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Discovering Group Theory
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Book Synopsis Discovering Group Theory by : Tony Barnard
Download or read book Discovering Group Theory written by Tony Barnard and published by CRC Press. This book was released on 2016-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
Book Synopsis Discovering Group Theory by : Tony Barnard
Download or read book Discovering Group Theory written by Tony Barnard and published by CRC Press. This book was released on 2016-12-19 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
Book Synopsis Discovering Modern Set Theory. I: The Basics by : Winfried Just
Download or read book Discovering Modern Set Theory. I: The Basics written by Winfried Just and published by American Mathematical Soc.. This book was released on 1996 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Book Synopsis Groups and Symmetry: A Guide to Discovering Mathematics by : David W. Farmer
Download or read book Groups and Symmetry: A Guide to Discovering Mathematics written by David W. Farmer and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Visual Group Theory by : Stephan Rosebrock
Download or read book Visual Group Theory written by Stephan Rosebrock and published by Springer Nature. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A First Course in Group Theory by : Bijan Davvaz
Download or read book A First Course in Group Theory written by Bijan Davvaz and published by Springer Nature. This book was released on 2021-11-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Book Synopsis A Book of Abstract Algebra by : Charles C Pinter
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Book Synopsis Discovering Mathematics with Magma by : Wieb Bosma
Download or read book Discovering Mathematics with Magma written by Wieb Bosma and published by Springer Science & Business Media. This book was released on 2007-07-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.
Book Synopsis Groups and Symmetry by : Mark A. Armstrong
Download or read book Groups and Symmetry written by Mark A. Armstrong and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Groups and Symmetry by : Bijan Davvaz
Download or read book Groups and Symmetry written by Bijan Davvaz and published by Springer Nature. This book was released on 2021-11-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Book Synopsis Pure Math: Discovering the Beauty of Abstract Mathematics by : Lexa N. Palmer
Download or read book Pure Math: Discovering the Beauty of Abstract Mathematics written by Lexa N. Palmer and published by Book Lovers HQ. This book was released on 2024-09-30 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure Math: Discovering the Beauty of Abstract Mathematics offers a unique approach to exploring the captivating world of pure mathematics. It's where logic meets imagination, and abstract thought gives rise to profound beauty. This book takes you beyond the formulas and calculations, uncovering the hidden elegance that lies at the heart of mathematical structures, patterns, and theories. From the concept of infinity to symmetry in group theory, this book delves into the core ideas of pure math that have fascinated thinkers for centuries. You’ll discover the aesthetic appeal of mathematical proofs, each one a treasure waiting to be unearthed, explore the intricate relationships in number theory, and journey through the strange worlds of non-Euclidean geometry and topology. Whether you're intrigued by the mysteries of prime numbers or the paradoxes that challenge conventional logic, Pure Math illuminates these abstract concepts in a way that is both engaging and intellectually stimulating. Written for those who appreciate the beauty of ideas, this book is a celebration of the intellectual creativity that drives pure mathematics. It's perfect for mathematicians, students, and curious readers who want to see math as more than a tool for problem-solving. It’s a testament to the wonder that can be found in abstract reasoning. What you will find in this book: The concept of infinity and its role in set theory and calculus The elegance of mathematical proofs and the joy of discovering them Patterns and symmetry in number theory, geometry, and algebra Paradoxes that challenge the boundaries of logic and intuition The philosophical implications of pure mathematics as a universal language Exploration of the beauty and complexity found in abstract mathematical structures Embark on a fascinating journey into the depths of pure mathematics and discover a new way of thinking about the world around you!
Book Synopsis Discovering the Principles of Mechanics 1600-1800 by : David Speiser
Download or read book Discovering the Principles of Mechanics 1600-1800 written by David Speiser and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book assembles 21 essays on the history of mechanics and mathematical physics written by David Speiser. Covering a period from the beginning of the seventeenth century to the eighteenth, the essays discuss developments in elasticity, rigid bodies, gravitation, the principle of relativity, optics, and first principles. They examine the work of Galileo, Huygens, Newton, Leibniz, the Bernoullis, Euler, Maupertuis, and Lambert.
Book Synopsis Combinatorial Group Theory, Discrete Groups, and Number Theory by : Benjamin Fine
Download or read book Combinatorial Group Theory, Discrete Groups, and Number Theory written by Benjamin Fine and published by American Mathematical Soc.. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.
Book Synopsis Exploring University Mathematics with Python by : Siri Chongchitnan
Download or read book Exploring University Mathematics with Python written by Siri Chongchitnan and published by Springer Nature. This book was released on 2023-12-01 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique tour of university mathematics with the help of Python. Written in the spirit of mathematical exploration and investigation, the book enables students to utilise Python to enrich their understanding of mathematics through: Calculation: performing complex calculations and numerical simulations instantly Visualisation: demonstrating key theorems with graphs, interactive plots and animations Extension: using numerical findings as inspiration for making deeper, more general conjectures. This book is for all learners of mathematics, with the primary audience being mathematics undergraduates who are curious to see how Python can enhance their understanding of core university material. The topics chosen represent a mathematical overview of what students typically study in the first and second years at university, namely analysis, calculus, vector calculus and geometry, differential equations and dynamical systems, linear algebra, abstract algebra and number theory, probability and statistics. As such, it can also serve as a preview of university mathematics for high-school students. The prerequisites for reading the book are a familiarity with standard A-Level mathematics (or equivalent senior high-school curricula) and a willingness to learn programming. For mathematics lecturers and teachers, this book is a useful resource on how Python can be seamlessly incorporated into the mathematics syllabus, assuming only basic knowledge of programming.
Book Synopsis A Book of Set Theory by : Charles C Pinter
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Book Synopsis A Tour through Graph Theory by : Karin R Saoub
Download or read book A Tour through Graph Theory written by Karin R Saoub and published by CRC Press. This book was released on 2017-11-02 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course. Employs graph theory to teach mathematical reasoning Expressly written for non-mathematical students Promotes critical thinking and problem solving Provides rich examples and clear explanations without using proofs
Book Synopsis An Introduction to Number Theory with Cryptography by : James Kraft
Download or read book An Introduction to Number Theory with Cryptography written by James Kraft and published by CRC Press. This book was released on 2018-01-29 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.
