Introduction to Mathematical Thinking
Introduction to Mathematical Thinking is a book by Keith Devlin, a well-known mathematician and popular science writer who has authored over 30 books on various mathematical topics. The book, published in 2012, is intended for students who are transitioning from high school to college-level mathematics, as well as for anyone interested in improving their mathematical thinking skills.
In the introduction, Devlin sets out to answer the question, "What is mathematics?" He argues that while most people think of mathematics as a set of rules for solving problems, it is actually a way of thinking that can be applied to a wide range of problems. Devlin believes that mathematical thinking involves three key elements: abstraction, generalization, and logical reasoning.
The book is divided into six chapters, each of which focuses on a different aspect of mathematical thinking. In Chapter 1, Devlin introduces the concept of mathematical thinking and discusses the importance of abstraction in mathematics. In Chapter 2, he explores the idea of mathematical proof and how it differs from other forms of argumentation. Chapter 3 covers the topic of logic and its role in mathematics.
In Chapters 4 and 5, Devlin looks at two specific areas of mathematics: number theory and geometry. He uses these examples to illustrate the power of mathematical thinking and how it can be applied to different areas of study. Finally, in Chapter 6, Devlin discusses the practical applications of mathematical thinking in fields such as science, engineering, and finance.
Overall, among the best books on mathematics, Introduction to Mathematical Thinking is a valuable resource for anyone looking to improve their mathematical thinking skills. Devlin's engaging writing style and clear explanations make the book accessible to a wide audience, while his insights into the nature of mathematics provide a thought-provoking read for even the most experienced mathematicians.
Author: Keith Devlin
Link to buy: https://www.amazon.com/Introduction-Mathematical-Thinking-Keith-Devlin/dp/0615653634
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