -- Elliptic integrals -- Theory of numbers -- Theory of functions -- Calculus of variations -- Lagrange multipliers -- Laplace and probability -- Celestial mechanics and operators -- Political changes --
23. The time of Gauss and Cauchy -- Nineteenth-century overview -- Gauss : early work -- Number theory -- Reception of the Disquisitiones arithmeticae -- Gauss's contributions to astronomy -- Gauss's middle years -- The beginnings of differential geometry -- Gauss's later work -- Paris in the 1820s -- Cauchy -- Gauss and Cauchy compared -- Non-Euclidean geometry -- Abel and Jacobi -- Galois -- Diffusion -- Reforms in England and Prussia -- 24. Geometry -- The school of Monge -- Projective geometry : Poncelet and Chasles -- Synthetic metric geometry : Steiner -- Synthetic nonmetric geometry : von Staudt -- Analytic geometry -- Riemannian geometry -- Spaces of higher dimensions -- Felix Klein -- Post-Riemannian algebraic geometry -- 25. Analysis -- Berlin and Gèottingen at mid-century -- Riemann in Gèottingen -- Mathematical physics in Germany -- Mathematical physics in the English-speaking countries -- Weierstrass and students -- The arithmetization of analysis -- Cantor and Dedekind -- Analysis in France --
26. Algebra -- Introduction -- British algebra and the operational calculus of functions -- Boole and the algebra of logic -- De Morgan -- Hamilton -- Grassmann and Ausdehnungslehre -- Cayley and Sylvester -- Linear associative algebras -- Algebraic geometry -- Algebraic and arithmetic integers -- Axioms of arithmetic -- 27. Poincarâe and Hilbert -- Turn-of-the-century overview -- Poincarâe -- Mathematical physics and other applications -- Topology -- Other fields and legacy -- Hilbert -- Invariant theory -- Hilbert's Zahlbericht -- The foundations of geometry -- The Hilbert problems -- Hilbert and analysis -- Waring's problem and Hilbert's work after 1909 -- 28. Aspects of the twentieth century -- General overview -- Integration and measure -- Functional analysis and general topology -- Algebra -- Differential geometry and tensor analysis -- The 1930s and World War II -- Probability -- Homological algebra and category theory -- Bourbaki -- Logic and computing -- Future outlook -- References -- General bibliography -- Appendix : Chronological table -- Index
"The initial revision [i.e. 2nd ed.], which appeared two years ago, was designed for classroom use. The exercises found there, and in the original edition, have been dropped in this edition"--P. ix
Includes bibliographical references (p. 665-675) and index
Origins -- Egypt -- Mesopotamia -- Ionia and the Pythagoreans -- Heroic age -- Age of Plato and Aristotle -- Euclid of Alexandria -- Archimedes of Syracuse -- Apollonius of Perga -- Greek trigonometry and mensuration -- Revival and decline of Greek mathematics -- China and India -- Arabic hegemony -- Europe in the Middle Ages -- Renaissance -- Prelude to modern mathematics -- Time of Fermat and Descartes -- Transitional period -- Newton and Leibniz -- Bernoulli era -- Age of Euler -- Mathematicians of the French Revolution -- Time of Gauss and Cauchy -- Geometry -- Analysis -- Algebra -- Poincare and Hilbert -- Aspects of the twentieth century -- References -- General bibliography -- Appendix: Chronological table -- Index
1. Origins -- The concept of number -- Early number bases -- Number language and the origin of counting -- Origin of geometry -- 2. Egypt -- Early records -- Hieroglyphic notation -- Ahmes papyrus -- Unit fractions -- Arithmetic operations -- Algebraic problems -- Geometric problems -- A trigonometric ratio -- Moscow papyrus -- Mathematical weaknesses -- 3. Mesopotamia -- Cuneiform records -- Positional numeration -- Sexagesimal fractions -- Fundamental operations -- Algebraic problems -- Quadratic equations -- Cubic equations -- Pythagorean triads -- Polygonal areas -- Geometry as applied arithmetic -- Mathematical weaknesses -- 4. Ionia and the Pythagoreans -- Greek origins -- Thales of Miletus -- Pythagoras of Samos -- The Pythagorean pentagram -- Number mysticism -- Arithmetic and cosmology -- Figurate numbers -- Proportions -- Attic numeration -- Ionian numeration -- Arithmetic and logistic --
