Author | Bell, John L. author |
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Title | The Art of the Intelligible [electronic resource] : An Elementary Survey of Mathematics in its Conceptual Development / by John L. Bell |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-94-011-4209-0 |
Descript | XI, 250 p. online resource |
1 Numerals and Notation -- 2 The Mathematics of Ancient Greece -- 3 The Development of The Number Concept -- The Theory of Numbers -- Perfect Numbers -- Prime Numbers -- Sums of Powers -- Fermat?s Last Theorem -- The Number ? -- What are Numbers? -- 4 The Evolution of Algebra, I -- Greek Algebra -- Chinese Algebra -- Hindu Algebra -- Arabic Algebra -- Algebra in Europe -- The Solution of the General Equation of Degrees 3 and 4 -- The Algebraic Insolubility of the General Equation of Degree Greater than 4 -- Early Abstract Algebra -- 5 The Evolution of Algebra, II -- Hamilton and Quaternions -- Grassmann?s โCalculus of Extensionโ -- Finite Dimensional Linear Algebras -- Matrices -- Lie Algebras -- 6 The Evolution of Algebra, III -- Algebraic Numbers and Ideals -- Abstract Algebra -- Groups -- Rings and Fields -- Ordered Sets -- Lattices and Boolean Algebras -- Category Theory -- 7 The Development of Geometry, I -- Coordinate/Algebraic/Analytic Geometry -- Algebraic Curves -- Cubic Curves -- Geometric Construction Problems -- Higher Dimensional Spaces -- Noneuclidean Geometry -- 8 The Development of Geometry, II -- Projective Geometry -- Differential Geometry -- The Theory of Surfaces -- Riemann?s Conception of Geometry -- Topology -- Combinatorial Topology -- Point-set topology -- 9 The Calculus and Mathematical Analysis -- The Origins and Basic Notions of The Calculus -- Mathematical Analysis -- Infinite Series -- Differential Equations -- Complex Analysis -- 10 The Continuous and The Discrete -- 11 The Mathematics of The Infinite -- 12 The Philosophy of Mathematics -- Classical Views on the Nature of Mathematics -- Logicism -- Formalism -- Intuitionism -- Appendix 1 The Insolubility of Some Geometric Construction Problems -- Appendix 2 The Gรdel Incompleteness Theorems -- Appendix 3 The Calculus in Smooth Infinitesimal Analysis -- Appendix 4 The Philosophical Thought of A Great Mathematician: Hermann Weyl -- Index of Names -- Index of Terms