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Ants, Bikes, and Clocks: Problem Solving for Undergraduates [Paperback]

William Briggs (Author)
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

0898715741 978-0898715743 January 1, 2004
Mathematics educators agree that problem solving is one of the essential skills their students should possess, yet few mathematics courses or textbooks are devoted entirely to developing this skill. Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. The book, which provides hundreds of mathematical problems, gives special emphasis to problems in context, often called story problems or modeling problems, that require mathematical formulation as a preliminary step. Both analytical and computational approaches, as well as the interplay between them, are included. This engaging book will strengthen students' mathematical skills, introduce them to new mathematical ideas, demonstrate the connectedness of mathematics, and improve both their analytical and computational problem solving. Students are encouraged to use the computer, or any tool at hand, for experimentation or to test their ideas.

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Editorial Reviews

Review

‘Briggs's book is in some sense an update of Polya's classic, How to Solve It. Certainly Briggs pays due homage to the master, cites his four main principles of problem solving, and organizes his text in a manner that at least pays homage to Polya. But Briggs goes much further. His writing style is lively and attractive. He gets in the reader's face and stays in his/her face from page one. He does this in a friendly way, one that gets the reader involved and keeps him/her involved as the work progresses. …The student will be carried along by this book, and ever anxious to learn the next new idea. I like Briggs's book so well that I would certainly make considerable use of his text the next time that I teach problem-solving.’ Steven G. Krantz, Washington University in St. Louis

‘More than 50 years ago, G. Polya wrote a book on problem solving strategies which became very popular, How to Solve It. Briggs's book is not intended to replace, but rather to complement Polya's classic book. For example, not only are Polya's principles of analytical problem solving cited and discussed in Briggs's book, but they are also adapted to computational problems. In fact, the interplay between the analytical and computational approaches to problem solving is very useful since computers became part of our daily lives. … In summary, this is an excellent and opportune book about problem solving, not only for undergraduates, but for everyone who is interested in problem solving strategies.’ Eduardo Abreu, Department of Orthopaedic Surgery, Childrens' Hospital of Boston, BioMedical Engineering

‘It is the problems that make this book worth a look. Nearly every mathematical puzzle that I can recall is represented in this book. If you believe (as I do) that problem solving can only be learned by solving problems, then this is the book for you.’ Dr Jeffrey A. Graham, Asst. Professor of Mathematical Sciences, Susquehanna University, MAA Reviews

Book Description

Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. This book, which provides hundreds of mathematical problems, demonstrates the connectedness of mathematics, and improves students analytical and computational problem solving.

Product Details

  • Paperback: 174 pages
  • Publisher: SIAM: Society for Industrial and Applied Mathematics (January 1, 2004)
  • Language: English
  • ISBN-10: 0898715741
  • ISBN-13: 978-0898715743
  • Product Dimensions: 9.8 x 6.9 x 0.3 inches
  • Shipping Weight: 11.4 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,040,612 in Books (See Top 100 in Books)

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1 of 1 people found the following review helpful:
5.0 out of 5 stars Challenging and fun applied math problems, August 4, 2007
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science-buff (Fremont, CA, USA) - See all my reviews
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This review is from: Ants, Bikes, and Clocks: Problem Solving for Undergraduates (Paperback)
This is a wonderful collection of applied math problems from diverse sources used to illustrate the mathematical problem solving process. The beauty of this book is the liberal use of math problems of the applied variety such as the following:

(Problem 6.26) Ants on a stick: One hundred ants are placed on a stick that is one meter in length. Each ant crawls to either the left or the right with a constant speed of 1 meter per minute. When 2 ants meet, they bounce off each other and reverse direction. When an ant reaches an end of the stick, it falls off. What is the maximum amount of time you would need to wait for all of the ants to fall off the stick?

(Problem 6.15) Bike race: Two cyclists racing on parallel roads maintain constant speeds of 30mph and 25 mph. The faster cyclist crosses the finish line one hour before the slower cyclist. How long was the race (in miles)?

(Problem 1.15) Chiming clock: If a clock takes 5 seconds to strike 5:00 (chiming 5 times), how long does it take to strike 10:00 (chiming 10 times)? Assume that the chimes occur instantaneously.

The book, like other SIAM series books, is a bit pricey at 168 pages. But if you like challenging applied math problems, it's worth it.
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5.0 out of 5 stars great collections of thought provoking problems., July 17, 2008
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This review is from: Ants, Bikes, and Clocks: Problem Solving for Undergraduates (Paperback)
the book is thin but full of flesh.
i did not finish it yet, but i can tell you the first chapter worth the price.
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Inside This Book (learn more)
First Sentence:
For students of mathematics, science, and engineering, the name of the game is problem solving. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
left pan drops, untested coins, hat derivatives, third weighing, percent alcohol solution, test coins, blind prisoner, random chord, second weighing, lump sum option, pan rises, remaining flasks, positive mammogram, dart lands, current tuition, runners pass, annuity option, needle problem, red pair, pursuit problem, first weighing, pans balance, outflow rate, hiring rate, pink book
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New Jersey, Lewis Carroll, Black Brown White Total Left, Follow Example, University of Colorado
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