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The Art and Craft of Problem Solving summary
Brief summary
The Art and Craft of Problem Solving by Paul Zeitz is a comprehensive guide that equips readers with the essential tools and techniques needed to tackle mathematical problems with confidence and creativity. It provides valuable insights for both students and instructors.
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Table of Contents
The Art and Craft of Problem Solving
Summary of key ideas
Understanding the Nature of Problem Solving
In The Art and Craft of Problem Solving by Paul Zeitz, we embark on a journey to understand the nature of problem solving. Zeitz, a mathematics professor, begins by emphasizing the importance of developing problem-solving skills, which he believes are essential for success in any field. He introduces the concept of 'problem solving' as an art and a craft, emphasizing that it is not just about finding solutions, but about the process of exploration and discovery.
Zeitz then delves into the psychology of problem solving, discussing the mindset and attitudes that are conducive to effective problem solving. He emphasizes the importance of perseverance, creativity, and the willingness to take risks. He also introduces the concept of 'mathematical maturity' - the ability to think abstractly, to reason logically, and to express oneself clearly - as a key component of problem-solving ability.
Tools and Techniques for Problem Solving
Having laid the foundation, Zeitz moves on to discuss various tools and techniques that can be employed in problem solving. He introduces the concept of problem classification, emphasizing the importance of recognizing patterns and similarities between different problems. He also discusses the importance of visualization, abstraction, and generalization in problem solving.
Zeitz then introduces a variety of problem-solving strategies, such as working backwards, using symmetry, and exploiting the pigeonhole principle. He also discusses the importance of problem decomposition - breaking down complex problems into simpler, more manageable parts. Throughout these discussions, he provides numerous examples and exercises to illustrate the application of these techniques.
Exploring Problem-Solving Heuristics
In the latter part of the book, Zeitz explores problem-solving heuristics - general strategies or rules of thumb that can be used to guide the problem-solving process. He discusses the importance of making systematic lists, using diagrams and tables, and employing the process of elimination. He also introduces the concept of invariants - quantities that remain constant throughout a problem - as a powerful problem-solving tool.
Zeitz then discusses the role of intuition in problem solving, emphasizing that while rigorous logical reasoning is important, intuition can often provide valuable insights. He also discusses the importance of testing and refining solutions, and the need to be open to alternative approaches. Throughout these discussions, he provides numerous examples and exercises to illustrate the application of these heuristics.
Conclusion: A Holistic Approach to Problem Solving
In conclusion, The Art and Craft of Problem Solving by Paul Zeitz offers a comprehensive and holistic approach to problem solving. He emphasizes that effective problem solving requires a combination of mathematical knowledge, problem-solving skills, and the right mindset. He encourages readers to approach problem solving as a creative and exploratory process, rather than a mechanical exercise in finding the 'right' answer.
Throughout the book, Zeitz's passion for problem solving shines through, and his engaging writing style makes even complex mathematical concepts accessible. By the end of the book, readers are equipped not only with a toolkit of problem-solving techniques, but also with a deeper understanding of the nature of problem solving itself.
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What is The Art and Craft of Problem Solving about?
The Art and Craft of Problem Solving by Paul Zeitz is a comprehensive guide that teaches the techniques and strategies necessary for solving complex mathematical problems. Through a combination of theory, examples, and exercises, the book aims to develop the reader's problem-solving skills and mathematical intuition. It is a valuable resource for students, teachers, and anyone interested in honing their problem-solving abilities.
The Art and Craft of Problem Solving Review
The Art and Craft of Problem Solving (2007) is a book that offers valuable insights and techniques to approach problem-solving. Here is why this book is worth reading:
- It provides practical strategies that can be applied to various problem-solving situations, enabling readers to develop their problem-solving skills.
- The book offers a wide range of problem examples, showcasing different approaches and methods, making it applicable and relevant for readers.
- With its engaging and accessible explanations, the book ensures that readers can grasp complex concepts easily, making the learning process enjoyable and enriching.
Who should read The Art and Craft of Problem Solving?
- Dedicated learners who want to develop their problem-solving skills
- Math enthusiasts looking to improve their mathematical intuition and reasoning abilities
- High school and college students preparing for mathematics competitions or exams
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The Art and Craft of Problem Solving FAQs
What is the main message of The Art and Craft of Problem Solving?
The main message of The Art and Craft of Problem Solving is to equip readers with problem-solving skills applicable in various fields.
How long does it take to read The Art and Craft of Problem Solving?
The reading time for The Art and Craft of Problem Solving varies depending on the reader's speed. However, the Blinkist summary can be read in just 15 minutes.
Is The Art and Craft of Problem Solving a good book? Is it worth reading?
The Art and Craft of Problem Solving is worth reading as it provides valuable insights and techniques for effective problem-solving.
Who is the author of The Art and Craft of Problem Solving?
The author of The Art and Craft of Problem Solving is Paul Zeitz.
What to read after The Art and Craft of Problem Solving?
If you're wondering what to read next after The Art and Craft of Problem Solving, here are some recommendations we suggest:
- Feel the Fear and Do It Anyway by Susann Jeffers
- Making It All Work by David Allen
- The Power of Habit by Charles Duhigg
- The 4-Hour Workweek by Tim Ferriss
- Mindset by Carol Dweck
- Predictably Irrational by Dan Ariely
- Switch by Chip Heath & Dan Heath
- The Da Vinci Curse by Leonardo Lospennato
- The Defining Decade by Meg Jay
- The Art Of Non-Conformity by Chris Guillebeau