Taking Sudoku Seriously: The Math Behind the World’s Most Popular Pencil Puzzle by Jason Rosenhouse
Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics.
How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square–an object of long-standing interest to mathematicians–of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations–just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself.
A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.
Michael J. Cloud
Inequalities: With Applications to Engineering
A working knowledge of inequalities can be beneficial to the practicing engineer, and inequalities are central to the definitions of all limiting processes, including differentiation and integration. When exact solutions are unavailable, inconvenient, or unnecessary, inequalities can be used to obtain error bounds for numerical approximation.
Handbook of Linear Algebra, Second Edition
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.
New to the Second Edition
Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets
New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems
More chapters on applications of linear algebra, including epidemiology and quantum error correction
New chapter on using the free and open source software system Sage for linear algebra
Additional sections in the chapters on sign pattern matrices and applications to geometry
Conjectures and open problems in most chapters on advanced topics
Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.
Geometric Modeling: Techniques, Applications, Systems and Tools
This book aims to provide a valuable source, which focuses on interdisciplinary methods and affiliate research in the area of Geometric Modeling and Graphics. It aims to provide the user community with a variety of Geometric Modeling techniques, applications, systems and tools necessary for various real life problems in areas such as Designing objects, Medical Visualization, Scientific Data Visualization, Archaeology, Toon Rendering, Virtual Reality, Body Simulation, etc. It also aims to collect and disseminate information from various disciplines including Curve and Surface Fitting, Geometric Algorithms, Scientific Visualization, Shape Abstraction and Modeling, Intelligent CAD Systems, Computational Geometry, Solid Modeling, Shape Analysis and Description, Medical and Industrial Applications. The major goal of this book is to stimulate views and provide a source where researchers and practitioners can find the latest developments in the field of Geometric Modeling and related practical issues.
Mathematics and Art: Mathematical Visualization in Art and Education
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology.
For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.