The Art And Craft Of Problem Solving By Paul Zeitz
Paul Zeitz is a mathematician and professor who wrote the book "The Art and Craft of Problem Solving" as a guide for people who want to learn how to solve problems in a creative and effective way. This book is intended for students, teachers, professionals, and anyone who wants to improve their problem-solving skills.
Introduction
Problem-solving is an essential skill that we need in our daily lives, whether it's to overcome a challenge at work or to solve a personal problem. It involves thinking creatively, critically, and logically to identify the root cause of a problem and apply the right solution to solve it.
Overview Of The Book
"The Art and Craft of Problem Solving" is a comprehensive guide that covers all aspects of problem-solving, including:
- The problem-solving process
- Problem-solving strategies
- Problem-solving techniques
- Mathematical concepts and tools
- Real-world examples and applications
The Problem-Solving Process
The book starts by introducing the problem-solving process, which involves four main steps:
- Understanding the problem
- Devising a plan
- Carrying out the plan
- Evaluating the solution
Each step is discussed in detail, with examples and exercises to help readers practice and master the process.
Problem-Solving Strategies
The book then covers various problem-solving strategies, such as:
- Guess and check
- Draw a picture
- Make a table or chart
- Look for a pattern
- Solve a simpler problem
- Work backward
- Use logical reasoning
Each strategy is explained in detail, with examples and exercises to help readers understand and apply them.
Problem-Solving Techniques
The book also covers various problem-solving techniques, such as:
- Induction
- Strong induction
- Recursion
- Counting
- Combinatorics
- Probability
- Number theory
- Geometry
- Topology
Each technique is explained in detail, with examples and exercises to help readers understand and apply them.
Mathematical Concepts And Tools
The book also covers various mathematical concepts and tools that are essential for problem-solving, such as:
- Logic and proof
- Set theory
- Functions
- Sequences and series
- Graph theory
- Matrices
- Complex numbers
- Calculus
Each concept and tool is explained in detail, with examples and exercises to help readers understand and apply them.
Real-World Examples And Applications
The book also includes numerous real-world examples and applications of problem-solving, such as:
- Business and economics
- Engineering and technology
- Science and medicine
- Art and music
- Sports and games
- Politics and society
Each example and application is discussed in detail, with examples and exercises to help readers understand and apply them.
Conclusion
"The Art and Craft of Problem Solving" is an excellent book that provides a comprehensive guide to problem-solving. It covers all aspects of problem-solving, from the problem-solving process to problem-solving strategies, techniques, and mathematical concepts and tools. It also includes numerous real-world examples and applications to help readers understand and apply problem-solving in various fields. I highly recommend this book to anyone who wants to improve their problem-solving skills.