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
- Item Size
- 1.2G
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
- 100
- Page_number_module_version
- 1.0.5
- 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
(1)
There is 1 review for this item. .
9,188 Views
206 Favorites
Purchase options
DOWNLOAD OPTIONS
No suitable files to display here.
IN COLLECTIONS
Internet Archive BooksUploaded by Unknown on