The Mathematical Experience |
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Page 181
... solution is now complete . The details of the argument are supplied by the properties of the real number system and of continuous functions defined on that system . Solution I is algorithmic mathematics . Solution II is the dialectic ...
... solution is now complete . The details of the argument are supplied by the properties of the real number system and of continuous functions defined on that system . Solution I is algorithmic mathematics . Solution II is the dialectic ...
Page 258
... solution could be extended to this situation . If the shape of the traveling waves matched the shape of the initial displacement , then Euler claimed the solution was still valid , even though it was not given by a single function but ...
... solution could be extended to this situation . If the shape of the traveling waves matched the shape of the initial displacement , then Euler claimed the solution was still valid , even though it was not given by a single function but ...
Page 304
... solution : Lay out a half dozen plausible routes . Collect time - cost - patronage data from the bus runs and adopt the maximizing solution . Analytical solution : Make a model of the mileage , toll , and traffic conditions . Solve the ...
... solution : Lay out a half dozen plausible routes . Collect time - cost - patronage data from the bus runs and adopt the maximizing solution . Analytical solution : Make a model of the mileage , toll , and traffic conditions . Solve the ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
Common terms and phrases
abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero