离散数学 – 开放式导论，第四版

离散数学 – 开放式导论，第四版
Discrete Mathematics – An Open Introduction, 4th edition

原始链接: https://discrete.openmathbooks.org/dmoi4.html

《离散数学：开放式导论》第四版已出版。第三版仍然可供访问。更新后的书籍提供了许多增强功能和修订的内容结构。它从逻辑探索和逻辑证明的演示开始，然后通过图论进行应用。随后的部分涵盖了与计数相关的方面，并以题为“概率的应用”的新视角为特色。后半部分深入研究序列。为了促进学生学习，新的安排已被证明是有益的，强调与计算机科学相关的离散结构。此外，人们越来越关注互动功能，包括在通过符石学院免费教学时完成后奖励分数的练习。还包括针对特定主题结合 Sage 和 Python 代码的补充材料。尽管纸质版要等到 CRC Press 后续出版后才能获得，但数字版很快就会推出。即使没有印刷出版物，这本书也将永远可以在线访问。对其内容的所有修改均属于知识共享许可的范围 - 具体而言，新的 CC BY-NC-SA 4.0 许可条款要求归属于原作者并允许非商业性的重新分发或修改，前提是衍生作品带有兼容的开放许可证。任何有关将本书中的章节与不同许可证下的其他文本相结合的询问必须事先寻求许可证变更的批准。

由于允许教师将问题分配给学生以及降低制作成本等原因，数学教科书通常不提供解决方案。为了最大限度地从教科书中学习，请将每个陈述视为一个练习，旨在在继续之前证明或证明命题。逐步进行，尤其是对于复杂的主题，必要时利用可用的资源，例如校样草图或提示。与被动阅读相比，通过主动解决问题来积极参与材料可以促进更好的理解。阅读数学需要练习，但对于那些无法获得个人辅导的人来说仍然是有益的。解决方案或问题可以帮助肌肉记忆学习和解决问题的技能，同时也提供一种有益的进步感。然而，没有解决方案或问题会使自学变得困难，因为检查自己的理解变得具有挑战性。一个有用的折衷方案可能是为一半的问题提供解决方案，同时保留剩余的问题用于教学目的。此外，像法学硕士这样的在线学习工具可以为自学者批判性思维、产生问题和获得见解提供有效的帮助。这些策略促进了对数学概念的更深入的参与，最终提高了对主题的掌握。

原文

4th Edition Information

This page details progress on the 4th edition of the book. The 3rd edition remains available.

After many years of development, I am please to announce that the 4th edition of Discrete Mathematics: an Open Introduction is now available, here and on Runestone Academy.

The new edition brings many improvements and a new organization of content. In particular, the book now starts with logic and proofs, then practices those proofs with graph theory. The second half of the book contains material on counting (with a new "application to probability" section) and sequences. Over the last few years, I have found that students have more success with this arrangement. There is also a stronger emphasis on discrte structures, which should make the book more useful for students in computer science, while still focusing on understanding mathematical concepts essential for math majors and future math teachers.

There is more interactivity as well. More interactive exercises (which you can give students credit for if you create a course with the book on Runestone Academy; it is completely free for you and your students) and some interactive Sage and Python code to explore some topics.

A PDF of the book will be made available soon. There will not be a print edition available until next year, when CRC Press will release it. The online version will remain available and free forever, and the book is still released under a Creative Commons License (but note the new NC-Non Commercial addition to the license).

License

Discrete Mathematics: an Open Introduction, 4th edition by Oscar Levin is licensed under CC BY-NC-SA 4.0

You are free to download, use, and print as you wish to, for noncommercial purposes. You can also modify the text as much as you like (create a custom edition for your students, for example), as long as you attribute the parts of the text you use to the author and release your modified version under a compatible license.

If you are interested in using parts of the book combined with another text with a similar but different license (GFDL, for example), please reach out to get permission to modify the license.