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The 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 Continuum collection brings the classic sisal look to outdoor spaces and high-traffic indoor areas. The soft Theorem design features a linear pattern with cream and taupe, high-low pile for added dimension. The polypropylene fibers are stain and water resistant for an easy-care accent piece that suits any area of the home. Color: Taupe/Cream. Pattern: Striped.

The Continuum collection brings the classic sisal look to outdoor spaces and high-traffic indoor areas. The soft Theorem design features a linear pattern with cream and taupe, high-low pile for added dimension. The polypropylene fibers are stain and water resistant for an easy-care accent piece that suits any area of the home. Color: Taupe/Cream. Pattern: Striped.

The Continuum collection brings the classic sisal look to outdoor spaces and high-traffic indoor areas. The soft Quantum design features a linear pattern with cream and beige, high-low pile for added dimension. The polypropylene fibers are stain and water resistant for an easy-care accent piece that suits any area of the home. Color: Cream/Beige. Pattern: Striped.

The Continuum collection brings the classic sisal look to outdoor spaces and high-traffic indoor areas. The soft Theorem design features a linear pattern with cream and taupe, high-low pile for added dimension. The polypropylene fibers are stain and water resistant for an easy-care accent piece that suits any area of the home. Color: Taupe/Cream. Pattern: Striped.

This oversized linear geometric grid of 10.5 in. squares is reminiscent of tracery. Used in the creation of stained glass, these lines provide depth and additional dimension, much like this large trellis effect, but without an overwhelming commitment to pattern. Theorem comes in three neutral colors and gold metallic. Color: Blue and White. Material: Paper.

This oversized linear geometric grid of 10.5 in. squares is reminiscent of tracery. Used in the creation of stained glass, these lines provide depth and additional dimension, much like this large trellis effect, but without an overwhelming commitment to pattern. Theorem comes in three neutral colors and gold metallic. Color: Black and White. Material: Paper.

This 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.

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.

Text: English (translation) Original Language: Italian

Traditional theorem painting involves making multiple-overlay stencils and using them to paint primitive, three-dimensional pictures on velvet. In this book, acclaimed painter Linda E. Brubaker offers expert advice on selecting tools and materials, making stencils, mounting velvet, and mixing colors, along with painting exercises and tips for removing mistakes. Step-by-step instructions and patterns are provided for 9 complete projects, including designs for fruits, flowers, a butterfly, a mallard duck, and a bucolic memorial scene. Techniques for attractive and safe framing are also discussed.

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.

The 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.

This 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.

As we enter our 40s and beyond, our skin craves more than just surface-level what is an all in one "anti-aging" skincare. This revolutionary serum is your answer to age-defying pro-aging skincare, specially formulated for grown-up skin. Imagine waking up to a reflection that looks 5 years younger. Our groundbreaking formula helps to stimulate your skin's natural Hyaluronic Acid production - the key molecule in maintaining that youthful glow we all miss - by infusing a tiniest to larger molecular weight of Hyaluronic Acid. Coupled with our biofermented Growth Factor Peptide skin becomes visibly firmer & smoother. This isn't just another serum; it's a fountain of youth in a bottle; an all-in-one face and eye serum, targeting fine lines, sagging skin, eye bags, dark circles, and eye droop. SERUM DIRECTIONS Simply Apply & Dry Apply one to two dropperfuls morning and night after cleansing. We are serious when we say to apply the skin firming serum twice a day; otherwise, those unique regenerative skin-building hyaluronic acid benefits may never happen. More Information Apply before other serums, retinols or a moisturizer, or facial oil. After using Caire's serum for smooth skin you may elect not to use a moisturizer depending on your skin type. Use the multi-molecular hyaluronic serum s on the face, neck, chest, and/or back of hands and wherever else you feel the need. Eye-vantage: Pat gently around eyes but don’t miss the undereye, eyelid, and all around. Feeding this ocular area is a win. Because with consistent use, you can help lift up sags and bags around the eye area - one of the top skin concerns from hormone-caused aging. FULL INGREDIENT LIST Water, Glycerin, Propanediol, Sodium Hyaluronate, Betaine, Disodium Edetate, Hydrolyzed Sodium Hyaluronate, Jasminum Sambac (Jasmine) Flower Extract, Crataegus Monogyna Flower Extract, Yeast Extract, Tetradecyl Aminobutyroylvalyaminobutyric Urea Trifluoroacetate, Caprylhydroxamic Acid, Sodium Benzoate, Soy Amino Acids, Melia Azadirachta Leaf Extract, Melia Azadirachta Flower Extract, Amino-Esters-1, Coccinia Indica Fruit Extract, Corallina Officinalis Extract

Witness a vision of the techno-philosophical future from Terry Gilliam, the visionary director of BRAZIL, 12 MONKEYS, and FEAR AND LOATHING IN LAS VEGAS. Qohen Leth (2-time Academy Award winner Christoph Waltz) is a computer genius plagued with existential angst. Eccentric and reclusive, he lives in a burnt-out church, toiling on a top-secret project personally assigned by Management (Matt Damon) - to discover the meaning of life. If there is one. His supervisor (David Thewlis) is unstable. He d

Interactive theorem proving is the modern way of formalizing mathematics using a computer as a proof assistant, helping solve simple tasks andkeeping an order on the proofs.Still, it is a tedious task, as such mechanical proofs contain detail that humans do not want to see.When it comes to the verification of real world applications in software engineering, as required for the assurance of safety and security properties of embedded systems, the level of detail becomes even more annoying. In fact, it is a gargantuan task to prove a program correct or prove that an implementation conforms to its UML-specification.The sheer mass of proof obligations alone - apart from the hidden subtlety of such challenges - obstructs quality assurance of software artifacts with interactive theorem provers. This book draws a line to show up how far current cutting edge research has succeeded in tackling this long standing quest.Using examples from algorithm development, Java bytecode verification and UML state machine analysis the author introduces current trends in interactive theorem proving technology using Coq, Isabelle, andmodel checking.

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures

This book contains classic material dating back to the 1900s and before. The content has been carefully selected for its interest and relevance to a modern audience. Carefully selecting the best articles from our collection we have compiled a series of historical and informative publications on the subject of mathematics. The titles in this range include "Ratio and Proportion" "Simple Equations" "Simultaneous Equations" and many more. Each publication has been professionally curated and includes all details on the original source material. This particular instalment, "The Binomial Theorem" contains a selection of classic educational articles containing examples and exercises on the subject of algebra. It is intended to illustrate aspects of the Binomial Theorem and serves as a guide for anyone wishing to obtain a general knowledge of the subject. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.