Invitation To Nonlinear Algebra

Author : Mateusz Michałek,Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 41,5 Mb
Release : 2021-03-22
Category : Education
ISBN : 9781470465513

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Invitation to Nonlinear Algebra by Mateusz Michałek,Bernd Sturmfels Pdf

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.

Author : Mateusz Michałek,Bernd Sturmfels
Publisher : American Mathematical Society
Page : 226 pages
File Size : 52,6 Mb
Release : 2021-03-05
Category : Mathematics
ISBN : 9781470453671

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Invitation to Nonlinear Algebra by Mateusz Michałek,Bernd Sturmfels Pdf

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.

Author : David C. Mello
Publisher : CRC Press
Page : 409 pages
File Size : 46,8 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781498779579

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Invitation to Linear Algebra by David C. Mello Pdf

Invitation to Linear Algebra is an informative, clearly written, flexible textbook for instructors and students. Based on over 30 years of experience as a mathematics professor, the author invites students to develop a more informed understanding of complex algebraic concepts using innovative, easy-to-follow methods. The book is organized into lessons rather than chapters. This limits the size of the mathematical morsels that students must digest, making it easier for instructors to budget class time. Each definition is carefully explained with detailed proofs of key theorems, including motivation for each step. This makes the book more flexible, allowing instructors to choose material that reflects their and their students’ interests. A larger than normal amount of exercises illustrate how linear and nonlinear algebra apply in the students’ areas of study. Features The book’s unique lesson format enables students to better understand algebraic concepts Students will learn key elements of linear algebra in an enjoyable fashion Large number of exercises illustrate the applications of the course material Allows instructors to create a course around individual lessons Detailed solutions and hints are provided to selected exercises

Author : Masoud Khalkhali,Matilde Marcolli
Publisher : World Scientific
Page : 515 pages
File Size : 44,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812814333

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An Invitation to Noncommutative Geometry by Masoud Khalkhali,Matilde Marcolli Pdf

A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.

Author : Morozov Alexei,Dolotin Valery
Publisher : World Scientific Publishing Company
Page : 288 pages
File Size : 53,9 Mb
Release : 2007-10-02
Category : Mathematics
ISBN : 9789813107007

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Introduction To Non-linear Algebra by Morozov Alexei,Dolotin Valery Pdf

This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.

Author : Edward R. Scheinerman
Publisher : Courier Corporation
Page : 408 pages
File Size : 51,8 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486275321

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Invitation to Dynamical Systems by Edward R. Scheinerman Pdf

This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Author : Morozov
Publisher : Unknown
Page : 128 pages
File Size : 54,9 Mb
Release : 2007-10
Category : Electronic
ISBN : 9812770062

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Introduction to Non-Linear Algebra by Morozov Pdf

Author : Brian Osserman
Publisher : American Mathematical Society
Page : 259 pages
File Size : 46,9 Mb
Release : 2021-12-06
Category : Mathematics
ISBN : 9781470466657

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A Concise Introduction to Algebraic Varieties by Brian Osserman Pdf

Author : Michael Artin
Publisher : American Mathematical Society
Page : 104 pages
File Size : 42,8 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470471118

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Algebraic Geometry by Michael Artin Pdf

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.

Author : Andrea Ferretti
Publisher : American Mathematical Society
Page : 394 pages
File Size : 51,9 Mb
Release : 2023-09-26
Category : Mathematics
ISBN : 9781470471279

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Commutative Algebra by Andrea Ferretti Pdf

This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra. Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.

Author : Andrea Ferretti
Publisher : American Mathematical Society
Page : 432 pages
File Size : 42,6 Mb
Release : 2023-11-30
Category : Mathematics
ISBN : 9781470471286

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Homological Methods in Commutative Algebra by Andrea Ferretti Pdf

This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra. The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.

Author : Harry Dym
Publisher : American Mathematical Society
Page : 512 pages
File Size : 42,9 Mb
Release : 2023-07-18
Category : Mathematics
ISBN : 9781470472061

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Linear Algebra in Action by Harry Dym Pdf

This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.

Author : Thorsten Theobald
Publisher : American Mathematical Society
Page : 312 pages
File Size : 47,9 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470474317

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Real Algebraic Geometry and Optimization by Thorsten Theobald Pdf

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.

Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 45,7 Mb
Release : 2002
Category : Equations
ISBN : 9780821832516

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Solving Systems of Polynomial Equations by Bernd Sturmfels Pdf

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.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 54,7 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf