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Change and invariance = a textbook on algebraic insight into numbers and shapes /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Change and invariance/ by Ilya Sinitsky, Bat-Sheva Ilany.
Reminder of title:	a textbook on algebraic insight into numbers and shapes /
Author:	Sinitsky, Ilya.
other author:	Ilany, Bat-Sheva.
Published:	Rotterdam :SensePublishers : : 2016.,
Description:	xiv, 378 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Symmetry (Mathematics) -
Online resource:	http://dx.doi.org/10.1007/978-94-6300-699-6
ISBN:	9789463006996

Change and invariance = a textbook on algebraic insight into numbers and shapes /
Sinitsky, Ilya.

Change and invariancea textbook on algebraic insight into numbers and shapes /[electronic resource] :by Ilya Sinitsky, Bat-Sheva Ilany. - Rotterdam :SensePublishers :2016. - xiv, 378 p. :ill., digital ;24 cm.

"What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book. The world is an interplay of variation and constancy - a medley of differences and similarities - and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes. After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter's theme. Some examples: "How to represent all the integers from zero to 1000 using ten fingers?", "How to win at the game of Nim?", "Why do different square lattice polygons with the same area often have the same perimeter?" This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."

ISBN: 9789463006996

Standard No.: 10.1007/978-94-6300-699-6doiSubjects--Topical Terms:

788067
Symmetry (Mathematics)

LC Class. No.: QA174.7.S96 / S58 2016

Dewey Class. No.: 516.1

Change and invariance = a textbook on algebraic insight into numbers and shapes /
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520 $a "What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book. The world is an interplay of variation and constancy - a medley of differences and similarities - and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes. After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter's theme. Some examples: "How to represent all the integers from zero to 1000 using ten fingers?", "How to win at the game of Nim?", "Why do different square lattice polygons with the same area often have the same perimeter?" This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."
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