Number Shape Symmetry
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Number, Shape, & Symmetry
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
Number, Shape, & Symmetry
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.
Patterns: Numbers, Shapes, and Connections
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-07-12
Embark on an enthralling journey into the captivating world of patterns, numbers, shapes, and connections with this comprehensive guide. Within these pages, you'll discover a treasure trove of knowledge that will ignite your curiosity, expand your understanding, and leave you in awe of the interconnectedness and beauty of the universe. Explore the fascinating realm of prime numbers, where infinite possibilities unfold. Unravel the mysteries of infinity, a concept that has captivated mathematicians and philosophers for centuries. Delve into the enigmatic world of fractals, where intricate patterns emerge from simple rules. Uncover the secrets of logical reasoning, the foundation of critical thinking and problem-solving. Witness the power of algorithms, the driving force behind technological advancements. Decipher the intricacies of counting and probability, essential tools for understanding the world around us. Venture into the realm of graphs, where intricate networks reveal hidden patterns and connections. Unlock the puzzles of discrete optimization, where mathematical techniques empower us to find optimal solutions to real-world problems. Through engaging explanations, captivating examples, and thought-provoking exercises, this book brings abstract concepts to life. It's an indispensable resource for students, educators, and anyone seeking to deepen their understanding of the fundamental principles that govern our universe. Immerse yourself in the beauty and elegance of patterns, numbers, shapes, and connections. Discover how these concepts have shaped our understanding of the universe, fueled technological advancements, and transformed our lives. Prepare to be amazed by the wonders that await within these pages. If you like this book, write a review!