Number, Shape, & Symmetry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number, Shape, & Symmetry write by Diane L. Herrmann. This book was released on 2012-10-18. Number, Shape, & Symmetry available in PDF, EPUB and Kindle. Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Shapes, Space, and Symmetry
Shapes, Space, and Symmetry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Shapes, Space, and Symmetry write by Alan Holden. This book was released on 1991-01-01. Shapes, Space, and Symmetry available in PDF, EPUB and Kindle. Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.
Symmetry: A Very Short Introduction
Symmetry: A Very Short Introduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry: A Very Short Introduction write by Ian Stewart. This book was released on 2013-05-30. Symmetry: A Very Short Introduction available in PDF, EPUB and Kindle. In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Symmetry, Causality, Mind
Symmetry, Causality, Mind - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry, Causality, Mind write by Michael Leyton. This book was released on 1992. Symmetry, Causality, Mind available in PDF, EPUB and Kindle. In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. Michael Leyton's arguments about the nature of perception and cognition are fascinating, exciting, and sure to be controversial. In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. He elaborates a system of rules by which the conversion to memory takes place and presents a number of detailed case studies--in perception, linguistics, art, and even political subjugation--that support these rules. Leyton observes that the mind assigns to any shape a causal history explaining how the shape was formed. We cannot help but perceive a deformed can as a dented can. Moreover, by reducing the study of shape to the study of symmetry, he shows that symmetry is crucial to our everyday cognitive processing. Symmetry is the means by which shape is converted into memory. Perception is usually regarded as the recovery of the spatial layout of the environment. Leyton, however, shows that perception is fundamentally the extraction of time from shape. In doing so, he is able to reduce the several areas of computational vision purely to symmetry principles. Examining grammar in linguistics, he argues that a sentence is psychologically represented as a piece of causal history, an archeological relic disinterred by the listener so that the sentence reveals the past. Again through a detailed analysis of art he shows that what the viewer takes to be the experience of a painting is in fact the extraction of time from the shapes of the painting. Finally he highlights crucial aspects of the mind's attempt to recover time in examples of political subjugation.
Groups and Symmetry: A Guide to Discovering Mathematics
Groups and Symmetry: A Guide to Discovering Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups and Symmetry: A Guide to Discovering Mathematics write by David W. Farmer. This book was released on 1996. Groups and Symmetry: A Guide to Discovering Mathematics available in PDF, EPUB and Kindle. Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
