Problem-Solving Strategies

Problem-Solving Strategies
Author: Arthur Engel
Publisher: Springer Science & Business Media
Total Pages: 404
Release: 2008-01-19
Genre: Mathematics
ISBN: 0387226419

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Problem-Solving Through Problems

Problem-Solving Through Problems
Author: Loren C. Larson
Publisher: Springer Science & Business Media
Total Pages: 322
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461254981

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

The Art of Problem Solving, Volume 1

The Art of Problem Solving, Volume 1
Author: Sandor Lehoczky
Publisher: Mitchell Beazley
Total Pages: 0
Release: 2006
Genre: Mathematics
ISBN: 9780977304561

" ... offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover

A First Course in Real Analysis

A First Course in Real Analysis
Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
Total Pages: 249
Release: 2012-09-10
Genre: Mathematics
ISBN: 1441985484

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

A Problem Seminar

A Problem Seminar
Author: D.J. Newman
Publisher: Springer Science & Business Media
Total Pages: 118
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461382149

There was once a bumper sticker that read, "Remember the good old days when air was clean and sex was dirty?" Indeed, some of us are old enough to remember not only those good old days, but even the days when Math was/un(!), not the ponderous THEOREM, PROOF, THEOREM, PROOF, . . . , but the whimsical, "I've got a good prob lem. " Why did the mood change? What misguided educational philoso phy transformed graduate mathematics from a passionate activity to a form of passive scholarship? In less sentimental terms, why have the graduate schools dropped the Problem Seminar? We therefore offer "A Problem Seminar" to those students who haven't enjoyed the fun and games of problem solving. CONTENTS Preface v Format I Problems 3 Estimation Theory 11 Generating Functions 17 Limits of Integrals 19 Expectations 21 Prime Factors 23 Category Arguments 25 Convexity 27 Hints 29 Solutions 41 FORMAT This book has three parts: first, the list of problems, briefly punctuated by some descriptive pages; second, a list of hints, which are merely meant as words to the (very) wise; and third, the (almost) complete solutions. Thus, the problems can be viewed on any of three levels: as somewhat difficult challenges (without the hints), as more routine problems (with the hints), or as a textbook on "how to solve it" (when the solutions are read). Of course it is our hope that the book can be enjoyed on any of these three levels.

Street-Fighting Mathematics

Street-Fighting Mathematics
Author: Sanjoy Mahajan
Publisher: MIT Press
Total Pages: 152
Release: 2010-03-05
Genre: Education
ISBN: 0262265591

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Industrial Colonies and Village Settlements for the Consumptive (Classic Reprint)

Industrial Colonies and Village Settlements for the Consumptive (Classic Reprint)
Author: German Woodhead
Publisher: CUP Archive
Total Pages: 172
Release: 2018-01-19
Genre: Social Science
ISBN:

Excerpt from Industrial Colonies and Village Settlements for the Consumptive Symonds, and we together examined the patients, sampled the climate and other conditions, and argued with Unger and Ruedi. Then for the second time came Hope; more solid Hope. Given a fairly early case, and three years, and recovery was in the offing. And so we went on cheerfully with Davos. But Davos was not for every one; nor was every case an early 'one. Then came the discovery that lower altitudes would do if certain conditions were obtained; and so arose the great sanatorium movement. But slowly we found that patients could not spend their lives in sanatoriums; and one day on making my way up to one of them in England, I met on the way patient after patient, slouching along, bored to death with themselves and with each other; and even worse in morale than in body. Better discipline and better notions of thera peutics mended some of that; still I could not forget those listless saunterers, and it became evident to some of us, however unwillingly, that Hope was drooping again. The sanatorium was doing a great educative work no doubt; but at the end of its four or six months - what then? To send the patient away with recommendations about light jobs, and a regime, was almost a mockery or quite. What about the wage, and the family to be supported? The next lesson was brought home to me by a visit with other commissioners to certain cities, concerning some such problems. Before me now I see a gaunt hollow-eyed man, coughing, and leaning against the wall as he tried to talk to us, saying that his mates when he came out of the sanatorium - good fellows as they were - had bought him a milk that he might creep round, and earn a bit. The brave wife, shawl on head and mill apron on, had just come from the factory, and apologised for the dirty house - as well she might. The poor thing was working all day at the factory to keep the wolf from the door. All being dragged down together into the pit! What is the value of a good house, or a clean house, if no wages! What is there for the children? And what is to stop the infection! Who then would have the imagination, the initiative, the business capacity, to lift this burden, like lifting a world? About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The Rescued Dog Problem Solver

The Rescued Dog Problem Solver
Author: Tracy J. Libby
Publisher: Fox Chapel Publishing
Total Pages: 313
Release: 2014-10-21
Genre: Pets
ISBN: 1621870987

The tides of dog ownership are changing, and thanks to Hollywood A-Listers like George Clooney and Sandra Bullock and music icons like Justin Bieber and Taylor Swift, animal rescue has become as fashionable as the latest Valentino or Armani. Millions of ordinary Americans—heroes one and all—have opened their hearts and homes to rescue dogs, and fewer abandoned pets are euthanized in the U.S. than ever before. And still, a look at HSUS statistics reminds us how far we have to go: an estimated three to four million pets are euthanized annually, a very significant improvement from the 1980s when the number was closer to sixteen million.To keep America's adoption trend moving forward and to guarantee that rescued dogs stay in their new forever homes, Tracy Libby's The Rescue Dog Problem Solver seeks to make the story of every adopted dog a predestined success. While most dogs wind up in shelters due to no fault of their own, many rescue dogs develop unwanted behaviors while living with their previous owners. To assure their success with their adopted dogs, rescuers must be prepared to handle and confidently resolve behavioral problems that arise through proven positive-training methods. This eye-opening problem-solving guide, filled with empowering stories of rescued dogs that defied the odds, is dedicated to the success of every rescuer and his happy, health companion dog.INSIDE TITLE OF BOOK50 ways rescuers can overcome potential challenges with their adoptive dogs200 training and behavior tips for a well-mannered dog25 secrets to unraveling common behavior issues, from house-soiling and escaping the yard to biting, barking, and hyperactivityA dozen heartwarming stories of real-life rescue dogs and their adoptive parentsCountless ways dog lovers can raise awareness about animal rescue and responsible pet ownership in their communities

Beyond IQ

Beyond IQ
Author: Garth Sundem
Publisher: Crown
Total Pages: 242
Release: 2014-07-22
Genre: Self-Help
ISBN: 0770435971

Forget the IQ tests and tweak those parts of intelligence that matter most to real world success. Sure, having a high IQ is great. But surprisingly, science shows that mental abilities not captured in IQ tests can have the most impact in the real world—attributes like creativity, willpower, emotional intelligence, and intuition. And yes—you can train those skills. In these pages, journalist Garth Sundem draws on interviews with psychology’s top experts and the latest research to show you how. Beyond IQ is a new kind of braintraining guide, one packed with useful, engaging exercises scientifically shown to help you make the most of the brain you've got in the arena that matters most—life!" BEYOND IQ is filled with simple pen-and-paper exercises that will help you: --teach your mind to hear that "eureka" moment of insight --improve your problem-solving skills --use divergent thinking to boost your creativity --retrain your intuition to become more trustworthy --avoid the cognitive "blinkering" that too often comes with expertise --expand your working memory --practice your performance under pressure --improve your pattern-recognition skills --sharpen your emotional intelligence --strengthen your willpower And more!