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National Union Catalog
Includes entries for maps and atlases.
Topology Now!
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
From Geometry to Topology
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.
The Elements of Non-Euclidean Geometry
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Inhuman Nature
Collection of essays examining the ways in which humanity is enmeshed in its surroundings.
Crocheting Adventures with Hyperbolic Planes
Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.
A Motif of Mathematics
The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.
Dynamic Patterns
Dynamic Patterns explores the role of patterns in designed landscapes. Patterns are inherently relational, and the search for and the creation of patterns are endemic to many scientific and artistic endeavors. Recent advances in optical tools, sensors, and computing have expanded our understanding of patterns as a link between natural and cultural realms. Looking beyond the surface manifestation of pattern, M’Closkey and VanDerSys delve into a multifaceted examination that explores new avenues for engagement with patterns using digital media. Examining the theoretical implications of pattern-making, they probe the potential of patterns to conjoin landscape’s utilitarian and aesthetic functions. With full color throughout and over one hundred and twenty images, Dynamic Patterns utilizes work from a wide range of artists and designers to demonstrate how novel modes of visualization have facilitated new ways of seeing patterns and therefore of understanding and designing landscapes.
The Mathematical Traveler
As he persuasively argues, the mathematical concepts that arose and flourished in the ancient world enabled the creation of architectural masterpieces as well as the establishment of vast trade networks.
