The Master Theorem
Author:
Publisher:
Published: 2019-06
Total Pages:
ISBN-13: 9780692189825
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Theorems of the 21st Century
Author: Bogdan Grechuk
Publisher: Springer
Published: 2019-06-15
Total Pages: 455
ISBN-13: 303019096X
DOWNLOAD EBOOKThis book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.
Existence Theorems for Ordinary Differential Equations
Author: Francis J. Murray
Publisher: Courier Corporation
Published: 2013-11-07
Total Pages: 178
ISBN-13: 0486154955
DOWNLOAD EBOOKThis text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.
Theorems and Problems in Functional Analysis
Author: A. A. Kirillov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 351
ISBN-13: 1461381533
DOWNLOAD EBOOKEven the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Theorems and Counterexamples in Mathematics
Author: Bernard R. Gelbaum
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 339
ISBN-13: 1461209935
DOWNLOAD EBOOKThe gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.
The Little Book of Maths Theorems, Theories and Things
Author: Surendra Verma
Publisher: New Holland Publishers (AU)
Published: 2008
Total Pages: 169
ISBN-13: 1921655321
DOWNLOAD EBOOKMathematics is indeed fun as this little book testifies. This book presents a unique collection of mathematical ideas, theories, theorems, conjectures, rules, facts, equations, formulas, paradoxes, fallacies and puzzles with short, simple and witty explanations that require no background in mathematics.
Problems and Theorems in Classical Set Theory
Author: Peter Komjath
Publisher: Springer Science & Business Media
Published: 2006-11-22
Total Pages: 492
ISBN-13: 0387362193
DOWNLOAD EBOOKThis volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
The Art and Craft of Problem Solving
Author: Paul Zeitz
Publisher: John Wiley & Sons
Published: 2017
Total Pages: 389
ISBN-13: 1119239907
DOWNLOAD EBOOKThis text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.
Minimax Theorems
Author: Michel Willem
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 168
ISBN-13: 1461241464
DOWNLOAD EBOOKMany boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
An Introduction to Gödel's Theorems
Author: Peter Smith
Publisher: Cambridge University Press
Published: 2007-07-26
Total Pages: 376
ISBN-13: 1139465937
DOWNLOAD EBOOKIn 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
