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Bolts from the Blue
We have discovered a pattern for cultural bifurcations involving artists making significant contributions to the history of mathematics.How much of this material would you recognize as mathematics on the basis of your school education? How much appears on standard tests? And what kind of training best supports the development of your natural mathematical skills? How is the integration of mathematics and culture faring today? The six stories of this book-in addition to being examples of cultural ecologies, mathematical mentalities, and bolts from the blue-exhibit the integration of math and cultural history, the basis of a new way of teaching math in school.
Chaos in Discrete Dynamical Systems
The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.
Dynamics
The study of chaos provides a new paradigm for the sciences, and Dynamics: The Geometry of Behavior is a comprehensive exploration of this important branch of mathematics. The book shows a new way to learn a new mathematics -- it is a visual tour that's accessible to a wide range of academic levels. Imaginative, full color graphics translate dynamical systems theory for the layman as well as the seasoned researcher. Dynamics: The Geometry of Behavior is a profusely illustrated, inventive book designed for anyone who wants to learn more about dynamical system theory. This is the first part of a four part series, which is also published as a single volume.
Introduction to Differential Geometry
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to...
Hip Santa Cruz
First person accounts from the pioneers of the Hip Culture of Santa Cruz in the 1960s, including: Pat Bisconti, Rick Gladstone, Max Hartstein, Peter Demma, Bob Hall, Fred McPherson, Paul Lee, Judy Hill, Leon Tabory, Joe Lysowski, Ralph Abraham, and Rivkah Barmore. Ralph Abraham is a Professor of Mathematics at the University of of California at Santa Cruz.
Foundations Of Mechanics
Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