5. The Heroic Age -- Centers of activity -- Anaxagoras as Clazomenae -- Three famous problems -- Quadrature of lunes -- Continued proportions -- Hippias of Elis -- Philolaus and Archytas of Tarentum -- Duplication of the cube -- Incommensurability -- The golden section -- Paradoxes of Zeno -- Deductive reasoning -- Geometric algebra -- Democritus of Abdera -- 6. The age of Plato and Aristotle -- The seven liberal arts -- Socrates -- Platonic solids -- Theodorus of Cyrene -- Platonic arithmetic and geometry -- Origin of analysis -- Eudoxus of Cnidus -- Method of exhaustion -- Mathematical astronomy -- Menaechmus -- Duplication of the cube -- Dinostratus and the squaring of the circle -- Autolycus of Pitane -- Aristotle -- End of the Hellenic period -- 7. Euclid of Alexandria -- Author of the Elements -- Other works -- Purpose of the Elements -- Definitions and postulates -- Scope of Book I -- Geometric algebra -- Books III and IV -- Theory of proportion -- Theory of numbers -- Prime and perfect numbers -- Incommensurability -- Solid geometry -- Apocrypha -- Influence of the Elements --
8. Archimedes of Syracuse -- The siege of Syracuse -- Law of the lever -- The hydrostatic principle -- The Sand-Reckoner -- Measurement of the circle -- Angle trisection -- Area of a parabolic segment -- Volume of a paraboloidal segment -- Segment of a sphere -- On the sphere and cylinder -- Books of Lemmas -- Semiregular solids and trigonometry -- The Method -- Volume of a sphere -- Recovery of The Method -- 9. Apollonius of Perga -- Lost works -- Restoration of lost works -- The problem of Apollonius -- Cycles and epicycles -- The Conics -- Names of the conic sections -- The double-napped cone -- Fundamental properties -- Conjugate diameters -- Tangents and harmonic division -- The three- and four-line locus -- Intersecting conics -- Maxima and minima, tangents and normals -- Similar conics -- Foci of conics -- Use of coordinates -- 10. Greek trigonometry and mensuration -- Early trigonometry -- Aristarchus of Samos -- Eratosthenes of Cyrene -- Hipparchus of Necaea -- Menelaus of Alexandria -- Ptolemy's Almagest -- The 360-degree circle -- Construction of tables -- Ptolemaic astronomy -- Other works by Ptolemy -- Optics and astronomy -- Heron of Alexandria -- Principle of least distance -- Decline of Greek mathematics --
11. Revival and decline of Greek mathematics -- Applied mathematics -- Diophantus of Alexandria -- Nicomachus of Gerasa -- The Arithmetica of Diophantus -- Diophantine problems -- The place of Diophantus in algebra -- Pappus of Alexandria -- The Collection -- Theorems of Pappus -- The Pappus problem -- The Treasury of analysis -- The Pappus-Guldin theorems -- Proclus of Alexandria -- Boethius -- End of the Alexandrian period -- The Greek anthology -- Byzantine mathematicians of the sixth century -- 12. China and India -- The oldest documents -- The Nine chapters -- Magic squares -- Rod numerals -- The abacus and decimal fractions -- Values of pi -- Algebra and Horner's method -- Thirteenth-century mathematicians -- The arithmetic triangle -- Early mathematics in India -- The Sulvasåutras -- The Siddhåantas -- Aryabhata -- Hindu numerals -- The symbol for zero -- Hindu trigonometry -- Hindu multiplication -- Long division -- Brahmagupta -- Brahmagupta's formula -- Indeterminate equations -- Bhaskara -- The Lilavati -- Ramanujan --
