Mostly Surfaces

· Student Mathematical Library Книга 60 · American Mathematical Soc.
Π•Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
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Π‘Ρ‚Ρ€Π°Π½ΠΈΡ†ΠΈ
ΠžΡ†Π΅Π½ΠΊΠΈΡ‚Π΅ ΠΈ ΠΎΡ‚Π·ΠΈΠ²ΠΈΡ‚Π΅ Π½Π΅ са ΠΏΠΎΡ‚Π²ΡŠΡ€Π΄Π΅Π½ΠΈ  НаучСтС ΠΏΠΎΠ²Π΅Ρ‡Π΅

Всичко Π·Π° Ρ‚Π°Π·ΠΈ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°

This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem.

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigourous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.

Π—Π° Π°Π²Ρ‚ΠΎΡ€Π°

Richard Evan Schwartz is at Brown University, Providence, RI, USA.

ΠžΡ†Π΅Π½Π΅Ρ‚Π΅ Ρ‚Π°Π·ΠΈ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°

ΠšΠ°ΠΆΠ΅Ρ‚Π΅ Π½ΠΈ ΠΊΠ°ΠΊΠ²ΠΎ мислитС.

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Π—Π° Π΄Π° Ρ‡Π΅Ρ‚Π΅Ρ‚Π΅ Π½Π° устройства с Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΎ мастило, ΠΊΠ°Ρ‚ΠΎ Π½Π°ΠΏΡ€ΠΈΠΌΠ΅Ρ€ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈΡ‚Π΅ Ρ‡Π΅Ρ‚Ρ†ΠΈ ΠΎΡ‚ Kobo, трябва Π΄Π° ΠΈΠ·Ρ‚Π΅Π³Π»ΠΈΡ‚Π΅ Ρ„Π°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡ€Π΅Ρ…Π²ΡŠΡ€Π»ΠΈΡ‚Π΅ Π½Π° устройството си. Π˜Π·ΠΏΡŠΠ»Π½Π΅Ρ‚Π΅ ΠΏΠΎΠ΄Ρ€ΠΎΠ±Π½ΠΈΡ‚Π΅ инструкции Π² ΠŸΠΎΠΌΠΎΡ‰Π½ΠΈΡ Ρ†Π΅Π½Ρ‚ΡŠΡ€, Π·Π° Π΄Π° ΠΏΡ€Π΅Ρ…Π²ΡŠΡ€Π»ΠΈΡ‚Π΅ Ρ„Π°ΠΉΠ»ΠΎΠ²Π΅Ρ‚Π΅ Π² ΠΏΠΎΠ΄Π΄ΡŠΡ€ΠΆΠ°Π½ΠΈΡ‚Π΅ Π΅Π»Π΅ΠΊΡ‚Ρ€ΠΎΠ½Π½ΠΈ Ρ‡Π΅Ρ‚Ρ†ΠΈ.