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• catalog abstract ""This is a textbook on the history, philosophy, and foundations of mathematics. One of its aims is to present some interesting mathematics, not normally taught in other courses, in a historical and philosophical setting. The book is intended mainly for undergraduate mathematics students, but is also suitable for students in the sciences, humanities, and education with a strong interest in mathematics. It proceeds in historical order from about 1800 BC to 1800 AD and then presents some selected topics of foundational interest from the 19th and 20th centuries. Among other material in the first part, the authors discuss the renaissance method for solving cubic and quartic equations and give rigorous elementary proofs that certain geometrical problems posed by the ancient Greeks (e.g. the problem of trisecting an arbitary angle) cannot be solved by ruler and compass constructions. In the second part, they sketch a proof of Godel's incompleteness theorem and discuss some of its implications, and also present the elements of category theory, among other topics. The authors' approach to a number of these matters is new."--BOOK JACKET.".
• catalog contributor b9190418.
• catalog contributor b9190419.
• catalog created "c1995.".
• catalog date "1995".
• catalog date "c1995.".
• catalog dateCopyrighted "c1995.".
• catalog description ""This is a textbook on the history, philosophy, and foundations of mathematics. One of its aims is to present some interesting mathematics, not normally taught in other courses, in a historical and philosophical setting. The book is intended mainly for undergraduate mathematics students, but is also suitable for students in the sciences, humanities, and education with a strong interest in mathematics. It proceeds in historical order from about 1800 BC to 1800 AD and then presents some selected topics of foundational interest from the 19th and 20th centuries. Among other material in the first part, the authors discuss the renaissance method for solving cubic and quartic equations and give rigorous elementary proofs that certain geometrical problems posed by the ancient Greeks (e.g. the problem of trisecting an arbitary angle) cannot be solved by ruler and compass constructions. In the second part, they sketch a proof of Godel's incompleteness theorem and discuss some of its implications, and also present the elements of category theory, among other topics. The authors' approach to a number of these matters is new."--BOOK JACKET.".
• catalog description "Egyptian mathematics -- Scales of notation -- Prime numbers -- Sumerian-Babylonian mathematics -- More about Mesopotamian mathematics -- The dawn of Greek mathematics -- Pythagoras and his school -- Perfect numbers -- Regular polyhedra -- The crisis of incommensurables -- From Heraclitus to Democritus -- Mathematics in Athens -- Plato and Aristotle on mathematics -- Constructions with ruler and compass -- The impossibility of solving the classical problems -- Euclid -- Non-Euclidean geometry and Hilbert's axioms -- Alexandria from 300 BC to 200 BC -- Archimedes -- Alexandria from 200 BC to 500 AD -- Mathematics in China and India -- Mathematics in Islamic countries -- New beginnings in Europe -- Mathematics in the Renaissance -- The cubic and quartic equations -- Renaissance mathematics continued -- The seventeenth century in France -- The seventeenth century continued -- Leibniz -- The eighteenth century -- The law of quadratic reciprocity -- The number system -- Natural numbers (Peano's approach) -- The integers -- The rationals -- The real numbers -- Complex numbers -- The fundamental theorem of algebra -- Quaternions -- Quaternions applied to number theory -- Quaternions applied to physics -- Quaternions in quantum mechanics -- Cardinal numbers -- Cardinal arithmetic -- Continued fractions -- The fundamental theorem of arithmetic -- Linear diophantine equations -- Quadratic surds -- Pythagorean triangles and Fermat's last theorem -- What is a calculation? -- Recursive and recursively enumerable sets -- Hilbert's tenth problem -- Lambda calculus -- Logic from Aristotle to Russell -- Intuitionistic propositional calculus -- How to interpret intuitionistic logic -- Intuitionistic predicate calculus -- Intuitionistic type theory -- Godel's theorems -- Proof of Godel's incompleteness theorem -- More about Godel's theorems -- Concrete categories -- Graphs and categories -- Functors -- Natural transformations -- A natural transformation between vector spaces".
• catalog description "Includes bibliographical references (p. [311]-320) and index.".
• catalog extent "x, 327 p. :".
• catalog identifier "038794544X (hc : alk. paper)".
• catalog isPartOf "Undergraduate texts in mathematics. Readings in mathematics".
• catalog issued "1995".
• catalog issued "c1995.".
• catalog language "eng".
• catalog publisher "New York, NY, USA : Springer,".
• catalog subject "510/.9 20".
• catalog subject "Mathematics History.".
• catalog subject "Mathematics Philosophy.".
• catalog subject "QA21 .A535 1995".
• catalog tableOfContents "Egyptian mathematics -- Scales of notation -- Prime numbers -- Sumerian-Babylonian mathematics -- More about Mesopotamian mathematics -- The dawn of Greek mathematics -- Pythagoras and his school -- Perfect numbers -- Regular polyhedra -- The crisis of incommensurables -- From Heraclitus to Democritus -- Mathematics in Athens -- Plato and Aristotle on mathematics -- Constructions with ruler and compass -- The impossibility of solving the classical problems -- Euclid -- Non-Euclidean geometry and Hilbert's axioms -- Alexandria from 300 BC to 200 BC -- Archimedes -- Alexandria from 200 BC to 500 AD -- Mathematics in China and India -- Mathematics in Islamic countries -- New beginnings in Europe -- Mathematics in the Renaissance -- The cubic and quartic equations -- Renaissance mathematics continued -- The seventeenth century in France -- The seventeenth century continued -- Leibniz -- The eighteenth century -- The law of quadratic reciprocity -- The number system -- Natural numbers (Peano's approach) -- The integers -- The rationals -- The real numbers -- Complex numbers -- The fundamental theorem of algebra -- Quaternions -- Quaternions applied to number theory -- Quaternions applied to physics -- Quaternions in quantum mechanics -- Cardinal numbers -- Cardinal arithmetic -- Continued fractions -- The fundamental theorem of arithmetic -- Linear diophantine equations -- Quadratic surds -- Pythagorean triangles and Fermat's last theorem -- What is a calculation? -- Recursive and recursively enumerable sets -- Hilbert's tenth problem -- Lambda calculus -- Logic from Aristotle to Russell -- Intuitionistic propositional calculus -- How to interpret intuitionistic logic -- Intuitionistic predicate calculus -- Intuitionistic type theory -- Godel's theorems -- Proof of Godel's incompleteness theorem -- More about Godel's theorems -- Concrete categories -- Graphs and categories -- Functors -- Natural transformations -- A natural transformation between vector spaces".
• catalog title "The heritage of Thales / W.S. Anglin, J. Lambek.".
• catalog type "History. fast".
• catalog type "text".