Thinking Geometrically

Thinking Geometrically

Author: Thomas Q. Sibley

Publisher: The Mathematical Association of America

ISBN: 9781939512086

Category: Mathematics

Page: 586

View: 295

Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

Thinking Geometrically

Thinking Geometrically

Author: John T. Waisanen

Publisher: Peter Lang Pub Incorporated

ISBN: STANFORD:36105122196541

Category: Art

Page: 198

View: 221

What skills do we need to negotiate the changing technological circumstances of our lives? How should we respond to the changing space of the visual, the technological? We are bombarded with answers to these questions: by media, by government, and by education. For the most part we are told that what we need to do is utilize the latest technologies and develop the newest skills (computer literacy prominent among them). Here, with keen interdisciplinary insight, historical sensitivity, and corporate design experience, John T. Waisanen offers a different kind of argument. He looks to particular skills we might be losing (and might have for some time been losing): drawing in particular; and to the «art» of integrating complex vision, thought and practice, what he calls design - or geometrical thinking. This points to the importance of the arts as a physical practice and to the cultivation of complex vision and thought gained in and through an education where geometry and literature are equally important, where physical intelligence (not just dexterity) and philosophical intelligence are equally important.

Mathematical Thinking and Problem Solving

Mathematical Thinking and Problem Solving

Author: Alan H. Schoenfeld

Publisher: Routledge

ISBN: 9781135440930

Category: Education

Page: 360

View: 256

In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

Future Curricular Trends in School Algebra And Geometry

Future Curricular Trends in School Algebra And Geometry

Author: Zalman Usiskin

Publisher: IAP

ISBN: 9781617350085

Category: Education

Page: 347

View: 720

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

Contemporary Trends in Algebraic Geometry and Algebraic Topology

Contemporary Trends in Algebraic Geometry and Algebraic Topology

Author: Shiing-Shen Chern

Publisher: World Scientific

ISBN: 9812777415

Category: Mathematics

Page: 278

View: 987

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc.This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen''s interated integrals, algebraic fiber spaces, and others.

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Author: Ewa Swoboda

Publisher: Springer

ISBN: 9783319442723

Category: Education

Page: 50

View: 380

This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula.

Applying Geometry to Everyday Life

Applying Geometry to Everyday Life

Author: Erik Richardson

Publisher: Cavendish Square Publishing, LLC

ISBN: 9781502619723

Category: Juvenile Nonfiction

Page: 128

View: 271

The fundamental shapes of geometry can be built into the grand sweeps of the Sydney Opera House or something as small as a snowflake. This title takes geometric concepts like polygons, platonic solids, and angles and demonstrates their myriad appearances in the world around us. From the Great Pyramid of Giza to sinking a bank shot in pool, geometry abounds.

The Geometry of Biological Time

The Geometry of Biological Time

Author: Arthur T. Winfree

Publisher: Springer Science & Business Media

ISBN: 9783662224922

Category: Mathematics

Page: 530

View: 301

As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.

Peter Lax, Mathematician: An Illustrated Memoir

Peter Lax, Mathematician: An Illustrated Memoir

Author: Reuben Hersh

Publisher: American Mathematical Soc.

ISBN: 9781470417086

Category: Mathematics

Page: 253

View: 464

This book is a biography of one of the most famous and influential living mathematicians, Peter Lax. He is virtually unique as a preeminent leader in both pure and applied mathematics, fields which are often seen as competing and incompatible. Although he has been an academic for all of his adult life, his biography is not without drama and tragedy. Lax and his family barely escaped to the U.S. from Budapest before the Holocaust descended. He was one of the youngest scientists to work on the Manhattan Project. He played a leading role in coping with the infamous "kidnapping" of the NYU mathematics department's computer, in 1970. The list of topics in which Lax made fundamental and long-lasting contributions is remarkable: scattering theory, solitons, shock waves, and even classical analysis, to name a few. His work has been honored many times, including the Abel Prize in 2005. The book concludes with an account of his most important mathematical contributions, made accessible without heavy prerequisites. Reuben Hersh has written extensively on mathematics. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science. Hersh is emeritus professor of mathematics at the University of New Mexico.

Algebraic Geometry and Singularities

Algebraic Geometry and Singularities

Author: Antonio Campillo Lopez

Publisher: Springer Science & Business Media

ISBN: 3764353341

Category: Mathematics

Page: 448

View: 402

The volume contains both general and research papers. Among the first ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The research papers deal on topics related to, or close to, those listed_above. The contributions are organized in three parts according to their contents. Part I presents a set of papers on resolution of singularities, a topic of renewed activity. It deals with important topics of current interest, such as canonical, algorithmic, combinatorial and graphical procedures (Villamayor, Oka, Marijmin), as well as special results on desingularization in characteristic p (Cossart, Moh), and connections between resolution and structure of the space of arcs through a singularity (Gonz81ez-Sprinberg-Lejeune-Jalabert). Part II contains a series of papers on the study~of singularities and its connections with differential systems and deformation or perturbation theo­ ries. Two expository papers (Maisonobe-Briam;on, :'vlebkhout) describe, in an algebro-geometric way, the interaction between singularities and D-module t.he­ ory including recent progress on Bernstein polynomials and Newton polygon techniques. Geometry of foliations (Henaut, Garcfa-Reguera), polar varieties and stratifications (Hajto) are also topics treated here. Two other papers (Wall, Greuel-Pfister) deal with quasihomogeneous singularities in the contexts of per­ turbations and moduli spaces. Globalization of deformations of singularities (de Jong) and determination of complex topology from the real one (~10nd) com­ plete this series of papers. Part III consists of papers on algebraic geometry of curves and surfaces.

Teaching Secondary Mathematics With Ict

Teaching Secondary Mathematics With Ict

Author: Johnston-Wilder, Sue

Publisher: McGraw-Hill Education (UK)

ISBN: 9780335213818

Category: Education

Page: 273

View: 195

This practical book shows the reader how to use Information and Communication Technology (ICT) to enhance mathematics teaching in the secondary sschool.