Computational And Algorithmic Linear Algebra And N Dimensional Geometry
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| Author | : Katta Gopalakrishna Murty |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 479 |
| Release | : 2014-07-31 |
| Genre | : Mathematics |
| ISBN | : 9814632155 |
This undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences. These are classical subjects on which there are many mathematics books in theorem-proof style, but this unique volume has its focus on developing the mathematical modeling as well as computational and algorithmic skills in students at this level. The explanations in this book are detailed, lucid, and supported with numerous well-constructed examples to capture the interest and encourage the student to master the material.
| Author | : Katta G. Murty |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 0 |
| Release | : 2014 |
| Genre | : Algebras, Linear |
| ISBN | : 9789814366632 |
This undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences. These are classical subjects on which there are many mathematics books in theorem-proof style, but this unique volume has its focus on developing the mathematical modeling as well as computational and algorithmic skills in students at this level. The explanations in this book are detailed, lucid, and supported with numerous well-constructed examples to capture the interest and encourage the student to master the material.
| Author | : Bhubaneswar Mishra |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 427 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461243440 |
Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.
| Author | : Katta G. Murty |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 502 |
| Release | : 2010-03-14 |
| Genre | : Mathematics |
| ISBN | : 1441912916 |
Linear programming (LP), modeling, and optimization are very much the fundamentals of OR, and no academic program is complete without them. No matter how highly developed one’s LP skills are, however, if a fine appreciation for modeling isn’t developed to make the best use of those skills, then the truly ‘best solutions’ are often not realized, and efforts go wasted. Katta Murty studied LP with George Dantzig, the father of linear programming, and has written the graduate-level solution to that problem. While maintaining the rigorous LP instruction required, Murty's new book is unique in his focus on developing modeling skills to support valid decision making for complex real world problems. He describes the approach as 'intelligent modeling and decision making' to emphasize the importance of employing the best expression of actual problems and then applying the most computationally effective and efficient solution technique for that model.
| Author | : A. Ravi Ravindran |
| Publisher | : CRC Press |
| Total Pages | : 498 |
| Release | : 2008-11-12 |
| Genre | : Business & Economics |
| ISBN | : 1420091832 |
A single source guide to operations research (OR) techniques, this book covers emerging OR methodologies in a clear, concise, and unified manner. Building a bridge between theory and practice, it begins with coverage of fundamental models and methods such as linear, nonlinear, integer, and dynamic programming, networks, simulation, queuing, invento
| Author | : A. Ravi Ravindran |
| Publisher | : CRC Press |
| Total Pages | : 900 |
| Release | : 2016-04-19 |
| Genre | : Business & Economics |
| ISBN | : 1420009710 |
Operations Research (OR) began as an interdisciplinary activity to solve complex military problems during World War II. Utilizing principles from mathematics, engineering, business, computer science, economics, and statistics, OR has developed into a full fledged academic discipline with practical application in business, industry, government and m
| Author | : Franco P. Preparata |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 413 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210984 |
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
| Author | : Wolfram Decker |
| Publisher | : Cambridge University Press |
| Total Pages | : 127 |
| Release | : 2013-02-07 |
| Genre | : Computers |
| ISBN | : 1107612535 |
A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.
| Author | : John Scherk |
| Publisher | : CRC Press |
| Total Pages | : 344 |
| Release | : 2018-10-03 |
| Genre | : Mathematics |
| ISBN | : 1351989685 |
Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. A variety of factors set this text apart. Its clear exposition, with each chapter building upon the previous ones, provides greater clarity for the reader. The author first introduces permutation groups, then linear groups, before finally tackling abstract groups. He carefully motivates Galois theory by introducing Galois groups as symmetry groups. He includes many computations, both as examples and as exercises. All of this works to better prepare readers for understanding the more abstract concepts. By carefully integrating the use of Mathematica® throughout the book in examples and exercises, the author helps readers develop a deeper understanding and appreciation of the material. The numerous exercises and examples along with downloads available from the Internet help establish a valuable working knowledge of Mathematica and provide a good reference for complex problems encountered in the field.
| Author | : Jiří Matoušek |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 196 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821849778 |
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)
