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Solan Eilon: Borel Games

Borel Games

Series In Algebraic And Differential Geometry

This book serves as an accessible introduction to schemes, coherent sheaves, and their cohomology, designed for readers with only a foundational knowledge of commutative algebra. Developed from years of teaching experience, the author has carefully crafted the text to be self-contained, covering all the essential concepts necessary for a solid understanding of algebraic geometry.Many readers will find it invaluable for grasping the subject, appreciating its clear explanations and lack of prerequisites. In addition to laying a strong foundation, the book provides ample background for those seeking to explore more advanced topics in the field.

Algebraic Geometry: Schemes, Coherent Sheaves And Cohomology

Series On Analysis, Applications And Computation

The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability

Many of the deepest and most important areas of mathematics have arisen from questions about extremes - shortest lines, smallest areas, densest packings, fewest colours. Mathematicians have been grappling with such issues for centuries, and some go back thousands of years. The isoperimetric problem, for example - which asks for the shortest path enclosing a given area - dates back to the mythological founding of the city of Carthage. By contrast, it was only in 2017 that the densest ways to pack identical spheres into a space of 24 dimensions was finally proved. Many of these problems are more than mere thought experiments. The origins of the Travelling Salesperson Problem - find the shortest route that visits a given set of cities - are self-explanatory. The Plateau problem, about the geometry of soap bubbles, now has applications as diverse as cosmology and biological development. Reaching for the Extreme tells the stories of these and other similar problems: their historical roots, the struggles to solve them, and the uses that can be made of the results, when such uses exist.

How the Quest for the Biggest, Fewest and Weirdest Makes Maths

Reaching for the Extreme

Hypocrisy++: On Philosophy Of Probability And Sociology Of Ideologies

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

Explore Set Theory, Abstract Algebra, and Category Theory with Functional Programming

The Book of Functions

Gewinnstrategien für die bekanntesten Karten-, Würfel-, Brett- und Gewinnspiele

Spielend gewinnen

Probability theory is a discipline that studies the quantitative regularity of random phenomena. The fact that random phenomena arise, especially in the era of big data and artificial intelligence, determines the importance of this discipline. This volume introduces various concepts that quantitatively describe random phenomena, including probability, random variables, distribution functions, density functions, mathematical expectations, variances, moments, and characteristic functions. It finishes off by presenting probability limit theory, including various convergences.Throughout the volume, great importance is attached to the elaboration of probability thoughts. For this reason, some practical examples to illustrate the introduced concept are always used. In order to meet the needs of different levels of readers, there is a section on Supplements and Notes at the end of each chapter to enhance and expand the content in the body of the textbook. This volume contains a large number of problems of varying levels for the reader with the purpose to review, consolidate, deepen and expand their knowledge.As the only branch of mathematics that studies the quantitative regularity of random phenomena, probability theory has not only theoretical significance, but it is also a main theoretical basis of mathematical statistics. Therefore, it will be of interest to scholars from other disciplines related to random phenomena.

Probability Theory: An Elementary Course

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields This book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

Calculus for the Curious

A Hybrid Texas Style Approach

An Introduction to Point-Set Topology

Science Networks. Historical Studies

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.
The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory.
This set comprises both volumes I and II, covering the letters from A through Z.

Volumes I and II

A Historical Dictionary of Mathematical Terms

Series On Multivariate Analysis

This is a thoroughly revised and updated edition of the earlier research monograph Topics in Circular Statistics by the first two authors. While maintaining the spirit as a research monograph, this book now covers the broader theme of directional statistics. Starting with an introduction to the area for those who wish to learn about this novel field, it goes on to survey the recent advances and developments in terms of theory, methodology, and applications. The book will be equally handy for the scientists in various application areas where methods based on directional data are being recognized as crucial and critical tools. As this novel area gets recognized as an important topic within statistics, this book can also serve as an essential resource for students to learn from.

Statistical Methods For Directional Data

Borel Games

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