Oscar Levin writes to share news about his open discrete math text:

After many years of development, I am pleased to announce that the 4th edition of Discrete Mathematics: an Open Introduction is now available, on the both the book’s home page and on Runestone Academy.

The 4th 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.

The new edition contains 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.

There is not currently a print version of the 4th edition. Some time in the next year, CRC will publish the physical version, but the online versions will remain available and free forever.

The third edition will also remain available indefinitely.

Dana Ernst’s An Introduction to Proof via Inquiry-Based Learning, which was recently added to our list of approved textbooks, is designed to support a one-semester introduction to proofs course incorporating inquiry-based learning (IBL). Following the IBL paradigm, a typical section begins by introducing a new topic and then presents a number of examples and problems meant to engage students in discovery-based learning and to develop their capacity for thinking mathematically.

In addition to the text, the author provides guidance for sequencing topics within a one-semester course and offers an instructor’s manual that provides additional support for instructors, particularly those who may be new to IBL. For example, there are links to sample syllabi and a journal describing day-to-day class activities.

This textbook is available in HTML and PDF versions, and a low-cost print version is published by the AMS/MAA Press. The PreTeXt source is also available for those who may wish to contribute to its further development.

We recently added Sheldon Axler’s Linear Algebra Done Right to our list of approved textbooks. While Springer publishes a print edition, Axler recently made a PDF freely available online. The fourth edition of the book, released last month, contains many new examples and exercises.

This text, written to support a second course in linear algebra, provides a rigorous treatment of its subject with an emphasis on abstract vector spaces and linear maps. The “done right” in the title refers to the author’s perspective that the theory of eigenvalues and eigenvectors is best developed without relying on determinants. While the language is clear and precise, the tone is also colloquial and inviting.

In addition to the text, Axler’s website provides an extensive collection of videos, roughly one for each section of the book, and accompanying slides of lecture notes.

We have recently redesigned the website for the Open Textbook Initiative and moved it to a new server. While the visual appearance has changed somewhat, users should find that the content and its organization have not. If you notice any issues, please reach out and let us know.

As we continue our promotion of open-access mathematics textbooks, we plan to use this blog to announce newly approved books and to highlight other news from the open textbook community. We also welcome hearing from anyone interested in open texts, particularly authors and instructors looking to adopt a text, so please contact us at textbooks@aimath.org.