This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

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

Whether you are a student or a working professional, you can benefit from being better at solving the complex problems that come up in your life. Strategic Thinking in Complex Problem Solving provides a general framework and the necessary tools to help you do so. Based on his groundbreaking course at Rice University, engineer and former strategy consultant Arnaud Chevallier provides practical ways to develop problem solving skills, such as investigating complex questions with issue maps, using logic to promote creativity, leveraging analogical thinking to approach unfamiliar problems, and managing diverse groups to foster innovation. This book breaks down the resolution process into four steps: 1) frame the problem (identifying what needs to be done), 2) diagnose it (identifying why there is a problem, or why it hasn't been solved yet), 3) identify and select potential solutions (identifying how to solve the problem), and 4) implement and monitor the solution (resolving the problem, the 'do'). For each of these four steps - the what, why, how, and do - this book explains techniques that promotes success and demonstrates how to apply them on a case study and in additional examples. The featured case study guides you through the resolution process, illustrates how these concepts apply, and creates a concrete image to facilitate recollection. Strategic Thinking in Complex Problem Solving is a tool kit that integrates knowledge based on both theoretical and empirical evidence from many disciplines, and explains it in accessible terms. As the book guides you through the various stages of solving complex problems, it also provides useful templates so that you can easily apply these approaches to your own personal projects. With this book, you don't just learn about problem solving, but how to actually do it.

By examining the links and interactions between elements of a system, systems thinking is becoming increasingly relevant when dealing with global challenges, from terrorism to energy to healthcare. Addressing these seemingly intractable systems problems in our society, Systems Thinking: Coping with 21st Century Problems focuses on the inhere

Wall Street Journal Bestseller New York Times bestselling author Dan Heath explores how to prevent problems before they happen, drawing on insights from hundreds of interviews with unconventional problem solvers. So often in life, we get stuck in a cycle of response. We put out fires. We deal with emergencies. We stay downstream, handling one problem after another, but we never make our way upstream to fix the systems that caused the problems. Cops chase robbers, doctors treat patients with chronic illnesses, and call-center reps address customer complaints. But many crimes, chronic illnesses, and customer complaints are preventable. So why do our efforts skew so heavily toward reaction rather than prevention? Upstream probes the psychological forces that push us downstream—including “problem blindness,” which can leave us oblivious to serious problems in our midst. And Heath introduces us to the thinkers who have overcome these obstacles and scored massive victories by switching to an upstream mindset. One online travel website prevented twenty million customer service calls every year by making some simple tweaks to its booking system. A major urban school district cut its dropout rate in half after it figured out that it could predict which students would drop out—as early as the ninth grade. A European nation almost eliminated teenage alcohol and drug abuse by deliberately changing the nation’s culture. And one EMS system accelerated the emergency-response time of its ambulances by using data to predict where 911 calls would emerge—and forward-deploying its ambulances to stand by in those areas. Upstream delivers practical solutions for preventing problems rather than reacting to them. How many problems in our lives and in society are we tolerating simply because we’ve forgotten that we can fix them?

Design-oriented firms such as Apple and IDEO have demonstrated how design thinking can directly affect business results. Yet most managers lack a real sense of how to put this new approach to use for issues other than product development and sales growth. Solving Problems with Design Thinking details ten real-world examples of managers who successfully applied design methods at 3M, Toyota, IBM, Intuit, and SAP; entrepreneurial start-ups such as MeYou Health; and government and social sector organizations including the City of Dublin and Denmark’s The Good Kitchen. Using design skills such as ethnography, visualization, storytelling, and experimentation, these managers produced innovative solutions to problems concerning strategy implementation, sales force support, internal process redesign, feeding the elderly, engaging citizens, and the trade show experience. Here they elaborate on the challenges they faced and the processes and tools they used, offering their personal perspectives and providing a clear path to implementation based on the principles and practices laid out in Jeanne Liedtka and Tim Ogilvie’s Designing for Growth: A Design Thinking Tool Kit for Managers.

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

*Major New York Times Bestseller *More than 2.6 million copies sold *One of The New York Times Book Review's ten best books of the year *Selected by The Wall Street Journal as one of the best nonfiction books of the year *Presidential Medal of Freedom Recipient *Daniel Kahneman's work with Amos Tversky is the subject of Michael Lewis's best-selling The Undoing Project: A Friendship That Changed Our Minds In his mega bestseller, Thinking, Fast and Slow, Daniel Kahneman, world-famous psychologist and winner of the Nobel Prize in Economics, takes us on a groundbreaking tour of the mind and explains the two systems that drive the way we think. System 1 is fast, intuitive, and emotional; System 2 is slower, more deliberative, and more logical. The impact of overconfidence on corporate strategies, the difficulties of predicting what will make us happy in the future, the profound effect of cognitive biases on everything from playing the stock market to planning our next vacation—each of these can be understood only by knowing how the two systems shape our judgments and decisions. Engaging the reader in a lively conversation about how we think, Kahneman reveals where we can and cannot trust our intuitions and how we can tap into the benefits of slow thinking. He offers practical and enlightening insights into how choices are made in both our business and our personal lives—and how we can use different techniques to guard against the mental glitches that often get us into trouble. Topping bestseller lists for almost ten years, Thinking, Fast and Slow is a contemporary classic, an essential book that has changed the lives of millions of readers.

Thought you had it bad? In this book, you will be: Imprisoned by a sadistic logician. Challenged to raise dogs from the dead. Trapped on a burning island. And much more besides . . . Everything is at stake in this compendium of more than 150 ingenious puzzles, selected to reveal the wonderful diversity of brainteasers that have confounded and intrigued solvers for the last thousand years. You'll need to pit your wits against probability problems, wrestle with wordplay, grapple with geometry and scrabble for survival. Along the way you will discover stories of whip-smart thinkers, eccentric novelists and a poodle with allegedly supernatural powers. You will absorb fascinating and important mathematical ideas. Some solutions will rely on ingenuity, some will challenge you to spot hidden patterns, others call for extreme rationality. All will surprise, entertain and stretch your brain. Will you make it out with your puzzling pride intact?