Problem Solving Through Recreational Mathematics

Last updated
Problem Solving Through Recreational Mathematics
Problem Solving Through Recreational Mathematics.jpg
Author Bonnie Averbach and Orin Chein
GenreMathematics
Publisher W. H. Freeman and Company
Publication date
1980

Problem Solving Through Recreational Mathematics is a textbook in mathematics on problem solving techniques and their application to problems in recreational mathematics, intended as a textbook for general education courses in mathematics for liberal arts education students. It was written by Bonnie Averbach and Orin Chein, published in 1980 by W. H. Freeman and Company, and reprinted in 2000 by Dover Publications.

Contents

Audience and reception

Problem Solving Through Recreational Mathematics is based on mathematics courses taught by the authors, who were both mathematics professors at Temple University. [1] [2] It follows a principle in mathematics education popularized by George Pólya, of focusing on techniques for mathematical problem solving, motivated by the idea that by doing mathematics rather than being told about its "history, culture, or applications", liberal arts education students (for whom this might be their only college-level mathematics course) can gain a better idea of the nature of mathematics. [1] [3] By concentrating on problems in recreational mathematics, Averbach and Chein hope to motivate students by the fun aspect of these problems. However, this approach may also lead the students to lose sight of the important applications of the mathematics they learn, [3] and contains little to no material on mathematical proof. [2] [4]

The book's exercises include some with detailed solutions, some with less-detailed answers, and some that provide only hints to the solution, providing flexibility to instructors in using this book as a textbook. [1] [5] Cartoons and other illustrations of the concepts help make the material more inviting to students. [1]

As well as for general education at the college level, this book could also be used to help prepare students going into mathematics education, [1] and for mathematics appreciation for secondary school students. It could also be used as a reference by secondary school mathematics teachers in providing additional examples for their students, [5] [6] or as personal reading for anyone teenaged or older who is interested in mathematics. [6] Alternatively, reviewer Murray Klamkin suggests using the books of Polyá for these purposes, but adding Problem Solving Through Recreational Mathematics as a supplement to these books. [3]

Topics

The book begins with an introductory chapter on problem-solving techniques in general, [4] including six problems to motivate these techniques. [1] The rest of the book is organized into eight thematic chapters, each of which can stand alone or be read in an arbitrary order. [3] [4] The topics of these chapters are:

Related Research Articles

<span class="mw-page-title-main">George Pólya</span> Hungarian mathematician (1887–1985)

George Pólya was a Hungarian-American mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, an informal category which included one of his most famous students at ETH Zurich, John von Neumann.

Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research- and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults and inspiring their further study of the subject.

<i>How to Solve It</i> Book by George Pólya

How to Solve It (1945) is a small volume by mathematician George Pólya, describingmethods of problem solving.

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle.

Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics.

<i>Sideways Arithmetic from Wayside School</i> 1989 novel by Louis Sachar

Sideways Arithmetic From Wayside School is a children's novel by Louis Sachar in the Wayside School series. The book contains mathematical and logic puzzles for the reader to solve, presented as what The New Yorker called "absurdist math problems." The problems are interspersed with characteristically quirky stories about the students at Wayside School.

<i>General Relativity</i> (book) 1984 graduate textbook by Robert M. Wald

General Relativity is a graduate textbook and reference on Albert Einstein's general theory of relativity written by the gravitational physicist Robert Wald.

<i>Principles of Electronics</i> Textbook for the Electronics Technician distance education program

Principles of Electronics is a 2002 book by Colin Simpson designed to accompany the Electronics Technician distance education program and contains a concise and practical overview of the basic principles, including theorems, circuit behavior and problem-solving procedures of Electronic circuits and devices. The textbook reinforces concepts with practical "real-world" applications as well as the mathematical solution, allowing readers to more easily relate the academic to the actual.

A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.

Ross Honsberger (1929–2016) was a Canadian mathematician and author on recreational mathematics.

<i>Chases and Escapes</i> Mathematics book on pursuit-evasion games

Chases and Escapes: The Mathematics of Pursuit and Evasion is a mathematics book on continuous pursuit–evasion problems. It was written by Paul J. Nahin, and published by the Princeton University Press in 2007. It was reissued as a paperback reprint in 2012. The Basic Library List Committee of the Mathematical Association of America has rated this book as essential for inclusion in undergraduate mathematics libraries.

<i>In Pursuit of the Traveling Salesman</i> 2011 book by William J. Cook

In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. Cook, published in 2011 by the Princeton University Press, with a paperback reprint in 2014. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.

<i>Taking Sudoku Seriously</i> 2011 book about sudoku

Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. It was the 2012 winner of the PROSE Awards in the popular science and popular mathematics category.

Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year.

<i>The Tower of Hanoi – Myths and Maths</i>

The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.

<i>Polyominoes: Puzzles, Patterns, Problems, and Packings</i> Book on shapes formed from squares

Polyominoes: Puzzles, Patterns, Problems, and Packings is a mathematics book on polyominoes, the shapes formed by connecting some number of unit squares edge-to-edge. It was written by Solomon Golomb, and is "universally regarded as a classic in recreational mathematics". The Basic Library List Committee of the Mathematical Association of America has strongly recommended its inclusion in undergraduate mathematics libraries.

<i>Graph Theory, 1736–1936</i>

Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig. Graph Theory, 1736–1936 was edited by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson, and published in 1976 by the Clarendon Press. The Oxford University Press published a paperback second edition in 1986, with a corrected reprint in 1998.

Bonnie Averbach was an American mathematics and actuarial science educator who worked for many years on the faculty of Temple University and was known for her books in mathematics.

<i>Extrinsic Geometric Flows</i> Geometry textbook

Extrinsic Geometric Flows is an advanced mathematics textbook that overviews geometric flows, mathematical problems in which a curve or surface moves continuously according to some rule. It focuses on extrinsic flows, in which the rule depends on the embedding of a surface into space, rather than intrinsic flows such as the Ricci flow that depend on the internal geometry of the surface and can be defined without respect to an embedding.

Problems and Theorems in Analysis is a two-volume problem book in analysis by George Pólya and Gábor Szegő. Published in 1925, the two volumes are titled (I) Series. Integral Calculus. Theory of Functions.; and (II) Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry.

References

  1. 1 2 3 4 5 6 7 8 9 10 Dees, Roberta L. (November 1981), "Review of Problem Solving Through Recreational Mathematics", The Arithmetic Teacher, 29 (3): 54–55, JSTOR   41190004
  2. 1 2 Wolfe, Hugh C. (May 1981), "Review of Problem Solving Through Recreational Mathematics", Physics Today , 34 (5): 84–84, Bibcode:1981PhT....34e..84A, doi:10.1063/1.2914582
  3. 1 2 3 4 Klamkin, Murray S. (March 1983), "Review of Problem Solving Through Recreational Mathematics", The American Mathematical Monthly , 90 (3): 216–218, doi:10.2307/2975564, JSTOR   2975564
  4. 1 2 3 4 5 6 7 8 9 Mortimer, Mike (January 1982), "Review of Problem Solving Through Recreational Mathematics", Mathematics in School, 11 (1): 35, JSTOR   30213691
  5. 1 2 King, Richard H. (April 1981), "Review of Problem Solving Through Recreational Mathematics", The Mathematics Teacher , 74 (4): 301–302, JSTOR   27962454
  6. 1 2 3 4 5 6 7 8 Austin, Keith (March 1982), "Review of Problem Solving Through Recreational Mathematics", The Mathematical Gazette , 66 (435): 71–72, doi:10.2307/3617323, JSTOR   3617323
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.