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The (Mis)Behaviour of Markets

A Fractal View of Risk, Ruin and Reward

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This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they ... Read more

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This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they
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" With poignancy and audacity, Frame builds an unexpected bridge between mathematical beauty and human sorrow, illuminating both." —Francis Su, author of Mathematics for Human FlourishingWe all know the euphoria of intellectual epiphany—the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief *,
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Series series Sacred
Sacred Geometry exists all around us in the natural world, from the unfurling of a rose bud to the pattern of a tortoise shell, the sub-atomic to the galactic. A pure expression of number and form, it is the language of creation and navigates the unseen dimensions beyond our three-dimensional reality.Since its discovery, humans have found many ways - stone circles, mandalas, labyrinths, temples- ... Read more

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All the Math You Missed

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Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate ... Read more

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Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate
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A Tale of Two Fractals

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Series series Mathematics and Statistics (R0)
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. ... Read more

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Shape

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Exact Trigonometric Table for all Angles

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The Golden Geometry of the Interior Design of the Great Pyramid

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A golden-ratio-based geometric model unveils the Great Pyramid’s sophisticated design and accounts with astonishing accuracy for all details of its internal and external architecture. The model values match the measurements of W.F. Petrie or G. Dormion within 1 cm or 5', respectively for the lengths and angles, and in multiple cases exactly (within 1 mm or 1'). The model yields mathematical ... Read more

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A golden-ratio-based geometric model unveils the Great Pyramid’s sophisticated design and accounts with astonishing accuracy for all details of its internal and external architecture. The model values match the measurements of W.F. Petrie or G. Dormion within 1 cm or 5', respectively for the lengths and angles, and in multiple cases exactly (within 1 mm or 1'). The model yields mathematical
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The Maths Book

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Learn about the most important mathematical ideas, theorems, and movements in The Maths Book.Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Maths in this overview guide to the subject, great for novices looking to find out more and experts wishing to refresh their knowledge alike! The Maths Book brings a fresh ... Read more

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Geometry Of The Octonions, The

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There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric ... Read more

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There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric
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A First Course in Computational Algebraic Geometry

by Wolfram Decker, Gerhard Pfister ...

Series series AIMS Library of Mathematical Sciences
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Measurement

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Edited by Gebhard Böckle, Gabor Wiese ...

Series series Springer Nature Proceedings excluding Computer Science
This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment.The 14 papers offer readers both, instructional courses on the latest algorithms for ... Read more

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This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic ... Read more

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Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas
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Algebra Lineare e Geometria. Esercizi e temi d'esame con svolgimento

by Paolo Dulio, Walter Pacco ...

Il testo ha il duplice obiettivo di fornire allo studente nozioni di principi fondamentali dell’algebra lineare e di applicazioni del metodo delle coordinate della geometria analitica.Viene trattato lo studio dei vettori geometrici, delle matrici, delle operazioni relative e viene sviluppata la teoria dei sistemi lineari.Si considerano la costruzione e lo studio degli spazi vettoriali e delle ... Read more

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Il testo ha il duplice obiettivo di fornire allo studente nozioni di principi fondamentali dell’algebra lineare e di applicazioni del metodo delle coordinate della geometria analitica.Viene trattato lo studio dei vettori geometrici, delle matrici, delle operazioni relative e viene sviluppata la teoria dei sistemi lineari.Si considerano la costruzione e lo studio degli spazi vettoriali e delle
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Recent Progress on the Donaldson–Thomas Theory

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by Yukinobu Toda ...

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This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, ... Read more

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This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories,
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Lectures on Matrix Field Theory

by Badis Ydri ...

Series series Physics and Astronomy (R0)
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is ... Read more

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These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is
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Current Developments in Hodge Theory

Proceedings of Hodge Theory at IMSA

Edited by Phillip Griffiths, Ludmil Katzarkov, Carlos Simpson ...

Series series Springer Nature Proceedings excluding Computer Science
This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors’ participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.One of the main themes is the study of moduli spaces and their compactifications. Several articles speak of the singularities occuring ... Read more

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This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors’ participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.One of the main themes is the study of moduli spaces and their compactifications. Several articles speak of the singularities occuring
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Una rappresentazione geometrico-matematica del passato, del presente e del futuro escatologico della storia mondiale

by Federico Tambara ...

Un fascino non soltanto di carattere scientifico ma anche "esoterico" permea questo libro che investiga in vari campi della conoscenza raggiunta fino ad oggi. I lettori sufficientemente seri e motivati potranno fare scoperte interessanti e spesso sorprendenti quasi ad ogni pagina del presente Studio di Ricerca. In ultimo, nella CONCLUSIONE dell'opera, un ipotetico intervistatore (ben preparato ... Read more

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Un fascino non soltanto di carattere scientifico ma anche "esoterico" permea questo libro che investiga in vari campi della conoscenza raggiunta fino ad oggi. I lettori sufficientemente seri e motivati potranno fare scoperte interessanti e spesso sorprendenti quasi ad ogni pagina del presente Studio di Ricerca. In ultimo, nella CONCLUSIONE dell'opera, un ipotetico intervistatore (ben preparato
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Differential Geometry Of Curves And Surfaces

by Masaaki Umehara, Kotaro Yamada, Wayne Rossman ...

'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many ... Read more

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'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many
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Minimal Free Resolutions over Complete Intersections

by David Eisenbud, Irena Peeva ...

Series series Mathematics and Statistics (R0)
This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957.The theory extends the theory of matrix factorizations of a non ... Read more

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This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957.The theory extends the theory of matrix factorizations of a non
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Recent Trends in Combinatorics

Edited by Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali ...

Series series Mathematics and Statistics (R0)
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part ... Read more

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This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part
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Projective Geometry

Solved Problems and Theory Review

by Elisabetta Fortuna, Roberto Frigerio, Rita Pardini ...

Series series Mathematics and Statistics (R0)
This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are ... Read more

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This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are
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