13. The Arabic hegemony -- Arabic conquests -- The House of Wisdom -- Al-jabr -- Quadratic equations -- The father of algebra -- Geometric foundation -- Algebraic problems -- A problem from Heron -- 'Abd al-Hamid ibn-Turk -- Thabit ibn-Qurra -- Arabic numerals -- Arabic trigonometry -- Abu'l-Wefa and al-Karkhi -- Al-Biruni and Alhazen -- Omar Khayyam -- The parallel postulate -- Nasir Eddin -- Al-Kashi -- 14. Europe in the Middle Ages -- From Asia to Europe -- Byzantine mathematics -- The Dark Ages -- Alcuin and Gerbert -- The century of translation -- The spread of Hindu-Arabic numerals -- The Liber abaci -- The Fibonacci sequence -- A solution of a cubic equation -- Theory of numbers and geometry -- Jordanus Nemorarius -- Campanus of Novara -- Learning in the thirteenth century -- Medieval kinematics -- Thomas Bradwardine -- Nicole Oresme -- The latitute of forms -- Infinite series -- Decline of medieval learning --
15. The Renaissance -- Humanism -- Nicholas of Cusa -- Regiomontanus -- Application of algebra to geometry -- A transitional figure -- Nicolas Chuquet's Triparty -- Luca Pacioli's Summa -- Leonardo da Vinci -- Germanic algebras -- Cardan's Ars magna -- Solution of the cubic equation -- Ferrari's solution of the quartic equation -- Irreducible cubics and complex numbers -- Robert Recorde -- Nicholas Copernicus -- Georg Joachim Rheticus -- Pierre de la Ramâee -- Bombelli's Algebra -- Johannes Werner -- Theory of perspective -- Cartography -- 16. Prelude to modern mathematics -- Franðcois Viáete -- Concept of a parameter -- The analytic art -- Relations between roots and coefficients -- Thomas Harriot and William Oughtred -- Horner's method again -- Trigonometry and prosthaphaeresis -- Trigonometric solution of equations -- John Napier -- Invention of logarithms -- Henry Briggs -- Jobst Bèurgi -- Applied mathematics and decimal fractions -- Algebraic notations -- Galileo Galilei -- Values of pi -- Reconstruction of Apollonius' On Tangencies -- Infinitesimal analysis -- Johannes Kepler -- Galileo's Two new sciences -- Galileo and the infinite -- Bonaventure Cavalieri -- The spiral the and parabola --
17. The time of Fermat and Descartes -- Leading mathematicians of the time -- The Discours de la mâethode -- Invention of analytic geometry -- Arithmetization of geometry -- Geometric algebra -- Classification of curves -- Rectification of curves -- Identification of conics -- Normals and tangents -- Descartes' geometric concepts -- Fermat's loci -- Higher-dimensional analytic geometry -- Fermat's differentiations -- Fermat's integrations -- Gregory of St. Vincent -- Theory of numbers -- Theorems of Fermat -- Gilles Persone de Roberval -- Evangelista Torricelli -- New curves -- Girard Desargues -- Projective geometry -- Blaise Pascal -- Probability -- The cycloid -- 18. A transitional period -- Philippe de Lahire -- Georg Mohr -- Pietro Mengoli -- Frans van Schooten -- Jan De Witt -- Johann Hudde -- Renâe Franðcois de Sluse -- The pendulum clock -- Involutes and evolutes -- John Wallis -- On conic sections -- Arithmetica infinitorum -- Christopher Wren -- Wallis' formulas -- James Gregory -- Gregory's series -- Nicolaus Mercator and William Brouncker -- Barrow's method of tangents --
19. Newton and Leibniz -- Newton's early work -- The binomial theorem -- Infinite series -- The Method of fluxions -- The Principia -- Leibniz and the harmonic triangle -- The differential triangle and infinite series -- The differential calculus -- Determinants, notations, and imaginary numbers -- The algebra of logic -- The inverse square law -- Theorems on conics -- Optics and curves -- Polar and other coordinates -- Newton's method and Newton's parallelogram -- The Arithmetica universalis -- Later years -- 20. The Bernoulli era -- The Bernoulli family -- The logarithmic spiral -- Probability and infinite series -- L'Hospital's rule -- Exponential calculus -- Logarithms of negative numbers -- Petersburg paradox -- Abraham De Moivre -- De Moivre's theorem -- Roger Cotes -- James Stirling -- Colin Maclaurin -- Taylor's series -- The Analyst controversy -- Cramer's rule -- Tschirnhaus transformations -- Solid analytic geometry -- Michel Rolle and Pierre Varignon -- Mathematics in Italy -- The parallel postulate -- Divergent series --
