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Author: Svetoslav Savchev
Publisher: MAA
ISBN: 9780883856451
Category : Education
Languages : en
Pages : 244
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Book Description
Rather than simply a collection of problems, this book can be thought of as both a tool chest of mathematical techniques and an anthology of mathematical verse. The authors have grouped problems so as to illustrate and highlight a number of important techniques and have provided enlightening solutions in all cases. As well as this there are essays on topics that are not only beautiful but also useful. The essays are diverse and enlivened by fresh, non-standard ideas. This book not only teaches techniques but gives a flavour of their past, present and possible future implications. It is a collection of miniature mathematical works in the fullest sense.
Author: Svetoslav Savchev
Publisher: MAA
ISBN: 9780883856451
Category : Education
Languages : en
Pages : 244
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Book Description
Rather than simply a collection of problems, this book can be thought of as both a tool chest of mathematical techniques and an anthology of mathematical verse. The authors have grouped problems so as to illustrate and highlight a number of important techniques and have provided enlightening solutions in all cases. As well as this there are essays on topics that are not only beautiful but also useful. The essays are diverse and enlivened by fresh, non-standard ideas. This book not only teaches techniques but gives a flavour of their past, present and possible future implications. It is a collection of miniature mathematical works in the fullest sense.
Author: Jiří Matoušek
Publisher: American Mathematical Soc.
ISBN: 0821849778
Category : Mathematics
Languages : en
Pages : 196
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Book Description
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)
Author: D. B. Fuks
Publisher: American Mathematical Soc.
ISBN: 0821843168
Category : Mathematics
Languages : en
Pages : 482
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Book Description
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Author: Ida Kantor
Publisher: American Mathematical Soc.
ISBN: 1470422611
Category : Mathematics
Languages : en
Pages : 359
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Book Description
Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.
Author: Pramod Ganapathi
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 560
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Book Description
This book presents serious mathematical and algorithmic puzzles that are mostly counterintuitive. The presented puzzles are simultaneously entertaining, challenging, intriguing, and haunting. This book introduces its readers to counterintuitive mathematical ideas and revolutionary algorithmic insights from a wide variety of topics. The presented solutions that are discovered by many mathematicians and computer scientists are highly counterintuitive and show supreme mathematical beauty. These counterintuitive solutions are intriguing to the degree that they shatter our preconceived notions, shake our long-held belief systems, debunk our fundamental intuitions, and finally rob us of sleep and haunt us for a lifetime. Multiple ways of attacking the same puzzle are presented which teach the application of elegant problem-solving strategies.
Author: Anany Levitin
Publisher: Oxford University Press
ISBN: 0199876541
Category : Mathematics
Languages : en
Pages : 280
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Book Description
While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.
Author: Margaret Grace
Publisher: SCB Distributors
ISBN: 156474759X
Category : Fiction
Languages : en
Pages : 232
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Book Description
Tiny Houses Can Hold Big Clues. Geraldine Porter is thrilled to meet bestselling author and miniatures enthusiast Varena Young. The celebrity seems to seek friendship with Gerry and her crafts group, and makes a generous offer of a house from her collection for a library fund-raiser. But Young is suddenly murdered. Gerry and her eleven-year-old granddaughter Maddie delve for information on Young�s mysterious past, and find a clue to her murder in a secret room... in a dollhouse. "Perfectly written, with a cast of wonderful characters. This series keeps getting better and better.” -- Hannah Reed, Mind Your Own Beeswax
Author: Jennifer Beineke
Publisher: Princeton University Press
ISBN: 0691183473
Category : Mathematics
Languages : en
Pages : 290
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Book Description
The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more. Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.
Author: Heinrich Dörrie
Publisher: Courier Corporation
ISBN: 0486318478
Category : Mathematics
Languages : en
Pages : 418
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Book Description
Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge, Steiner, and other great mathematical minds. Features squaring the circle, pi, and similar problems. No advanced math is required. Includes 100 problems with proofs.
Author: Deniz Sarikaya
Publisher: Springer Nature
ISBN: 3658410612
Category : Mathematics
Languages : en
Pages : 234
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Book Description
Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights.
