Invitation To Nonlinear Algebra

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Invitation to Nonlinear Algebra

Author : Mateusz Michałek
Publisher : American Mathematical Society
ISBN 13 : 1470453673
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Invitation to Nonlinear Algebra by : Mateusz Michałek

Download or read book Invitation to Nonlinear Algebra written by Mateusz Michałek and published by American Mathematical Society. This book was released on 2021-03-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

Invitation to Nonlinear Algebra

Author : Mateusz Michałek
Publisher : American Mathematical Soc.
ISBN 13 : 1470465515
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Invitation to Nonlinear Algebra by : Mateusz Michałek

Download or read book Invitation to Nonlinear Algebra written by Mateusz Michałek and published by American Mathematical Soc.. This book was released on 2021-03-22 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

Invitation to Dynamical Systems

Author : Edward R. Scheinerman
Publisher : Courier Corporation
ISBN 13 : 0486485943
Total Pages : 402 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Invitation to Dynamical Systems by : Edward R. Scheinerman

Download or read book Invitation to Dynamical Systems written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2012-01-01 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for those who wish to study mathematics beyond linear algebra but are not ready for abstract material. Rather than a theorem-proof-corollary-remark style of exposition, it stresses geometry, intuition, and dynamical systems. An appendix explains how to write MATLAB, Mathematica, and C programs to compute dynamical systems. 1996 edition.

An Invitation to Mathematical Physics and Its History

Author : Jont Allen
Publisher : Springer Nature
ISBN 13 : 3030537595
Total Pages : 394 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis An Invitation to Mathematical Physics and Its History by : Jont Allen

Download or read book An Invitation to Mathematical Physics and Its History written by Jont Allen and published by Springer Nature. This book was released on 2020-09-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

Numerical Polynomial Algebra

Author : Hans J. Stetter
Publisher : SIAM
ISBN 13 : 0898715571
Total Pages : 475 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Numerical Polynomial Algebra by : Hans J. Stetter

Download or read book Numerical Polynomial Algebra written by Hans J. Stetter and published by SIAM. This book was released on 2004-05-01 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.

An Invitation to Applied Category Theory

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis An Invitation to Applied Category Theory by : Brendan Fong

Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

An Invitation To Noncommutative Geometry

Author : Matilde Marcolli
Publisher : World Scientific
ISBN 13 : 9814475629
Total Pages : 515 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis An Invitation To Noncommutative Geometry by : Matilde Marcolli

Download or read book An Invitation To Noncommutative Geometry written by Matilde Marcolli and published by World Scientific. This book was released on 2008-02-11 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

Author :
Publisher : American Mathematical Soc.
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4./5 ( download)

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Book Synopsis by :

Download or read book written by and published by American Mathematical Soc.. This book was released on with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solving Systems of Polynomial Equations

Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
ISBN 13 : 0821832514
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Solving Systems of Polynomial Equations by : Bernd Sturmfels

Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.

An Invitation to Modern Number Theory

Author : Steven J. Miller
Publisher : Princeton University Press
ISBN 13 : 0691215979
Total Pages : 526 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis An Invitation to Modern Number Theory by : Steven J. Miller

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2020-07-21 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

An Introductory Course on Mathematical Game Theory and Applications

Author : Julio González-Díaz
Publisher : American Mathematical Society
ISBN 13 : 1470475634
Total Pages : 432 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introductory Course on Mathematical Game Theory and Applications by : Julio González-Díaz

Download or read book An Introductory Course on Mathematical Game Theory and Applications written by Julio González-Díaz and published by American Mathematical Society. This book was released on 2023-12-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia.

Topological and Ergodic Theory of Symbolic Dynamics

Author : Henk Bruin
Publisher : American Mathematical Society
ISBN 13 : 1470469847
Total Pages : 481 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topological and Ergodic Theory of Symbolic Dynamics by : Henk Bruin

Download or read book Topological and Ergodic Theory of Symbolic Dynamics written by Henk Bruin and published by American Mathematical Society. This book was released on 2023-01-20 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.

