Download or read book Transformed Tower of Hanoi Mathematical Rules written by Jung Oh Choi and published by 최중오. This book was released on 2020-07-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transformed Tower of Hanoi is made by adding a condition to move a disc or by increasing the number of pegs. There are three ways to make Transformed Tower of Hanoi . ◇ Three ways ‣ Adding discs of the same size - In case that the number of discs with same size is all the same - In case that the number of discs with same size is different ‣ Adding moves condition of discs - Tower of Hanoi with Adjacency Requirement - Cyclic Tower of Hanoi ‣ Increase the number of pegs - Tower of Hanoi with 4 pegs or more - p-peg Tower of Hanoi

Download or read book Tower of Hanoi Mathematical Rules written by Jung oh Choi and published by 최중오. This book was released on 2020-07-09 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tower of Hanoi is a simple mathematical puzzle that finds the minimum number of moves to move all discs to another peg(column) under two conditions. But in Tower of Hanoi, which looks simple, you can find various mathematical rules. Also you can create some Transformed Tower of Hanoi by adding moving conditions of the disc or by increasing the number of pegs. I want to stress that finding rules and expressing them logically are different. Of course, you can only express the rules if you can find the rules of movement of the disc. Therefore, you should not stop by discovering the rules of the disc, but consider how to express the rules you have found. There are many other rules to be found in Tower of Hanoi besides the minimum number of movements. You can also know the minimum number of movements in which each disc has moved or you can explore the rules using binary. To do this, you must be able to understand and express ‘the rules of sequence’. If you can explore the rules of Tower of Hanoi, then you can also explore Transformed Tower of Hanoi. But you don’t have to rush. This is because you need to know the difficult sequence of rules, including recurrence formula, to explore Transformed Tower of Hanoi.

Download or read book The Concise Oxford Dictionary of Mathematics written by Richard Earl and published by Oxford University Press. This book was released on 2021-07-29 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: With over 4,000 entries, this informative A to Z provides clear, jargon-free definitions on a wide variety of mathematical terms. Its entries cover both pure and applied mathematics, and include key theories, concepts, methods, programmes, people, and terminology. For this sixth edition, around 800 new terms have been defined, expanding on the dictionary's coverage of topics such as algebra, differential geometry, algebraic geometry, representation theory, and statistics. Among this new material are articles such as cardinal arithmetic, first fundamental form, Lagrange's theorem, Navier-Stokes equations, potential, and splitting field. The existing entries have also been revised and updated to account for developments in the field. Numerous supplementary features complement the text, including detailed appendices on basic algebra, areas and volumes, trigonometric formulae, and Roman numerals. Newly added to these sections is a historical timeline of significant mathematicians lives and the emergence of key theorems. There are also illustrations, graphs, and charts throughout the text, as well as useful web links to provide access to further reading.

Download or read book Understanding and Enriching Problem Solving in Primary Mathematics written by Patrick Barmby and published by Critical Publishing. This book was released on 2014-05-19 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up to date book is essential reading for all those teaching or training to teach primary mathematics. Problem solving is a key aspect of teaching and learning mathematics, but also an area where teachers and pupils often struggle. Set within the context of the new primary curriculum and drawing on research and practice, the book identifies the key knowledge and skills required in teaching and learning problem solving in mathematics, and examines how these and can be applied in the classroom. It explores the issues in depth while remaining straightforward and relevant, emphasises the enrichment of maths through problem-solving, and provides opportunities for teachers to reflect on and further develop their classroom practice.

Download or read book Handbook of Learning and Cognitive Processes Volume 5 written by William K. Estes and published by Psychology Press. This book was released on 2014-06-20 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1978 Volume 5 of this Handbook reflects a single theoretical orientation, that characterized by the term human information processing in the literature at the time, but which ranges over a very broad spectrum of cognitive activities. The first two chapters give some overall picture of the background, goals, method, and limitations of the information-processing approach. The remaining chapters treat in detail some principal areas of application – visual processing, mental chronometry, representation of spatial information in memory, problem solving, and the theory of instruction. The first three volumes of the Handbook presented an overview of the field, followed by treatments of conditioning, behavior theory, and human learning and retention. With the fourth volume, the focus of attention shifted from the domain of learning theory to that of cognitive psychology.

Download or read book The Mathematics of Various Entertaining Subjects written by Jennifer Beineke and published by Princeton University Press. This book was released on 2019-08-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of mathematics is replete with examples of major breakthroughs resulting from solutions to recreational problems. The modern theory of probability arose out of problems of concern to gamblers, for example, and modern combinatorics grew out of various games and puzzles. Despite this track record and a wealth of popular-level books, there remain few conduits for research in recreational mathematics. The Mathematics of Various Entertaining Subjects now returns with an all-new third volume, presenting new research in diverse areas of recreational mathematics. This volume focuses on four areas: puzzles and brainteasers, games, algebra and number theory, and geometry and topology. Readers will create Spiral Galaxies, Japanese symmetric grid puzzles consisting of squares and circles whose solutions are letters and numbers; delve into a paradox in the game of Bingo; examine the card tricks of mathematician-philosopher Charles Sanders Peirce; learn about the mathematics behind Legos; and much more. Elucidating the many connections between mathematics and games, The Mathematics of Various Entertaining Subjects is sure to challenge and inspire mathematicians and math enthusiasts.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Download or read book Educate Train Transform Toolkit On Medical And Health Professions Education written by Dujeepa D Samarasekera and published by World Scientific. This book was released on 2021-04-21 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook contextualises medical and health professions education concepts using contemporary best evidence available with the relevant theoretical underpinnings.Each section is developed by internationally renowned experts in their respective fields. All chapters are succinct and concise, providing answers to everyday issues and challenges using practical solutions. Through its unique structure, this handbook facilitates learning by raising and providing solutions to the questions 'What', 'Why' and 'How'. It emphasises lifelong learning and future directions in medical and health professions education — highlighting trends, issues, priorities and strategies (TIPS).

