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This book is composed of the most interesting problems from a quarter century of regional mathematics competitions for students aged 11-14 in the province of Styria, Austria. The problems presented here range from pure puzzles to a more traditional mathematical type of question, but all are somehow special, posed with the intent of giving the reader something interesting to think about, with the promise of an entertaining moment of elucidation and enlightenment at the end.
Mathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10-20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.
Can we correctly predict the flip of a fair coin more than half the time — or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50-50 guesses.But mathematics is filled with counterintuitive results — and this book discusses some surprising and entertaining examples. It is possible to devise experiments in which a flipped coin lands heads completely at random half the time, but we can also correctly predict when it will land heads more than half the time. The Fate of Schrodinger's Cat shows how high-school algebra and basic probability theory, with the invaluable assistance of computer simulations, can be used to investigate both the intuitive and the counterintuitive.This book explores fascinating and controversial questions involving prediction, decision-making, and statistical analysis in a number of diverse areas, ranging from whether there is such a thing as a 'hot hand' in shooting a basketball, to how we can successfully predict, more than half the time, the decay of the radioactive atom that determines the fate of Schrodinger's Cat.
Sports analytics has gathered tremendous momentum as one of the most dynamic fields. Diving deep into the numbers of sports can be game changing or simply a fun exercise for fans. How do you get in the game with numbers? What questions can be explored? What actionable insights can be gleaned?Do you like sports? This book will detail ways to analyze athletics to gain insight that can otherwise be obscured. Like math? You'll find many mathematical topics not involving sports. You'll also see how sports analytics can train you broadly in mathematics.From coaching at the highest levels to national media broadcasts, analytics are becoming increasingly indispensable. Dive into the numbers behind soccer to basketball to baseball to boxing to swimming, dive into the numbers. Learn how to get in the game with sports and mathematics.
David Singmaster believes in the presentation and teaching of mathematics as recreation. When the Rubik's Cube took off in 1978, based on thinly disguised mathematics, he became seriously interested in mathematical puzzles which would provide mental stimulation for students and professional mathematicians. He has not only published the standard mathematical solution for the Rubik's cube still in use today, but he has also become the de facto scribe and noted chronicler of the recreational mathematics puzzles themselves.Dr Singmaster is also an ongoing lecturer of recreational mathematics around the globe, a noted mechanical puzzle collector, owner of thousands of books related to recreational mathematical puzzles and the 'go to' source for the history of individual mathematical puzzles.This set of two books provides readers with an adventure into previously unknown origins of ancient puzzles, which could be traced back to their Medieval, Chinese, Arabic and Indian sources. The puzzles are fully described, many with illustrations, adding interest to their history and relevance to contemporary mathematical concepts. These are musings of a respected historian of recreational mathematics.
This book contains the most interesting problems from the first 24 years of the 'Mathematical Duel', an annual international mathematics competition between the students of four schools: the Gymnázium Mikuláše Koperníka in Bílovec, Czech Republic, the Akademicki Zespół Szkół Ogólnokształcących in Chorzów, Poland, the Bundesrealgymnasium Kepler in Graz, Austria and the Gymnázium Jakuba Škody in Přerov, Czech Republic.The problems are presented by topic, grouped under the headings Geometry, Combinatorics, Number Theory and Algebra, which is typical for olympiad-style competitions.Above all, it is of interest to students preparing for mathematics competitions as well as teachers looking for material to prepare their students, as well as mathematically interested enthusiasts from all walks of life looking for an intellectual challenge.
The art or skill of problem solving in mathematics is mostly relegated to the strategies one can use to solve problems in the field. Although this book addresses that issue, it delves deeply into the psychological aspects that affect successful problem-solving. Such topics as decision-making, judgment, and reasoning as well as using memory effectively and a discussion of the thought processes that could help address certain problem-solving situations.Most books that address problem-solving and mathematics focus on the various skills. This book goes beyond that and investigates the psychological aspects to solving problems in mathematics.
This book gathers 22 papers which were presented at the 6th International Symposium of the ICA Commission on the History of Cartography in Dubrovnik, Croatia on 13–15 October 2016. The overall conference theme was ‘The Dissemination of Cartographic Knowledge: Production – Trade – Consumption – Preservation’. The book presents original research by internationally respected authors in the field of historical cartography, offering a significant contribution to the development of this field of study, but also of geography, history and the GIS sciences. The primary target audience includes researchers, educators, postgraduate students, map librarians and archivists.
This book defines and discusses the term “hidden geographies” in two ways: systematically and by presenting a variety of examples of the research fields and topics concerning hidden geographies, with the aim of stimulating further basic and applied research in this area. While the term is quite rarely used in the scientific literature (more often as a figure of speech than to illustrate or problematize its deeper meaning), we argue that hidden geographies are everywhere and many of them have significant impacts on (other) natural and social phenomena and processes, subsequently triggering changes, for example in landscape, economy, culture, health or quality of life. The introductory section of the book conceptualises hidden geographies and discusses cognitive geography, symbolization of space, and the hidden geographies in mystical literature. Case studies of hidden environmental geographies address soils, air pollution, coastal pollution and the allocation of an astronomical tourism site. Revealing hidden historical and sacred places is illustrated through examples of the visualisation of the subterranean mining landscape, the analysis of the historical road network and trade, border stones and historical spatial boundaries, and the monastic Carthusian space. Hidden urban geographies are discussed in terms of the urban development of an entire city, presenting the role of geography in rescuing architecture, revealing illegal urbanisation, and the quality of habitation in Roma neighbourhoods. Case studies of hidden population geographies shed light on the ageing of rural populations and the impact of spatial-demographic disparities on fertility variations. Discussions of hidden social and economic geographies problematize recent social changes and conflicts in a country, present the implementation of the fourth industrial revolution and borders as hidden obstacles in the organisation of public transport. Hidden geographies are explicitly linked to perceptions and explanations in case studies that address local responses to perceived marginalisation in a city, the solo women travellers’ perceived risk and safety, and hidden geographical contexts of visible post-war landscapes. The book brings such a diversity of views, ideas and examples related to hidden geographies that can serve both to deepen their understanding and their various impacts on our lives and environment, and to attract further cross-disciplinary interest in considering hidden geographies – in research and in our every-day lives.