How to Solve It

Synopsis

The bestselling book that has helped millions of readers solve any problem

A must-have guide by eminent mathematician G. Polya, How to Solve It shows anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can help you attack any problem that can be reasoned out-from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable-from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.

This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it's not just for the classroom. Generations of readers from all walks of life have relished Polya's brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem.

Summary

Chapter 1: The Art of Guessing

* Explains the importance of guessing as a starting point for solving problems.
* Example: A salesman wants to travel from city A to city B in the shortest time possible. He can choose three different routes, but doesn't know which one is the fastest. He guesses the middle route and takes it. After traveling for some time, he realizes it's not the fastest and switches to the other routes until he finds the quickest one.

Chapter 2: Heuristic and Systematic Approaches

* Introduces two main approaches to problem-solving: heuristic (trial-and-error) and systematic (following a logical process).
* Example: A student wants to solve a math problem but doesn't know the formula. They can use a heuristic approach by guessing different approaches until they find one that works. Alternatively, they can use a systematic approach by breaking the problem down into smaller steps and following a logical process to find the solution.

Chapter 3: Heuristic Reasoning: Ways of Looking

* Explores different heuristic strategies, such as analogy, function analysis, and reduction.
* Example: A doctor is diagnosing a patient with an unknown illness. They use an analogy to compare the patient's symptoms to similar cases they've seen in the past. This helps them narrow down the diagnosis and make a more accurate assessment.

Chapter 4: Systematic Reasoning: Mathematical Tools

* Provides mathematical tools for systematic problem-solving, such as algebra, calculus, and probability.
* Example: A physicist wants to calculate the trajectory of a projectile. They use mathematical equations to model the motion of the projectile and calculate its path.

Chapter 5: Originality: An Acquisition of Skills

* Emphasizes the importance of originality in problem-solving and provides techniques for developing it.
* Example: A designer wants to create a new product that meets the needs of a specific target audience. They use brainstorming, sketching, and prototyping to come up with original ideas and find the best solution for their customers.

Chapter 6: Analysis of the Thinking Process

* Analyzes the cognitive processes involved in problem-solving and provides techniques for improving them.
* Example: A researcher wants to understand the factors that contribute to student success. They use data analysis and research methods to identify patterns and develop strategies to improve student outcomes.

Chapter 7: Notes on the Solution of Problems

* Presents general advice for problem-solving, including the importance of perseverance, collaboration, and feedback.
* Example: A team of engineers is working on a complex engineering project. They face several challenges throughout the process, but they persevere, collaborate effectively, and seek feedback from experts to find solutions and complete the project successfully.