探索数学：问题解决与证明

English | PDF | 2018 | 308 Pages | ISBN : 3319903195 | 4.23 MB

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics.

Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book.

Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

你是否曾经面对一个数学问题，却不知道如何入手？或者你已经有了一种想法，但中途就被卡住了？这本书引导你在开发创造力的过程中探索数学之旅。 读者不仅会学习解决难题和逻辑推理的方法，还会了解证明的重要性以及各种证明技术。其他涵盖的主题包括递归、数学归纳法、图论、计数、基本数论以及鸽巢原理、极值原则与不变性原理。本书旨在帮助学生从中学水平过渡到大学水平，为读者提供了一个关于数学的新视角，并提供了许多有助于理解通用原则的深刻见解，这些原则远超此书的范围。 特别面向大学生和中学生以及教师，这本书对所有感兴趣的数学爱好者都有吸引力。基本的初中数学知识就足够了，包括数的概念和基本几何学的理解，但不需要微积分。书中附有诸多练习题，并提供了解答提示。本书既适用于自学，也适合与课堂课程结合使用。

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