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Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum)

Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum) Lowest new price: $38.36
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Author: David M. Bressoud
Brand: Brand: The Mathematical Association of America

This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses. The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While it was apparent that the conjecture must be true, the proof was elusive. As a result, researchers became drawn to this problem and made connections to aspects of the invariant theory of Jacobi, Sylvester, Cayley, MacMahon, Schur, and Young; to partitions and plane partitions; to symmetric functions; to hypergeometric and basic hypergeometric series; and, finally, to the six-vertex model of statistical mechanics. This volume is accessible to anyone with a knowledge of linear algebra, and it includes extensive exercises and Mathematica programs to help facilitate personal exploration. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something unique within Proofs and Confirmations.

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Graph Paper Notebook 1 inch Squares: Blank Quad Ruled 110 Square Grid Pages Large (8.5” x 11”) (Comosition Books)

Graph Paper Notebook 1 inch Squares: Blank Quad Ruled 110 Square Grid Pages Large (8.5” x 11”) (Comosition Books) Lowest new price: $5.99
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Author: Studio Kids JK

Graph Paper Notebook 1 inch Squares features pages covered with a continuous square grid. The squares have different sizes according to your preference. Perfect Graph Paper Notebook, Graph Paper Journal / Graph Paper, size with its 8.5" x 11" dimensions and has a high quality soft cover. Perfect for Kids and Teens.


Methods of Applied Mathematics for Engineers and Scientists

Methods of Applied Mathematics for Engineers and Scientists Lowest new price: $117.75
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Author: Tomas B. Co
Brand: Brand: Cambridge University Press

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications, and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasizes applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal coordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange-Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis, DAEs, high-order finite-difference formulas, Delaunay meshes, and others. MATLAB® implementations of the methods and concepts are fully integrated.

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Linear Models and the Relevant Distributions and Matrix Algebra (Chapman & Hall/CRC Texts in Statistical Science)

Linear Models and the Relevant Distributions and Matrix Algebra (Chapman & Hall/CRC Texts in Statistical Science) Lowest new price: $105.59
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Author: David A. Harville

Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance.

Features:

  • Provides coverage of matrix algebra that is extensive and relatively self-contained and does so in a meaningful context
  • Provides thorough coverage of the relevant statistical distributions, including spherically and elliptically symmetric distributions
  • Includes extensive coverage of multiple-comparison procedures (and of simultaneous confidence intervals), including procedures for controlling the k-FWER and the FDR
  • Provides thorough coverage (complete with detailed and highly accessible proofs) of results on the properties of various linear-model procedures, including those of least squares estimators and those of the F test.
  • Features the use of real data sets for illustrative purposes
  • Includes many exercises

David Harville served for 10 years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson AFB, Ohio, 20 years as a full professor in Iowa State University’s Department of Statistics where he now has emeritus status, and seven years as a research staff member of the Mathematical Sciences Department of IBM’s T.J. Watson Research Center. He has considerable relevant experience, having taught M.S. and Ph.D. level courses in linear models, been the thesis advisor of 10 Ph.D. graduates, and authored or co-authored two books and more than 80 research articles. His work has been recognized through his election as a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and as a member of the International Statistical Institute.

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Topics in Matrix Analysis

Topics in Matrix Analysis Lowest new price: $80.96
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Author: Roger A. Horn
Brand: Brand: Cambridge University Press

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work.

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Matrix Theory (Dover Books on Mathematics)

Matrix Theory (Dover Books on Mathematics) Lowest new price: $10.36
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Author: Joel N. Franklin

Not only is matrix theory significant in a wide range of fields mathematical economics, quantum physics, geophysics, electrical network synthesis, crystallography, and structural engineering, among others-but with the vast proliferation of digital computers, knowledge of matrix theory is a must for every modern engineer, mathematician, and scientist. Matrices represent linear transformations from a finiteset of numbers to another finite set of numbers.
Since many important problems are linear, and since digital computers with finite memory manipulate only finite sets of numbers, the solution of linear problems by digital computers usually involves matrices. Developed from the author's course on matrix theory at the California
Institute of Technology, the book begins with a concise presentation of the theory of determinants, continues with a discussion of classical linear algebra, and an optional chapter on the use of matrices to solve systems of linear triangularizations of Hermitian and nonHermitian matrices, as well as a chapter presenting a proof of the difficult and important matrix theory of Jordan. The book concludes with discussions of variational principles and perturbation theory of matrices, matrix numerical analysis, and an introduction to the subject of linear computations.
The book is designed to meet many different needs, and because it is mathematically rigorous, it may be used by students of pure and applied mathematics. Since it is oriented towards applications, it is valuable to students of engineering, science, and the social sciences. And because it contains the basic preparation in matrix theory required for numerical analysis, it can be used by students whose main interest is computers. The book assumes very little mathematical preparation, and except for the single section on the continuous dependence of eigenvalues on matrices, a knowledge of elementary algebra and calculus is sufficient.

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An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics) Lowest new price: $71.71
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Author: Greg W. Anderson

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

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A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics)

A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics) Lowest new price: $5.78
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Author: Marvin Marcus

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.
Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence matrices and generalizations of commutativity.
Part Two begins with a survey of elementary properties of convex sets and polyhedra and presents a proof of the Birkhoff theorem on doubly stochastic matrices. This is followed by a discussion of the properties of convex functions and a list of classical inequalities. This material is then combined to yield many of the interesting matrix inequalities of Weyl, Fan, Kantorovich and others. The treatment is along the lines developed by these authors and their successors and many of their proofs are included. This chapter contains an account of the classical Perron Frobenius-Wielandt theory of indecomposable nonnegative matrices and ends with some important results on stochastic matrices.
Part Three is concerned with a variety of results on the localization of the characteristic roots of a matrix in terms of simple functions of its entries or of entries of a related matrix. The presentation is essentially in historical order, and out of the vast number of results in this field the authors have culled those that seemed most interesting or useful. Readers will find many of the proofs of classical theorems and a substantial number of proofs of results in contemporary research literature.

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Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas - Revised and Expanded Edition

Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas - Revised and Expanded Edition Lowest new price: $181.00
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Author: Dennis S. Bernstein

The essential reference book on matrices―now fully updated and expanded, with new material on scalar and vector mathematics

Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject.

Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more.

Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index.

  • Fully updated and expanded with new material on scalar and vector mathematics
  • Covers the latest results in matrix theory
  • Provides a list of symbols and a summary of conventions for easy and precise use
  • Includes an extensive bibliography with back-referencing plus an author index

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Matrix Groups for Undergraduates (Student Mathematical Library,)

Matrix Groups for Undergraduates (Student Mathematical Library,) Lowest new price: $341.07
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Author: Kristopher Tapp
Brand: Brand: American Mathematical Society

Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory.

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