21. The age of Euler -- Life of Euler -- Notation -- Foundation of analysis -- Infinite series -- Convergent and divergent series -- Life of d'Alembert -- The Euler identities -- D'Alembert and limits -- Differential equations -- The Clairauts -- The Riccatis -- Probability -- Theory of numbers -- Textbooks -- Synthetic geometry -- Solid analytic geometry -- Lambert and the parallel postulate -- Bâezout and elimination -- 22. Mathematicians of the French Revolution -- The age of revolutions -- Leading mathematicians -- Publications before 1789 -- Lagrange and determinants -- Committee on Weights and Measures -- Condorcet on education -- Monge as administrator and teacher -- Descriptive geometry and analytic geometry -- Textbooks -- Lacroix on analytic geometry -- The organizer of victory -- Metaphysics of the calculus and geometry -- Gâeomâetrie de position -- Transversals -- Legendre's Geometry -- Elliptic integrals -- Theory of numbers -- Theory of functions -- Calculus of variations -- Lagrange multipliers -- Laplace and probability -- Celestial mechanics and operators -- Political changes --
23. The time of Gauss and Cauchy -- Nineteenth-century overview -- Gauss : early work -- Number theory -- Reception of the Disquisitiones arithmeticae -- Gauss's contributions to astronomy -- Gauss's middle years -- The beginnings of differential geometry -- Gauss's later work -- Paris in the 1820s -- Cauchy -- Gauss and Cauchy compared -- Non-Euclidean geometry -- Abel and Jacobi -- Galois -- Diffusion -- Reforms in England and Prussia -- 24. Geometry -- The school of Monge -- Projective geometry : Poncelet and Chasles -- Synthetic metric geometry : Steiner -- Synthetic nonmetric geometry : von Staudt -- Analytic geometry -- Riemannian geometry -- Spaces of higher dimensions -- Felix Klein -- Post-Riemannian algebraic geometry -- 25. Analysis -- Berlin and Gèottingen at mid-century -- Riemann in Gèottingen -- Mathematical physics in Germany -- Mathematical physics in the English-speaking countries -- Weierstrass and students -- The arithmetization of analysis -- Cantor and Dedekind -- Analysis in France --
26. Algebra -- Introduction -- British algebra and the operational calculus of functions -- Boole and the algebra of logic -- De Morgan -- Hamilton -- Grassmann and Ausdehnungslehre -- Cayley and Sylvester -- Linear associative algebras -- Algebraic geometry -- Algebraic and arithmetic integers -- Axioms of arithmetic -- 27. Poincarâe and Hilbert -- Turn-of-the-century overview -- Poincarâe -- Mathematical physics and other applications -- Topology -- Other fields and legacy -- Hilbert -- Invariant theory -- Hilbert's Zahlbericht -- The foundations of geometry -- The Hilbert problems -- Hilbert and analysis -- Waring's problem and Hilbert's work after 1909 -- 28. Aspects of the twentieth century -- General overview -- Integration and measure -- Functional analysis and general topology -- Algebra -- Differential geometry and tensor analysis -- The 1930s and World War II -- Probability -- Homological algebra and category theory -- Bourbaki -- Logic and computing -- Future outlook -- References -- General bibliography -- Appendix : Chronological table -- Index
- Access-restricted-item
- true
- Addeddate
- 2012-02-24 16:12:17
- Associated-names
- Merzbach, Uta C., 1933-
- Boxid
- IA178401
- Boxid_2
- CH129925
- Camera
- Canon EOS 5D Mark II
- City
- New York
- Containerid_2
- X0008
- Donor
- archbishopmittyhs
- Edition
- 2nd ed. [rev.].
