By Kenji Ueno, Koji Shiga, Shigeyuki Morita

This e-book will deliver the sweetness and enjoyable of arithmetic to the school room. It deals severe arithmetic in a full of life, reader-friendly type. integrated are routines and lots of figures illustrating the most suggestions.
The first bankruptcy provides the geometry and topology of surfaces. between different subject matters, the authors speak about the Poincaré-Hopf theorem on serious issues of vector fields on surfaces and the Gauss-Bonnet theorem at the relation among curvature and topology (the Euler characteristic). the second one bankruptcy addresses quite a few elements of the concept that of measurement, together with the Peano curve and the Poincaré method. additionally addressed is the constitution of third-dimensional manifolds. specifically, it's proved that the three-d sphere is the union of 2 doughnuts.
This is the 1st of 3 volumes originating from a sequence of lectures given by way of the authors at Kyoto college (Japan).

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This ebook will carry the wonder and enjoyable of arithmetic to the school room. It bargains critical arithmetic in a full of life, reader-friendly variety. integrated are workouts and lots of figures illustrating the most options.
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This is the 1st of 3 volumes originating from a chain of lectures given through the authors at Kyoto college (Japan).

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Additional info for A Mathematical Gift III: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World, Volume 23)

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Of Math.

Of Math.

20201] 31 32 33 34 35 36 37 38 39 40 41 Topologische Gruppen mit genügend vielen fastperiodischen Funktionen [1936b] Ann. of Math.

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