Prealgebra prepares students for the rigors of algebra, and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8.Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual contains full solutions to all of the problems, not just answers.
Author: Arthur Engel
Publisher: Springer Science & Business Media
Release Date: 2008-01-19
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.
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.
Author: Jon Koomey
Publisher: Analytics Press
Release Date: 2008
Genre: Business & Economics
"Mastering the art of problem solving takes more than proficiency with basic calculations; it requires understanding how people use information, recognizing the importance of ideology, learning the art of storytelling, and acknowledging the important distinction between facts and values. Intended for professors, managers, entrepreneurs, and students, this guide addresses these and other essential skills. With clear prose, quotations, and exercises for solving problems in the real world, this book serves as an ideal training manual for those who are new to or intimidated by quantitative analysis and an excellent refresher for those who have more experience but want to improve the quality of their data, the clarity of their graphics, and the cogency of their arguments." -- Publisher's description.
Author: John R. Koza
Publisher: Morgan Kaufmann
Release Date: 1999
Genetic programming is a method for getting a computer to solve a problem by telling it what needs to be done instead of how to do it. Koza, Bennett, Andre, and Keane present genetically evolved solutions to dozens of problems of design, optimal control, classification, system identification, function learning, and computational molecular biology. Among the solutions are 14 results competitive with human-produced results, including 10 rediscoveries of previously patented inventions. Researchers in artificial intelligence, machine learning, evolutionary computation, and genetic algorithms will find this an essential reference to the most recent and most important results in the rapidly growing field of genetic programming. * Explains how the success of genetic programming arises from seven fundamental differences distinguishing it from conventional approaches to artificial intelligence and machine learning * Describes how genetic programming uses architecture-altering operations to make on-the-fly decisions on whether to use subroutines, loops, recursions, and memory * Demonstrates that genetic programming possesses 16 attributes that can reasonably be expected of a system for automatically creating computer programs * Presents the general-purpose Genetic Programming Problem Solver * Focuses on the previously unsolved problem of analog circuit synthesis, presenting genetically evolved filters, amplifiers, computational circuits, a robot controller circuit, source identification circuits, a temperature-measuring circuit, a voltage reference circuit, and more * Introduces evolvable hardware in the form of field-programmable gate arrays * Includes an introduction to genetic programming for the uninitiated
Author: Robert J. Sternberg
Publisher: Academic Press
Release Date: 2013-10-22
Thinking and Problem-Solving presents a comprehensive and up-to-date review of literature on cognition, reasoning, intelligence, and other formative areas specific to this field. Written for advanced undergraduates, researchers, and academics, this volume is a necessary reference for beginning and established investigators in cognitive and educational psychology. Thinking and Problem-Solving provides insight into questions such as: how do people solve complex problems in mathematics and everyday life? How do we generate new ideas? How do we piece together clues to solve a mystery, categorize novel events, and teach others to do the same? Provides a comprehensive literature review Covers both historical and contemporary approaches Organized for ease of use and reference Chapters authored by leading scholars