- External-identifier
- urn:oclc:record:1035607906
urn:lcp:historyofmathema00boye:lcpdf:917b1423-d9dc-4e4c-9952-73c5b6791bd9
urn:lcp:historyofmathema00boye:epub:be55781b-8962-4a55-9be2-b56b9cd68db0
- Extramarc
- Princeton University Library
- Foldoutcount
- 0
- Identifier
- historyofmathema00boye
- Identifier-ark
- ark:/13960/t26988629
- Isbn
- 0471543977
9780471543978
- Lccn
- 89005325
- Ocr
- ABBYY FineReader 8.0
- Ocr_converted
- abbyy-to-hocr 1.1.11
- Ocr_module_version
- 0.0.14
- Openlibrary
- OL18198047M
- Openlibrary_edition
- OL18198047M
- Openlibrary_work
- OL4775276W
- Page_number_confidence
- 96.21
- Pages
- 742
- Pdf_module_version
- 0.0.20
- Ppi
- 514
- Related-external-id
-
urn:isbn:0470525487
urn:lccn:2010003424
urn:oclc:521733576
urn:oclc:705584605
urn:oclc:712204044
urn:oclc:713012306
urn:oclc:757870900
urn:oclc:758707918
urn:oclc:768443880
urn:oclc:777130662
urn:oclc:812409124
urn:oclc:839010064
urn:isbn:1282987550
urn:oclc:816640141
urn:isbn:0470630566
urn:oclc:864890070
urn:oclc:701718146
urn:isbn:0471093742
urn:lccn:68016506
urn:oclc:414892
urn:oclc:500130485
urn:isbn:0691023913
urn:lccn:84062250
urn:oclc:11930174
urn:oclc:263625874
urn:oclc:436066047
urn:oclc:750969913
urn:oclc:781853835
urn:oclc:79169262
urn:oclc:869059434
urn:isbn:0471097632
urn:lccn:89005325
urn:lccn:0089005325
urn:oclc:19122469
urn:oclc:229911662
urn:oclc:246822926
urn:oclc:265029543
urn:oclc:319690959
urn:oclc:395855146
urn:oclc:438985152
urn:oclc:471826444
urn:oclc:639831245
urn:oclc:644677840
urn:oclc:720077484
urn:oclc:802529476
urn:oclc:804039533
urn:oclc:810695589
urn:oclc:875911458
urn:oclc:856780974
urn:isbn:0471503576
urn:oclc:439992204
urn:oclc:655715825
urn:oclc:874280758
urn:isbn:047063054X
urn:oclc:700704005
urn:oclc:731794103
urn:oclc:797946530
urn:isbn:0470630396
- Republisher_date
- 20120502194652
- Republisher_operator
- scanner-shenzhen-lori@archive.org
- Scandate
- 20120429231419
- Scanner
- scribe2.shenzhen.archive.org
- Scanningcenter
- shenzhen
- Source
- removed
- Worldcat (source edition)
- 23823042
- Full catalog record
- MARCXML
comment
Reviews
7,743 Views
194 Favorites
Purchase options
DOWNLOAD OPTIONS
No suitable files to display here.
IN COLLECTIONS
Books for People with Print Disabilities Internet Archive Books Delaware County District Library (Ohio) American LibrariesUploaded by Unknown on