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A history of mathematics

Author: Carl B Boyer; Uta C Merzbach
Publisher: New York : Wiley, ©1989.
Edition/Format:   Print book : English : 2nd ed.View all editions and formats
Summary:
Develops world contributions to mathematics, from the inception of numbers and geometry to modern probability and Bourbaki's mathematics.
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Genre/Form: History
Additional Physical Format: Online version:
Boyer, Carl B. (Carl Benjamin), 1906-1976.
History of mathematics.
New York : Wiley, ©1989
(OCoLC)624469418
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Carl B Boyer; Uta C Merzbach
ISBN: 0471097632 9780471097631 0471503576 9780471503576
OCLC Number: 19122469
Description: xviii, 762 pages : illustrations ; 25 cm
Contents: 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 --
Mathemetical 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 of 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 Abdura. 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 the Book I --
Geometric algebra --
Books III and IV --
Theory of the 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 --
Book 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 3- and 4- line locus --
Intersecting conics --
Foci of conics --
Use of coordinates. 10. Greek trigonometry and mensuration. Early trigonometry --
Aristarchus of Samos --
Eratosthenes of Cyrene --
Hipparchus of Nicaea --
Menelaus of Alexandria --
Ptolemy's Almagest --
The 360-degree circle --
Construction of tables --
Ptolemaic astronomy --
Other works by Ptolemy --
Optics and astrology --
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 Sulvasūtras --
The Siddhāntas --
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 latitude 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 Chuguet'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 Ramée --
Bombelli's Algebra --
Johannes Werner --
Theory of perspective --
Cartography. Prelude to modern mathematics. Francois Vi`ete --
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 Bürgi --
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 --
Bonaventura Cavalieri --
The spiral and the parabola. 17. The time of Fermat and Descartes. Leading mathematicians of the time --
The Discours de la methode --
Invention of analytic geometry --
Arithmetization of geometry --
Geometric algebra --
Classificaition 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. Phillippe de Lahire --
George Mohr --
Pietro Mengoli --
Frans van Schooten --
Jan De Witt --
Johann Hudde --
René Franc̦ois 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 negataive 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 --
Synthetic geometry --
Solid analytic geometry --
Lambert and the parallel postulate --
Bézout and elimination. 22. Mathematicians of the French Revolution. The age of revolution --
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 --
Lacroix on analytic geometry --
The organizer of victory --
Metaphysics of the calculus and geometry --
Géométrie de position --
Transversals Legendre's Geometry --
Elliptic integrals --
Theory of numbers --
Theory of functions --
Calculus of variations --
Lagrange multipliers --
Laplace and probabililty --
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 Göttingen at mid-century --
Riemann in Göttingen --
Mathematical physics in Germany --
Mathematical physics in the English-speaking countries --
Weierstrass and students --
Arithmetization of analysis --
Cantor and Dedekind --
Analysis in France. 26. Algebra. 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. Poincaré and Hilbert. Turn-of-the-century overview --
Poincare --
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 --
Diffential geometry and tensor analysis --
The 1930s and World War II --
Probability --
Homological algebra and category theory --
Bourbaki --
Logic and computing --
Future outlook.
Responsibility: Carl B. Boyer.
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Abstract:

A chronological history of mathematics from its earliest origins to the present day, this edition has been revised and updated to include new information on the 19th century, further references and  Read more...

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    schema:description "Legendre's Geometry -- Elliptic integrals -- Theory of numbers -- Theory of functions -- Calculus of variations -- Lagrange multipliers -- Laplace and probabililty -- 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."@en ;
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    schema:description "Prelude to modern mathematics. Francois Vi`ete -- 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 Bürgi -- 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 -- Bonaventura Cavalieri -- The spiral and the parabola."@en ;
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    schema:description "26. Algebra. 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. Poincaré and Hilbert. Turn-of-the-century overview -- Poincare -- 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."@en ;
    schema:description "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 the Book I -- Geometric algebra -- Books III and IV -- Theory of the proportion -- Theory of numbers -- Prime and perfect numbers -- Incommensurability -- Solid geometry -- Apocrypha -- Influence of the Elements."@en ;
    schema:description "10. Greek trigonometry and mensuration. Early trigonometry -- Aristarchus of Samos -- Eratosthenes of Cyrene -- Hipparchus of Nicaea -- Menelaus of Alexandria -- Ptolemy's Almagest -- The 360-degree circle -- Construction of tables -- Ptolemaic astronomy -- Other works by Ptolemy -- Optics and astrology -- 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."@en ;
    schema:description "Develops world contributions to mathematics, from the inception of numbers and geometry to modern probability and Bourbaki's mathematics."@en ;
    schema:description "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 -- Synthetic geometry -- Solid analytic geometry -- Lambert and the parallel postulate -- Bézout and elimination. 22. Mathematicians of the French Revolution. The age of revolution -- 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 -- Lacroix on analytic geometry -- The organizer of victory -- Metaphysics of the calculus and geometry -- Géométrie de position -- Transversals"@en ;
    schema:description "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 negataive 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."@en ;
    schema:description "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 -- Mathemetical 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."@en ;
    schema:description "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 of 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 Abdura."@en ;
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    schema:description "18. A transitional period. Phillippe de Lahire -- George Mohr -- Pietro Mengoli -- Frans van Schooten -- Jan De Witt -- Johann Hudde -- René Franc̦ois 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"@en ;
    schema:description "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 Sulvasūtras -- The Siddhāntas -- Aryabhata -- Hindu numerals -- The symbol for zero -- Hindu trigonometry -- Hindu multiplication -- Long division -- Brahmagupta -- Brahmagupta's formula -- Indeterminate equations -- Bhaskara -- The Lilavati -- Ramanujan."@en ;
    schema:description "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 Göttingen at mid-century -- Riemann in Göttingen -- Mathematical physics in Germany -- Mathematical physics in the English-speaking countries -- Weierstrass and students -- Arithmetization of analysis -- Cantor and Dedekind -- Analysis in France."@en ;
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<http://viaf.org/viaf/98052945> # Uta C. Merzbach
    a schema:Person ;
    schema:birthDate "1933" ;
    schema:familyName "Merzbach" ;
    schema:givenName "Uta C." ;
    schema:name "Uta C. Merzbach" ;
    .

<http://worldcat.org/isbn/9780471097631>
    a schema:ProductModel ;
    schema:isbn "0471097632" ;
    schema:isbn "9780471097631" ;
    .

<http://worldcat.org/isbn/9780471503576>
    a schema:ProductModel ;
    schema:isbn "0471503576" ;
    schema:isbn "9780471503576" ;
    .

<http://www.worldcat.org/oclc/624469418>
    a schema:CreativeWork ;
    rdfs:label "History of mathematics." ;
    schema:description "Online version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/19122469> ; # A history of mathematics
    .


Content-negotiable representations

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