A First Course in Spectral Theory

Author : Milivoje Lukić
Publisher : American Mathematical Society
ISBN 13 : 1470466562
Total Pages : 494 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A First Course in Spectral Theory by : Milivoje Lukić

Download or read book A First Course in Spectral Theory written by Milivoje Lukić and published by American Mathematical Society. This book was released on 2023-01-04 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central topic of this book is the spectral theory of bounded and unbounded self-adjoint operators on Hilbert spaces. After introducing the necessary prerequisites in measure theory and functional analysis, the exposition focuses on operator theory and especially the structure of self-adjoint operators. These can be viewed as infinite-dimensional analogues of Hermitian matrices; the infinite-dimensional setting leads to a richer theory which goes beyond eigenvalues and eigenvectors and studies self-adjoint operators in the language of spectral measures and the Borel functional calculus. The main approach to spectral theory adopted in the book is to present it as the interplay between three main classes of objects: self-adjoint operators, their spectral measures, and Herglotz functions, which are complex analytic functions mapping the upper half-plane to itself. Self-adjoint operators include many important classes of recurrence and differential operators; the later part of this book is dedicated to two of the most studied classes, Jacobi operators and one-dimensional Schrödinger operators. This text is intended as a course textbook or for independent reading for graduate students and advanced undergraduates. Prerequisites are linear algebra, a first course in analysis including metric spaces, and for parts of the book, basic complex analysis. Necessary results from measure theory and from the theory of Banach and Hilbert spaces are presented in the first three chapters of the book. Each chapter concludes with a number of helpful exercises.

Geometric Structures on Manifolds

Author : William M. Goldman
Publisher : American Mathematical Society
ISBN 13 : 1470471035
Total Pages : 494 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric Structures on Manifolds by : William M. Goldman

Download or read book Geometric Structures on Manifolds written by William M. Goldman and published by American Mathematical Society. This book was released on 2022-12-29 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric structures are special cases of Cartan connections where the associated curvature vanishes. This theory received a big boost in the 1970s when W. Thurston put his geometrization program for 3-manifolds in this context. The subject of this book is more ambitious in scope. Unlike Thurston's eight 3-dimensional geometries, it covers structures which are not metric structures, such as affine and projective structures. This book describes the known examples in dimensions one, two and three. Each geometry has its own special features, which provide special tools in its study. Emphasis is given to the interrelationships between different geometries and how one kind of geometric structure induces structures modeled on a different geometry. Up to now, much of the literature has been somewhat inaccessible and the book collects many of the pieces into one unified work. This book focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a “moduli space”. Often the moduli space carries a rich geometry of its own reflecting the model geometry. The book is self-contained and accessible to students who have taken first-year graduate courses in topology, smooth manifolds, differential geometry and Lie groups.

Topics in Spectral Geometry

Author : Michael Levitin
Publisher : American Mathematical Society
ISBN 13 : 1470475251
Total Pages : 346 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topics in Spectral Geometry by : Michael Levitin

Download or read book Topics in Spectral Geometry written by Michael Levitin and published by American Mathematical Society. This book was released on 2023-11-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

Polynomial Optimization, Moments, and Applications

Author : Michal Kočvara
Publisher : Springer Nature
ISBN 13 : 3031386590
Total Pages : 274 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Polynomial Optimization, Moments, and Applications by : Michal Kočvara

Download or read book Polynomial Optimization, Moments, and Applications written by Michal Kočvara and published by Springer Nature. This book was released on 2024-01-28 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control. This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audience by gathering high-quality chapters on these hot topics. Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.

One-Dimensional Ergodic Schrödinger Operators

Author : David Damanik
Publisher : American Mathematical Society
ISBN 13 : 1470456060
Total Pages : 464 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis One-Dimensional Ergodic Schrödinger Operators by : David Damanik

Download or read book One-Dimensional Ergodic Schrödinger Operators written by David Damanik and published by American Mathematical Society. This book was released on 2022-08-18 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).