Active Calculus (2nd Edition) - Workbooks 1-4 and 5-8
These are the workbooks for Active Calculus (2nd Ed).
Active Calculus, 2nd Edition: Activity Workbooks 1–4 and 5-8 is the perfect companion to the Active Calculus textbook by Matthew Boelkins. Designed to support the text's active learning approach, this workbook provides students with a dedicated space to complete the preview activities, in-class explorations, and collaborative exercises that are central to the course.
Organized to match Chapters 1–4 and 5-8 of the textbook, the workbook helps students engage more deeply with fundamental calculus concepts through guided problem-solving, critical thinking, and concept-building activities. Whether used in class or for independent study, it encourages students to actively participate in the learning process rather than simply observe worked examples.
Ideal for single-variable calculus courses, this workbook is an essential resource for students and instructors using Active Calculus, making it easier to organize coursework, record solutions, and fully participate in an inquiry-based learning environment.
Learn more at activecalculus.org, and you can find more information here.
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Active Calculus (2nd Edition)
Active Calculus: Single Variable (2nd Ed) is an open-source textbook that is available free in HTML and PDF, as well as in this low-cost print version. The style of the text requires students to be active learners: there are very few worked examples in the text, with instead 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of fundamental calculus ideas. Each section begins with a brief introduction and a preview activity designed to be completed before class; each section concludes (in HTML) with live anonymous WeBWorK exercises for immediate feedback, followed by a few challenging non-WeBWorK exercises. The text is suitable for a 2-semester course in single variable calculus, and there’s a Spanish translation of the 1st edition. The author maintains a large repository of available-upon-request ancillary materials including sample syllabi and course calendars, additional WeBWorK exercises, supplementary written homework exercises, laboratory activities, weekly quizzes, and final exams. There is also a large instructor user community that is connected through an online Google group. Learn more at activecalculus.org, and you can find more information here.
Understanding Linear Algebra
WINNER OF THE 2025 SOLOW AWARD FOR BEST UNDERGRADUATE MATHEMATICS TEACHING MATERIALS!
Understanding Linear Algebra is an open textbook designed to support a two-course undergraduate linear algebra sequence. Topics include systems of equations, vector and matrix algebra, span, linear independence, bases, eigenvectors and eigenvalues, orthogonality, least squares, and singular value decompositions.
There are a few features that distinguish it from other linear algebra textbooks. First, it will always be freely available at http://gvsu.edu/s/0Ck in a number of formats, including accessible HTML, PDF, and even braille.
Until recently, linear algebra has mainly lived in the long shadow of calculus with many university linear algebra courses requiring several semesters of calculus as a prerequisite. Given the increasing prominence of linear algebra, Understanding Linear Algebra assumes no familiarity with calculus and, as such, can provide an alternative introduction into university-level mathematics.
Learners are supported as they develop a deep understanding of linear algebraic concepts and their ability to reason mathematically using those concepts. While not intended as an introduction to proofs, the text helps learners to express their thinking clearly and with precision. Following best pedagogical practices, numerous activities are interwoven with exposition to facilitate active learning and can be easily adapted for small group collaboration in a classroom. Each section begins with a preview activity to support a flipped class environment and concludes with numerous exercises of varying depth.
In addition, learners develop computational proficiency through the use of Sage, an open source computer algebra system. The online version of the text contains many embedded "Sage cells" that enable readers to perform computations directly in the book as they are reading. Readers first perform basic algorithms, such as Gaussian elimination and matrix multiplication, by hand but later automate them using Sage. In this way, learners can focus on higher-level linear algebraic thinking and develop their ability to deploy it in more realistic situations.
By introducing many in-depth applications, Understanding Linear Algebra also aims to develop an appreciation for the many significant ways in which linear algebra impacts our society. Examples include the JPEG image compression and Google's PageRank algorithms as well as important data science topics such as k-means clustering, linear regression, principal component analysis, and singular value decompositions. These applications give concrete meaning to many of the abstract algebraic concepts on which they rely, and the use of Sage enables learners to authentically explore them.
Besides the text itself, there is an accompanying workbook that contains the activities and is suitable for in-class use. There are also solution manuals for both the activities and the homework exercises that are available upon request of the author and a community of instructors who share their experiences and resources with one another through a Google Group.
Linear Optimization: A Geometric Inquiry Course
"Linear Optimization: A Geometric Inquiry Course" is an inquiry based learning text for an undergraduate course in linear optimization. Taking a geometric vantage point to build intuition, students work through a sequence of activities through which they discover and build the theory and concepts of the course. Numerous applications are also covered in the same manner. To reinforce the geometric and intuition building dimensions of the course, supplements in the form of videos and interactive elements are available through the open source, freely available online companion text.
A portion of the proceeds goes to support the Prison Math Project.
