Change and Invariance (A Textbook on Algebraic Insight into Numbers and Shapes)
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Product Details
Author:
Ilya Sinitsky, Bat-Sheva Ilany
Format:
Paperback
Pages:
392
Publisher:
Brill (January 1, 2016)
Imprint:
Brill
Language:
English
Audience:
Professional and scholarly
ISBN-13:
9789463006972
ISBN-10:
9463006974
Weight:
19.36oz
File:
TWO RIVERS-PERSEUS-Metadata_Only_Perseus_Distribution_Customer_Group_Metadata_20260319172121-20260319.xml
Folder:
TWO RIVERS
List Price:
$51.00
Country of Origin:
Netherlands
As low as:
$39.27
Publisher Identifier:
P-PER
Discount Code:
A
Overview
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?”
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?”
