Mathematics: People, Problems, Results, Volume 2Douglas M. Campbell, John C. Higgins Based upon the principle that graph design should be a science, this book presents the principles of graph construction. The orientation of the material is toward graphs in technical writings, such as journal articles and technical reports. But much of the material is relevant for graphs shown in talks and for graphs in nontechnical publications. -- from back cover. |
Contents
part one The Nature of Mathematics 3 Mathematics and Creativity Alfred Adler | 3 |
The Meaning of Mathematics Morris Kline | 11 |
Mathematics as a Creative Art P R Halmos | 19 |
Definitions in Mathematics Émile Borel | 30 |
The Role of Intuition R L Wilder | 37 |
Mathematics Our Invisible Culture Allen L Hammond | 46 |
On the Present Incompleteness of Mathematical Ecology L B Slobodkin | 61 |
Preface to The Common Sense of the Exact Sciences Bertrand Russell | 68 |
NonEuclidean Geometry Stephen F Barker | 112 |
The Idea of Chance Jacob Bronowski | 128 |
Hilberts 10th Problem Martin Davis and Reuben Hersh | 136 |
The Riemann Hypothesis Philip J Davis and Reuben Hersh | 149 |
The FourColor Problem Kenneth Appel and Wolfgang Haken | 154 |
Group Theory and the Postulational Method Carl H Denbow and Victor Goedicke | 174 |
Logicism Intuitionism and Formalism Ernst Snapper | 183 |
Proofs and Refutations Imre Lakatos | 194 |
part two Real Mathematics 74 The Early History of Fermats Last Theorem Paulo Ribenboim | 74 |
and e E C Titchmarsh | 83 |
Geometrical Constructions The Algebra of Number Fields Richard Courant and Herbert Robbins | 89 |
Bicycle Tubes Inside Out Herbert Taylor | 101 |
The Calculus According to Newton and Leibniz C H Edwards | 104 |
Coping with Finiteness Donald E Knuth | 209 |
Are Logic and Mathematics Identical? Leon Henkin | 223 |
Proof Philip J Davis and Reuben Hersh | 248 |
Analogies and Metaphors to Explain Gödels Theorem Douglas | 262 |
Other editions - View all
Mathematics: People, Problems, Results, Volume 2 Douglas M. Campbell,John C. Higgins No preview available - 1984 |
Common terms and phrases
abstract algebraic angle arithmetic axioms bers C. S. Peirce calculus called Cantor century circle colors concept construct counterexample cube defined definition developed Diophantine equation edge ematics ence equal essay Euclid's Euclidean geometry example exist fact false Fermat's field fifth postulate Figure finite number formal Four-Color Conjecture functions Georg Cantor given Gödel green-light machine Hilbert idea impossible infinite infinitesimals integers intuition intuitionism intuitionistic language latin squares Leibniz logic mathe Mathematical Papers mathematicians maticians matics means method natural numbers Newton non-Euclidean geometry normal map Peirce's philosophy physical polygon polyhedron possible prime Principia Principia Mathematica problem proof prove question rational real numbers reason result Reuben Hersh roots Russell sense sentence set theory solution solve square statement straight line TEACHER theorem things tion triangle trisecting trisecting the angle true unavoidable set understand University