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Science & Mathematics - Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library) (Student Mathematical Library, 53)

Description

Book Synopsis: 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 Lovász 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.

Details

Unlock the power of linear algebra with Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra. This book is a treasure trove of clever mathematical applications that span across combinatorics, geometry, and algorithms. With each chapter presenting a single main result, complete with motivation and a full proof within just ten pages, this book is accessible to anyone with a modest background in linear algebra. Whether you are an undergraduate student looking to enhance your understanding of linear algebra or a graduate student seeking advanced knowledge in linear-algebraic methods, this book has something for you.

Immerse yourself in the world of mathematical gems with Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra. From the famous Hamming codes to the intriguing matrix-tree theorem, this book introduces you to a collection of well-known mathematical results that will leave you in awe. But that's not all. You'll also discover lesser-known yet equally beautiful results, like fast associativity testing and a lemma of Steinitz on ordering vectors. So, if you're ready to explore the captivating world of linear algebra, don't miss out on this opportunity.

If you're looking for a book that combines beauty and utility, look no further than Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra. With chapters covering topics such as the Lovász bound on the Shannon capacity and a counterexample to Borsuk's conjecture, you'll find yourself captivated by the elegance of these mathematical concepts. Additionally, the book offers practical applications, including a monotonicity result for integer partitions and a bound for set pairs via exterior products. Whether you're a student, researcher, or simply someone with a love for mathematics, this book is a must-have addition to your collection.

Enhance your learning experience with Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra. This book goes beyond the traditional linear algebra curriculum, providing you with a rich selection of stimulating material that will keep you engaged from start to finish. With the simpler results suitable for undergraduate courses and the more advanced parts perfect for graduate courses or seminar presentations, this book offers flexibility in its usage. Don't miss out on the opportunity to expand your knowledge and deepen your understanding of linear-algebraic methods - grab your copy today!

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