Mathematics — The Music of ReasonSpringer Science & Business Media, 11 nov. 2013 - 287 sidor This book is of interest for students of mathematics or of neighboring subjects like physics, engineering, computer science, and also for people who have at least school level mathematics and have kept some interest in it. Also good for younger readers just reaching their final school year of mathematics. |
Innehåll
| 8 | |
Masters and Schools | 14 |
The Utilitarian Attacks | 25 |
Calculation of Ratios in Euclids Book V | 64 |
Applications of Elementary Algorithms of | 72 |
Some Problems of Classical Mathematics | 77 |
Appendix | 91 |
Bernoulli Numbers and the Zeta Function | 98 |
Additional Remarks on Rings and Fields | 174 |
Examples of Distances | 184 |
Fourier Series | 192 |
Problems and PseudoProblems about Foundations | 203 |
Paradoxes and their Consequences | 222 |
The Rise of Mathematical Logic | 228 |
The Concept of Rigorous Proof | 235 |
Models of the Real Numbers | 245 |
E Displacements and Affinities | 118 |
The Language of Sets and General Structures | 133 |
Isomorphisms and Classifications | 146 |
Appendix | 167 |
Index 255 | 254 |
| 281 | |
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algebraic algebraic geometry algebraic topology analysis angles Appendix arbitrary areas of mathematics arithmetic Axiom of Choice axioms Bezout's identity bijection calculation called Cantor Cauchy Chapter circle classes classical coefficients commutative complex numbers concept congruence considered curve Dedekind defined definition denoted Diophantus divisor element equation equipotent Euclid Euclidean Euclidean geometry Euler example exists fact Fermat field Figure formula functions Galois Gauss Gaussian integers geometry greatest common divisor Greeks Hilbert idea infinite set intuition isomorphism known length mathe mathematical objects mathematicians method metric space multiplication natural numbers nested intervals nineteenth century non-Euclidean notation obtained permutations plane polynomial possible prime numbers problems proof properties proved quadratic forms rational numbers real numbers relation satisfies segment sequence solution space square structure subgroup subset theorem topology triangle variables vector