In the domain of visual images, those of fine art form a tiny minority. This original and brilliant book calls upon art historians to look beyond their traditional subjects—painting, drawing, photography, and printmaking—to the vast array of "nonart" images, including those from science, technology, commerce, medicine, music, and archaeology. Such images, James Elkins asserts, can be as rich and expressive as any canonical painting. Using scores of illustrations as examples, he proposes a radically new way of thinking about visual analysis, one that relies on an object's own internal sense of organization.Elkins begins by demonstrating the arbitrariness of current criteria used by art historians for selecting images for study. He urges scholars to adopt, instead, the far broader criteria of the young field of image studies. After analyzing the philosophic underpinnings of this interdisciplinary field, he surveys the entire range of images, from calligraphy to mathematical graphs and abstract painting. Throughout, Elkins blends philosophic analysis with historical detail to produce a startling new sense of such basic terms as pictures, writing, and notation.
The Pythagorean Theorem is one of the most important ideas in all of mathematics. In this book, students study history and geometry as they explore eight elegant proofs of the theorem from across the centuries. Included are interesting facts about the theorem, a brief biography of Pythagoras, and a list of concepts needed to understand the proofs. Learn how Leonardo Da Vinci, President James A. Garfield, Pythagoras, the Chinese, Bhaskara, and others proved this famous theorem about the right triangle. This would be a useful book for any student taking Geometry, or anyone interested in Mathematics History. NOW WITH A LINK TO POWERPOINT SLIDES YOU CAN DOWNLOAD WITH ANIMATIONS, VIDEOS, PICTURES, AND HYPERLINKS TO SUPPLEMENT THE BOOK. Each proof is displayed in color with an explanation of the steps taken in its geometric presentation. Blackline masters for the proofs, and for manipulatives that offer students hands-on understanding, are included. The book is in PDF format.
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Thirty years after its publication, The Death and Life of Great American Cities was described by The New York Times as "perhaps the most influential single work in the history of town planning....[It] can also be seen in a much larger context. It is first of all a work of literature; the descriptions of street life as a kind of ballet and the bitingly satiric account of traditional planning theory can still be read for pleasure even by those who long ago absorbed and appropriated the book's arguments." Jane Jacobs, an editor and writer on architecture in New York City in the early sixties, argued that urban diversity and vitality were being destroyed by powerful architects and city planners. Rigorous, sane, and delightfully epigrammatic, Jacobs's small masterpiece is a blueprint for the humanistic management of cities. It is sensible, knowledgeable, readable, indispensable. The author has written a new foreword for this Modern Library edition.
Eclipses have long been seen as important celestial phenomena, whether as omens affecting the future of kingdoms, or as useful astronomical events to help in deriving essential parameters for theories of the motion of the moon and sun. This is the first book to collect together all presently known records of timed eclipse observations and predictions from antiquity to the time of the invention of the telescope. In addition to cataloguing and assessing the accuracy of the various records, which come from regions as diverse as Ancient Mesopotamia, China, and Europe, the sources in which they are found are described in detail. Related questions such as what type of clocks were used to time the observations, how the eclipse predictions were made, and how these prediction schemes were derived from the available observations are also considered. The results of this investigation have important consequences for how we understand the relationship between observation and theory in early science and the role of astronomy in early cultures, and will be of interest to historians of science, astronomers, and ancient and medieval historians.
Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Tells the story of the golden section, a line segment divided into two parts such that the ratio of the short portion to the longer portion is equal to the ratio of the longer portion to the whole, and its impact on civilization and the natural world.
Author: Charles Miller Grinstead,James Laurie Snell
Publisher: American Mathematical Soc.
This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. The text is also recommended for use in discrete probability courses. The material is organized so that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization does not emphasize an overly rigorous or formal view of probability and therefore offers some strong pedagogical value. Hence, the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. Features: Key ideas are developed in a somewhat leisurely style, providing a variety of interesting applications to probability and showing some nonintuitive ideas. Over 600 exercises provide the opportunity for practicing skills and developing a sound understanding of ideas. Numerous historical comments deal with the development of discrete probability. The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level. The book contains a lot of examples and an easy development of theory without any sacrifice of rigor, keeping the abstraction to a minimal level. It is indeed a valuable addition to the study of probability theory. --Zentralblatt MATH
First published in Liber ABA (Part II), Aleister Crowley's Magick is essential reading for students of Thelema and the occult. This guide to the principle tenets of black magic is a concise version of the more dense four-book magnum opus Liber ABA or 'Book 4' and is recommended to initiates.
The frames of classical art are often seen as marginal to the images that they surround. Traditional art history has tended to view framing devices as supplementary 'ornaments'. Likewise, classical archaeologists have often treated them as tools for taxonomic analysis. This book not only argues for the integral role of framing within Graeco-Roman art, but also explores the relationship between the frames of classical antiquity and those of more modern art and aesthetics. Contributors combine close formal analysis with more theoretical approaches: chapters examine framing devices across multiple media (including vase and fresco painting, relief and free-standing sculpture, mosaics, manuscripts and inscriptions), structuring analysis around the themes of 'framing pictorial space', 'framing bodies', 'framing the sacred' and 'framing texts'. The result is a new cultural history of framing - one that probes the sophisticated and playful ways in which frames could support, delimit, shape and even interrogate the images contained within.
The 'long twelfth century' (1075–1225) was an era of seminal importance in the development of the book in medieval Europe and marked a high point in its construction and decoration. This comprehensive study takes the cultural changes that occurred during the 'twelfth-century Renaissance' as its point of departure to provide an overview of manuscript culture encompassing the whole of Western Europe. Written by senior scholars, chapters are divided into three sections: the technical aspects of making books; the processes and practices of reading and keeping books; and the transmission of texts in the disciplines that saw significant change in the period, including medicine, law, philosophy, liturgy, and theology. Richly illustrated, the volume provides the first in-depth account of book production as a European phenomenon.
Proceedings From a Symposium Held in Strasbourg, France in March 1985 and Sponsored by the International Commission on Mathematical Instruction
Author: R. F. Churchhouse
Publisher: CUP Archive
First published in 1986, the first ICMI study is concerned with the influence of computers and computer science on mathematics and its teaching in the last years of school and at tertiary level. In particular, it explores the way the computer has influenced mathematics itself and the way in which mathematicians work, likely influences on the curriculum of high-school and undergraduate students, and the way in which the computer can be used to improve mathematics teaching and learning. The book comprises a report of the meeting held in Strasbourg in March 1985, plus several papers contributed to that meeting.
Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems. This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java. The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.