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The Four-Color Theorem: History, Topological Foundations, and Idea of Proof

cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued;

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A Course on Topological Groups

-Weyl theorem, the basic theorem in the representation theory of compact topological groups. The topological, analytical, and algebraic;

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Elementary Fixed Point Theorems

fixed theorem for a commuting family of analytic functions and Bergweiler's existence theorem on fixed points of the composition of certain;

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Topological Graph Theory

Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory;

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Foundations of Differentiable Manifolds and Lie Groups

integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic;

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The Four-Color Theorem

a computer. The book begins by discussing the history of the problem, and then goes into the mathematics, both pleasantly enough that anyone;

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Fermat's Last Theorem

achievements in the history of mathematics. Crucial arguments, including the so-called $3$-$5$ trick, $R=T$ theorem, etc., are explained in depth. The;

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Absolute Measurable Spaces

, the Oxtoby-Ulam theorem on Lebesgue-like measures on the unit cube, and the extensions of this theorem to many other topological spaces;

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Frobenius Algebras and 2-D Topological Quantum Field Theories

equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the;

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Frobenius Algebras & 2 D Topological Qua

equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the;

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Logical Foundations of Computer Science

of the Symposium is broad and includes constructive mathematics and type theory; logic, automata and automatic structures; computability and;

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Logical Foundations of Computer Science

in Deerfield Beach, FL, USA in January 2016. The 27 revised full papers were carefully reviewed and selected from 46 submissions. The scope of the;

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Theorems, Corollaries, Lemmas, And Methods Of Proof

many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems;

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Logical Foundations of Computer Science

in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the;

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Logical Foundations of Computer Science

in Deerfield Beach, FL, USA, in January 2018. The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the;

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Ramsey Theory

Covering all the major concepts, proofs, and theorems, the Second Edition of Ramsey Theory is the ultimate guide to understanding every aspect;

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The Four-Color Theorem and Basic Graph Theory

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Topological, Differential and Conformal Geometry of Surfaces

, the classification of compact connected oriented surfaces, Stokes' Theorem, fixed point theorems and rigidity theorems. There is also a novel;

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Ergodic Theory

topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the;

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Algebraic Number Theory and Fermat's Last Theorem

of algebraic numbers and explores one of the most intriguing stories in the history of mathematics-the quest for a proof of Fermat's Last Theorem. The;

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Algebraic Number Theory and Fermat's Last Theorem

of algebraic numbers and explores one of the most intriguing stories in the history of mathematics-the quest for a proof of Fermat's Last Theorem. The;

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Complex Integration and Cauchy's Theorem

Originally published in 1914 as number fifteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a;

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London Mathematical Society Lecture Note Series

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality;

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Homology Theory on Algebraic Varieties

Concise and authoritative, this monograph is geared toward advanced undergraduate and graduate students. The main theorems whose proofs are;

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Differential Manifolds

. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds;

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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition

Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics;

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Elliptic Operators, Topology, and Asymptotic Methods

Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics;

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