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Solutions Manual To Accompany Classical Geometry

Author: I. E. Leonard
Publisher: John Wiley & Sons
ISBN: 111890348X
Size: 45.24 MB
Format: PDF
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Solutions Manual to accompany Classical Geometry: Euclidean, Transformational, Inversive, and Projective Written by well-known mathematical problem solvers, Classical Geometry: Euclidean, Transformational, Inversive, and Projective features up-to-date and applicable coverage of the wide spectrum of geometry and aids readers in learning the art of logical reasoning, modeling, and proof. With its reader-friendly approach, this undergraduate text features self-contained topical coverage and provides a large selection of solved exercises to aid in reader comprehension. Material in this text can be tailored for a one-, two-, or three-semester sequence.

Geometry Of Convex Sets

Author: I. E. Leonard
Publisher: John Wiley & Sons
ISBN: 111902269X
Size: 64.72 MB
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A gentle introduction to the geometry of convex sets in n-dimensional space Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting. Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on an n-dimensional space. Geometry of Convex Sets also features: An introduction to n-dimensional geometry including points; lines; vectors; distance; norms; inner products; orthogonality; convexity; hyperplanes; and linear functionals Coverage of n-dimensional norm topology including interior points and open sets; accumulation points and closed sets; boundary points and closed sets; compact subsets of n-dimensional space; completeness of n-dimensional space; sequences; equivalent norms; distance between sets; and support hyperplanes · Basic properties of convex sets; convex hulls; interior and closure of convex sets; closed convex hulls; accessibility lemma; regularity of convex sets; affine hulls; flats or affine subspaces; affine basis theorem; separation theorems; extreme points of convex sets; supporting hyperplanes and extreme points; existence of extreme points; Krein–Milman theorem; polyhedral sets and polytopes; and Birkhoff’s theorem on doubly stochastic matrices Discussions of Helly’s theorem; the Art Gallery theorem; Vincensini’s problem; Hadwiger’s theorems; theorems of Radon and Caratheodory; Kirchberger’s theorem; Helly-type theorems for circles; covering problems; piercing problems; sets of constant width; Reuleaux triangles; Barbier’s theorem; and Borsuk’s problem Geometry of Convex Sets is a useful textbook for upper-undergraduate level courses in geometry of convex sets and is essential for graduate-level courses in convex analysis. An excellent reference for academics and readers interested in learning the various applications of convex geometry, the book is also appropriate for teachers who would like to convey a better understanding and appreciation of the field to students. I. E. Leonard, PhD, was a contract lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta. The author of over 15 peer-reviewed journal articles, he is a technical editor for the Canadian Applied Mathematical Quarterly journal. J. E. Lewis, PhD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004 as well as the PIMS Education Prize in 2002.

Mathematics Learning In Early Childhood

Author: National Research Council
Publisher: National Academies Press
ISBN: 9780309147439
Size: 21.37 MB
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Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

True Myth

Author: James W. Menzies
Publisher: The Lutterworth Press
ISBN: 071884341X
Size: 75.22 MB
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True Myth examines the meaning and significance of myth as understood by C.S. Lewis and Joseph Campbell and its place in the Christian faith in a technological society. C.S. Lewis defined Christianity, and being truly human, as a relationship between the personal Creator and his creation mediated through faith in his son, Jesus. The influential writer and mythologist Joseph Campbell had a different perspective, understanding Christianity as composed of mythical themes similar to those in other religious and secular myths. While accepting certain portions of the biblical record as historical, Campbell taught the theological and miraculous aspects as symbolic Ð as stories in which the reader discovers what it means to be human today. In contrast, Lewis presented the theological and the miraculous in a literal way. Although Lewis understood how one could see symbolism and lessons for life in miraculous events, he believed they were more than symbolic and indeed took place in human history. In True Myth, James W. Menzies skilfully balances the two writersÕ differing approaches to guide the reader through a complex interaction of myth with philosophy, media, ethics, history, literature, art, music and religion in a contemporary world.

A Simple Non Euclidean Geometry And Its Physical Basis

Author: I.M. Yaglom
Publisher: Springer Science & Business Media
ISBN: 146126135X
Size: 31.43 MB
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There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.

Representation And Invariance Of Scientific Structures

Author: Patrick Suppes
Publisher: Stanford Univ Center for the Study
ISBN: 9781575863337
Size: 67.16 MB
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A fundamental reason for using formal methods in the philosophy of science is the desirability of having a fixed frame of reference that may be used to organize the variety of doctrines at hand. This book—Patrick Suppes's major work, and the result of several decades of research—examines how set-theoretical methods provide such a framework, covering issues of axiomatic method, representation, invariance, probability, mechanics, and language, including research on brain-wave representations of words and sentences. This is a groundbreaking, essential text from a distinguished philosopher.

Ten Lectures On Cognitive Semantics

Author: Leonard Talmy
Publisher: BRILL
ISBN: 900434957X
Size: 21.82 MB
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In his ten Beijing lectures, Leonard Talmy represents the range of his work in cognitive semantics. This approach concerns the linguistic representation of conceptual structure: the patterns in which and processes by which conceptual content is organized in language.

The Cambridge Handbook Of Computational Psychology

Author: Ron Sun
Publisher: Cambridge University Press
ISBN: 0521674107
Size: 18.90 MB
Format: PDF, ePub
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This book is a definitive reference source for the growing, increasingly more important, and interdisciplinary field of computational cognitive modeling, that is, computational psychology. It combines breadth of coverage with definitive statements by leading scientists in this field. Research in computational cognitive modeling explores the essence of cognition and various cognitive functionalities through developing detailed, process-based understanding by specifying computational mechanisms, structures, and processes. Given the complexity of the human mind and its manifestation in behavioral flexibility, process-based computational models may be necessary to explicate and elucidate the intricate details of the mind. The key to understanding cognitive processes is often in fine details. Computational models provide algorithmic specificity: detailed, exactly specified, and carefully thought-out steps, arranged in precise yet flexible sequences. These models provide both conceptual clarity and precision at the same time. This book substantiates this approach through overviews and many examples.