The Art of Problem Solving Volume 1

The Art of Problem Solving  Volume 1 Author Sandor Lehoczky
ISBN-10 0977304566
Year 2006-08-01
Pages 272
Language en
Publisher Aops Incorporated

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


Calculus Author David Patrick
ISBN-10 1934124249
Year 2013-04-15
Pages 323
Language en
Publisher Aops Incorporated

A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.


Prealgebra Author Richard Rusczyk
ISBN-10 1934124214
Year 2011-08
Pages 608
Language en

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.

Beyond Constructivism

Beyond Constructivism Author Richard A. Lesh
ISBN-10 0805838228
Year 2003
Pages 597
Language en
Publisher Psychology Press

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

The Art of Insight in Science and Engineering

The Art of Insight in Science and Engineering Author Sanjoy Mahajan
ISBN-10 9780262526548
Year 2014-11-07
Pages 408
Language en
Publisher MIT Press

In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering.To master complexity, we can organize it or discard it. The Art of Insight in Science and Engineering first teaches the tools for organizing complexity, then distinguishes the two paths for discarding complexity: with and without loss of information. Questions and problems throughout the text help readers master and apply these groups of tools. Armed with this three-part toolchest, and without complicated mathematics, readers can estimate the flight range of birds and planes and the strength of chemical bonds, understand the physics of pianos and xylophones, and explain why skies are blue and sunsets are red.The Art of Insight in Science and Engineering will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Challenging Mathematical Problems with Elementary Solutions

Challenging Mathematical Problems with Elementary Solutions Author A. M. Yaglom
ISBN-10 9780486318578
Year 2013-04-26
Pages 239
Language en
Publisher Courier Corporation

Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. Most can be solved with elementary mathematics. Complete solutions.

The Structure of Scientific Revolutions

The Structure of Scientific Revolutions Author Thomas S. Kuhn
ISBN-10 9780226458144
Year 2012-04-18
Pages 264
Language en
Publisher University of Chicago Press

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.