Download or read book The Tower of Hanoi Myths and Maths written by Andreas M. Hinz and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Download or read book Mathematics From the Birth of Numbers written by Jan Gullberg and published by W. W. Norton & Company. This book was released on 1997-01-07 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.

Download or read book Advanced Calculus for Mathematical Modeling in Engineering and Physics written by David Stapleton and published by Elsevier. This book was released on 2024-06-20 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Calculus for Mathematical Modeling in Engineering and Physics introduces the principles and methods of advanced calculus for mathematical modeling, through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussion of how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script, in recognition of the rising importance of associated numerical models. - Adopts a state space/functional analysis approach to advanced calculus-based models to provide a better understanding of the development of models and the behaviors of their solutions - Uniquely includes discrete analogies to calculus-based models, as well as the derivation of many advanced calculus models of physics and engineering– instead of only seeking solutions to the models - Offers online teaching support for qualified instructors (for selected solutions) and study materials for students (MATLAB/Octave scripts)

Download or read book Transforming Education for Personalized Learning written by Munna, Afzal Sayed and published by IGI Global. This book was released on 2024-03-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pressing necessity to overhaul education systems to align with the demands of the contemporary world rises. Transforming Education for Personalized Learning delves into the imminent challenges besieging education, offering pragmatic solutions to metamorphose classrooms into dynamic learning environments with research, real-world illustrations, and expert perspectives. It scrutinizes fundamental shifts required in pedagogical methods, curriculum construction, assessment frameworks, and the judicious integration of technology. Central to its philosophy is the accentuation of personalized learning, the cultivation of critical thinking, and the nurturing of creativity and collaboration among students. Emphasizing an inclusive and equitable educational system, the book discerns the varied needs and strengths of learners. It advocates for a future where educators evolve into facilitators of learning, armed with strategies to adapt teaching styles, embrace innovative pedagogies, and craft engaging and purposeful learning experiences. It underscores the imperative for a paradigm shift in education, cognizant of the demands of the 21st century. It advocates for personalized learning approaches that cater to individual strengths, interests, and learning styles. The book also explores innovative teaching methodologies, instructional design, and the effective integration of technology to enhance critical thinking, collaboration, and creativity. The book targets educators, school leaders, policymakers, teacher educators, parents, educational researchers, students, professional development providers, educational consultants, advocacy groups, and non-profits.

Download or read book Five Golden Rules written by John Casti and published by . This book was released on 1996 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Five Golden Rules, John L. Casti serves as curator to a brilliant collection of 20th-century mathematical theories, leading us on a fascinating journey of discovery and insight. Probing the frontiers of modern mathematics, Casti examines the origins of some of the most important findings of this century. This is a tale of mystery and logic, elegance and reason; it is the story of five monumental mathematical breakthroughs and how they shape our lives. All those intrigued by the mathematical process, nonacademics and professionals alike, will find this an enlightening, eye-opening, and entertaining work. High school algebra or geometry - and enthusiasm - are the only prerequisites. From the theorem that provided the impetus for modern computers to the calculations that sent the first men to the Moon, these breakthroughs have transformed our lives. Casti illustrates each theorem with a dazzling array of real-world problems it has helped solve - how to calculate the shape of space, optimize investment returns, even chart the course of the development of organisms. Along the way, we meet the leading thinkers of the day: John von Neumann, L. E. J. Brouwer, Marston Morse, and Alan Turing, among others. And we come to understand the combination of circumstances that led each to such revolutionary discoveries as the Minimax Theorem, which spawned the exciting field of game theory, and the Simplex Method, which underpins the powerful tools of optimization theory.

Download or read book Ebook Essentials of Understanding Psychology written by Feldman and published by McGraw Hill. This book was released on 2016-09-16 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ebook: Essentials of Understanding Psychology

Download or read book Handbook of Discrete and Combinatorial Mathematics written by Kenneth H. Rosen and published by CRC Press. This book was released on 1999-09-28 with total page 1252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.

Download or read book Computing Possible Futures written by William B. Rouse and published by Oxford University Press, USA. This book was released on 2019-09-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modelling and simulation is an increasingly powerful area of mathematics and computer science, which in recent years has been fuelled by the unprecedented access to larger than ever stores of data. These techniques have an increasing number of applications in the professional and political spheres, and people try to predict the results of certain courses of action as accurately as possible. Computing Possible Futures explores the use of models on everyday phenomena such as waiting in lines and driving a car, before expanding the model's complexity to look at how large-scale computational models can help imagine big scale "what-if" scenarios like the effect self-driving cars on the US economy. The successes and failures of complex real world problems are examined, and it is shown how few, if any, failures are due to model errors or computational difficulties. It is also shown how real life decision makers have addressed important problems and used their model-based understanding of possible futures to inform these decisions. Written in an entertaining and accessible way, Computing Possible Futures will help those concerned about the futurity of their decisions to understand what fundamentally needs to be done, why it needs to be done, and how to do it.

Download or read book Math from Three to Seven written by Aleksandr K. Zvonkin and published by American Mathematical Soc.. This book was released on 2011 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).