Introduction to Commutative Algebra is a well-known commutative algebra textbook written by Michael Atiyah and Ian G. Macdonald. It deals with elementary concepts of commutative algebra including localization, primary decomposition, integral dependence, Noetherian and Artinian rings and modules, Dedekind rings, completions and a moderate amount of dimension theory. It is notable for being among the shorter English-language introductory textbooks in the subject, relegating a good deal of material to the exercises.

The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimation with a focus on applying these techniques to real systems.

This is the first attempt to collect published and unpublished results on incline algebra, which encompasses Boolean algebra and fuzzy algebra. In order to read this monograph, the reader should have had the usual first year graduate courses in mathematics plus an elementary knowledge of combinatorial theory, graph theory, lattice theory, matrix theory (including the Boolean and fuzzy cases), semi-group theory, and semiring theory.

Maple is a Symbolic Computation System or Computer Algebra System. Maple manipulates information in a symbolic or algebraic manner. Other conventional mathematical programs require numerical values for all variables. In contrast, Maple maintains and manipulates the underlying symbols and expressions, and evaluates numerical expressions.

This book arose from a series of courses on computer algebra which were given at Eindhoven Technical University. Its chapters present a variety of topics in computer algebra at an accessible (upper undergraduate/graduate) level with a view towards recentdevelopments. For those wanting to acquaint themselves somewhat further with the material, the book also contains seven 'projects', which could serve as practical sessions related to one or more chapters. The contributions focus on topics like Gröbner bases, real algebraic geometry, Lie algebras, factorisation of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must-read for everybody interested in computer algebra.

Travel made the United States. As both a country and a concept, America was founded on movement—of people, of ideas, of goods. Of course, international immigration has been central to American identity since the earliest European exploration, but travel within the continent likewise played a significant role in the creation and maintenance of the American nation. Struggle, too, has been a defining characteristic of the United States since its founding. In addition to battling against a colonial power for independence, the thirteen colonies struggled with themselves to forge a national identity. In fact, after the Revolutionary War, many Americans wondered whether the bonds among the original colonies were strong enough to establish a single nation. They were, but only after the states struggled to define that nation and fought to keep it intact. Numerous studies have pointed to these concepts to understand the United States, but often these works have defined “travel literature” narrowly or made struggle a precursor to, rather than a central fact of, American national identity. In both cases, scholars have too readily looked abroad, focusing on international travel or on struggles between the United States and other nations. Ironically, even though critics of travel literature often thrive on crossing academic and intellectual boundaries, many have neglected accounts of travel within national borders; likewise, many studies of early America have looked primarily at accounts by Europeans in America or by Americans in Europe to understand the culture of early America. But this international focus fails to appreciate the central role of “travel” itself in American national identity; in fact, far from simply constituting a leisure activity enjoyed only by the wealthy, travel has been one of the defining characteristics of the American people and their nation since its very creation. Furthermore, as conflict within the national borders was obviously central to the creation of the American republic, so, too, was travel within and among the various regions of the new nation.

Ideas about heredity and evolution are undergoing a revolutionary change. New findings in molecular biology challenge the gene-centered version of Darwinian theory according to which adaptation occurs only through natural selection of chance DNA variations. In Evolution in Four Dimensions, Eva Jablonka and Marion Lamb argue that there is more to heredity than genes. They trace four "dimensions" in evolution—four inheritance systems that play a role in evolution: genetic, epigenetic (or non-DNA cellular transmission of traits), behavioral, and symbolic (transmission through language and other forms of symbolic communication). These systems, they argue, can all provide variations on which natural selection can act. Evolution in Four Dimensions offers a richer, more complex view of evolution than the gene-based, one-dimensional view held by many today. The new synthesis advanced by Jablonka and Lamb makes clear that induced and acquired changes also play a role in evolution.

A central problem for cognitive science is how representations should be modeled. This book proposes a geometrical mode of representation based on what I call conceptual spaces. It presents a metatheory on the same level as the symbolic and connectionist modes of representation that, so far, have been dominant within cognitive science. I cast my net widely, trying to show that geometrical representations are viable for many areas within cognitive science. In particular, I suggest new ways of modeling concept formation, semantics, nonmonotonic inferences, and inductive reasoning

Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority make it also an essential reference for professionals in the area.

Vol. 1 : Ab - Cy. - 214 p.

This introduction to numerical analysis shows how the mathematics of calculus and linear algebra are implemented in computer algorithms. It develops a deep understanding of why numerical methods work and exactly what their limitations are.

У теории групп три исторических корня: теория алгебраических уравнений, теория чисел и геометрия. Математики, стоящие у истоков теории групп, — это Леонард Эйлер, Карл Фридрих Гаусс, Жозеф Луи Лагранж, Нильс Хенрик Абель и Эварист Галуа. Галуа был первым математиком, связавшим теорию групп с другой ветвью абстрактной алгебры — теорией полей, разработав теорию, ныне называемую теорией Галуа.

This new set helps students better understand commonly studied math concepts by illustrating their use in everyday life. Everyday tasks are designed to support the modern mathematics curriculum and contain examples related to the global economy. Grade 6-9-From concept to copyediting, this unwieldy survey of applied mathematics falls short in nearly every aspect. Each of the 80 alphabetically arranged chapters, from Addition to Zero-Sum Games, takes on a curriculum-centered topic. They open with a definition, close with a brief list of further sources, and in between quickly lay out fundamental terms and ideas, historical background, and descriptions of Real-life Applications. The latter often include word (rarely number) examples, but also tend to be nonspecific, if not outright simplistic; online purchasing over a secure connection is safe, for instance, because hackers can't decode the content even if they somehow manage to intercept the message somehow. Under Algebra, the entry on making tradeoffs between lifespan and voltage when Buying Light Bulbs assumes that small variations in voltage are an option. In addition, despite substantial duplication of topics, there are no see references to connect related entries, such as those for carbon dating or sports wagering. Printed in two large volumes of dense, double-columned, seldom-illustrated text, this is less likely than the textbooks that it is supposed to compliment.

The quadtree and octree are hierarchical data structures used to represent spatial data. They are based on the principle of recursive decomposition (similar to divide and con- conquer methods [Aho74]). This book focuses on the use of quadtree and octree representations of region data (in two and three dimensions, respectively) in applications in computer graphics, image processing, and geographic information systems (Gis), as well as computer vision, robotics, pattern recognition, solid modeling, and other areas. For a comprehensive treatment of related hierarchical representations of spatial data including points, lines, rectangles, regions, and volumes, see [Same90a]. To many people, the terms quadtree and octree have taken on a generic meaning synonymous with the term hierarchical data structure. Hierarchical data structures are useful because of their ability to focus on the interesting subsets of the data. This focusing results in an efficient representation and in improved execution times. Thus they are particularly convenient for performing set operations. Many of the operations described can often be performed as efficiently, or more so, with other data structures. Nevertheless, hierarchical data structures are attractive because of their conceptual clarity and ease of implementation. In addition, the use of some of them provides a spatial index. This is very useful in applications involving spatial databases.