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Visual Group Theory
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.
Group Theory
This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The contents focus on the properties of groups, subgroups, cyclic groups, permutation groups, cosets and Lagrange’s theorem, normal subgroups and factor groups, group homomorphisms and isomorphisms, automorphisms, direct products, group actions and Sylow theorems. Pedagogical elements such as end of chapter exercises and solved problems are included to help understand abstract notions. Intermediate lemmas are also carefully designed so that they not only serve the theorems but are also valuable independently. The book is a useful reference to undergraduate and graduate students besides academics.
Landscape of 21st Century Mathematics
Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.
The Mathematical Artist
This book brings together the impact of Prof. John Horton Conway, the playful and legendary mathematician's wide range of contributions in science which includes research areas—Game of Life in cellular automata, theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. It contains transcripts where some eminent scientists have shared their first-hand experience of interacting with Conway, as well as some invited research articles from the experts focusing on Game of Life, cellular automata, and the diverse research directions that started with Conway's Game of Life. The book paints a portrait of Conway's research life and philosophical direction in mathematics and is of interest to whoever wants to explore his contribution to the history and philosophy of mathematics and computer science. It is designed as a small tribute to Prof. Conway whom we lost on April 11, 2020.
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Innovations in Mechatronics Engineering
This book covers a variety of topics in the field of mechatronics engineering, with a special focus on innovative control and automation concepts for applications in a wide range of field, including industrial production, medicine and rehabilitation, education and transport. Based on a set of papers presented at the 1st International Conference “Innovation in Engineering”, ICIE, held in Guimarães, Portugal, on June 28-30, 2021, the chapters report on cutting-edge control algorithms for mobile robots and robot manipulators, innovative industrial monitoring strategies for industrial process, improved production systems for smart manufacturing, and discusses important issues related to user experience, training and education, as well as national developments in the field of mechatronics . This volume, which belongs to a three-volume set, provides engineering researchers and professionals with a timely overview and extensive information on trends and technologies behind the future developments of mechatronics systems in the era of Industry 4.0.
Encyclopedia of Play in Today's Society
Selected as an Outstanding Academic Title by Choice Magazine, January 2010 The Encyclopedia of Play: A Social History explores the concept of play in history and modern society in the United States and internationally. Its scope encompasses leisure and recreation activities of children as well as adults throughout the ages, from dice games in the Roman empire to video games today. As an academic social history, it includes the perspectives of several curricular disciplines, from sociology to child psychology, from lifestyle history to social epidemiology. This two-volume set will serve as a general, non-technical resource for students in education and human development, health and sports psychology, leisure and recreation studies and kinesiology, history, and other social sciences to understand the importance of play as it has developed globally throughout history and to appreciate the affects of play on child and adult development, particularly on health, creativity, and imagination.
100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection
This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes. Stephan Ramon Garcia is WM Keck Distinguished Service Professor and professor of mathematics at Pomona College. He is the author of four books and over eighty research articles...
Iconic Designs
Iconic Designs is a beautifully designed and illustrated guide to fifty classic 'things' – designs that we find in the city, in our homes and offices, on page and screen, and in our everyday lives. In her introduction, Grace Lees-Maffei explores the idea of iconicity and what makes a design 'iconic', and fifty essays by leading design and cultural critics address the development of each iconic 'thing', its innovative and unique qualities, and its journey to classic status. Subjects range from the late 19th century to the present day, and include the Sydney Opera House, the Post-It Note, Coco Chanel's classic suit, the Sony WalkmanTM, Hello KittyTM, Helvetica, the Ford Model T, Harry Beck's diagrammatic map of the London Underground and the Apple iMac G3. This handsome volume provides a treasure trove of 'stories' that will shed new light on the iconic designs that we use without thinking, aspire to possess, love or hate (or love to hate) and which form part of the fabric of our everyday lives.
Childhood, Learning & Everyday Life in Three Asia-Pacific Cities
This book introduces findings from an international, cross-cultural, and interdisciplinary study of children’s everyday experiences of growing up and going to school in the context of the three global cities of Hong Kong, Singapore and Melbourne. It takes the premise that children’s learning and orientations to educational success are shaped by everyday cultural practices at home and at school, by policy contexts that both produce and respond to educational and cultural norms, and by individual and familial desires and aspirations. Drawing on research conducted with primary school-aged children in Year 4, the book considers how day-to-day routines such as going to school, engaging in ext...
