Number Theory And Symmetry PDF Download
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Author | : Diane L. Herrmann |
Publisher | : CRC Press |
Total Pages | : 446 |
Release | : 2012-10-18 |
Genre | : Mathematics |
ISBN | : 1466554649 |
Download Number, Shape, & Symmetry Book 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.
Author | : Alex Berke |
Publisher | : MIT Press |
Total Pages | : 165 |
Release | : 2020-02-18 |
Genre | : Mathematics |
ISBN | : 026253892X |
Download Beautiful Symmetry Book in PDF, ePub and Kindle
A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.
Author | : Michel Planat |
Publisher | : MDPI |
Total Pages | : 206 |
Release | : 2021-01-20 |
Genre | : Computers |
ISBN | : 3039366866 |
Download Number Theory and Symmetry Book in PDF, ePub and Kindle
According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.
Author | : Mark A. Armstrong |
Publisher | : Springer Science & Business Media |
Total Pages | : 197 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475740344 |
Download Groups and Symmetry Book in PDF, ePub and Kindle
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.
Author | : Avner Ash |
Publisher | : Princeton University Press |
Total Pages | : 308 |
Release | : 2008-08-24 |
Genre | : Mathematics |
ISBN | : 0691138710 |
Download Fearless Symmetry Book in PDF, ePub and Kindle
Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.
Author | : William McClain |
Publisher | : Springer Science & Business Media |
Total Pages | : 672 |
Release | : 2010-03-12 |
Genre | : Science |
ISBN | : 0387734708 |
Download Symmetry Theory in Molecular Physics with Mathematica Book in PDF, ePub and Kindle
Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
Author | : Michel Planat |
Publisher | : |
Total Pages | : 206 |
Release | : 2020 |
Genre | : |
ISBN | : 9783039366873 |
Download Number Theory and Symmetry Book in PDF, ePub and Kindle
According to Carl Friedrich Gauss (1777-1855), mathematics is the queen of the sciences--and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal's triangle). The book should be of interest to all mathematicians, and physicists.
Author | : Richard C Powell |
Publisher | : Springer |
Total Pages | : 238 |
Release | : 2010-12-01 |
Genre | : Science |
ISBN | : 1441975985 |
Download Symmetry, Group Theory, and the Physical Properties of Crystals Book in PDF, ePub and Kindle
Complete with reference tables and sample problems, this volume serves as a textbook or reference for solid-state physics and chemistry, materials science, and engineering. Chapters illustrate symmetry, and its role in determining solid properties, as well as a demonstration of group theory.
Author | : Nathan Carter |
Publisher | : American Mathematical Soc. |
Total Pages | : 295 |
Release | : 2021-06-08 |
Genre | : Education |
ISBN | : 1470464330 |
Download Visual Group Theory Book in PDF, ePub and Kindle
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Author | : Giovanni Costa |
Publisher | : Springer |
Total Pages | : 300 |
Release | : 2012-02-03 |
Genre | : Science |
ISBN | : 3642154824 |
Download Symmetries and Group Theory in Particle Physics Book in PDF, ePub and Kindle
Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.