Problem Solving in Mathematics and Beyond – serie

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.

The two volumes of Engaging Young Students in Mathematics through Competitions present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume I contains a wide variety of fascinating mathematical problems of the type often presented at mathematics competitions as well as papers by an international group of authors involved in problem development, in which we can get a sense of how such problems are created in various specialized areas of competition mathematics as well as recreational mathematics.It will be of special interest to anyone interested in solving original mathematics problems themselves for enjoyment to improve their skills. It will also be of special interest to anyone involved in the area of problem development for competitions, or just for recreational purposes.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018.

The two volumes of Engaging Young Students in Mathematics through Competitions present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume I contains a wide variety of fascinating mathematical problems of the type often presented at mathematics competitions as well as papers by an international group of authors involved in problem development, in which we can get a sense of how such problems are created in various specialized areas of competition mathematics as well as recreational mathematics.It will be of special interest to anyone interested in solving original mathematics problems themselves for enjoyment to improve their skills. It will also be of special interest to anyone involved in the area of problem development for competitions, or just for recreational purposes.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018.

"The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers."CHOICEImmerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.

The two volumes of "Engaging Young Students in Mathematics through Competitions" present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more.It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018.

The two volumes of "Engaging Young Students in Mathematics through Competitions" present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more.It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018.

The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.

Suppose you have five muffins that you want to divide and give to Alice, Bob, and Carol. You want each of them to get 5/3. You could cut each muffin into 1/3-1/3-1/3 and give each student five 1/3-sized pieces. But Alice objects! She has large hands! She wants everyone to have pieces larger than 1/3.Is there a way to divide five muffins for three students so that everyone gets 5/3, and all pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a division where the smallest piece is 5/12. Is there a better division? Spoiler alert: No.In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up m muffins for s students so that everyone gets m/s muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.This problem takes us through much mathematics of interest, for example, combinatorics and optimization theory. However, the math is elementary enough for an advanced high school student.

Suppose you have five muffins that you want to divide and give to Alice, Bob, and Carol. You want each of them to get 5/3. You could cut each muffin into 1/3-1/3-1/3 and give each student five 1/3-sized pieces. But Alice objects! She has large hands! She wants everyone to have pieces larger than 1/3.Is there a way to divide five muffins for three students so that everyone gets 5/3, and all pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a division where the smallest piece is 5/12. Is there a better division? Spoiler alert: No.In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up m muffins for s students so that everyone gets m/s muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.This problem takes us through much mathematics of interest, for example, combinatorics and optimization theory. However, the math is elementary enough for an advanced high school student.

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.

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.

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.

"The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers."CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

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.

"The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers."CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

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.

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.

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.

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.

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.

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.

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.

In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters.The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college.We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of "noise." With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.

In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters.The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college.We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of "noise." With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.