Linear Optimization

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• Features
• Quotes
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Features

• Linear Optimization is an inquiry-based learning text. The approach for this course is meant for those interested in either the theoritical or practical facets of undergraduate linear optimization, and is appropriate for any student who has taken a linear algebra course. There is an emphasis on developing geometric intuition and refining that intuition into rigorous proofs, a valuable skill for any undergraduate math student. The book is designed for in class discussions between students followed by individual study and practice.

• While the body of the text is structured as a series of activities, worked through by students collaboratively, each chapter concludes with a summary chapter and videos. This scaffolds the learning experience and provides learners with resources for individual review.

• Each chapter contains numerous exercises with a variety of flavors, computational, conceptual demonstration and proofs.

• To help develop intuition and ease computation, numerous interactive elements from Doenet exercises, Sage cells and Desmos interactives are included throughout the document. These help students to engage in inquiry via exploration, and see concretely how the geometric, algebraic and computational elements of the course tie-in with each other.

Quotes

• Linear Optimization: A Geometric Inquiry Course provides an inquiry-based introduction to linear optimization (also called linear programming), a rich and increasingly important topic with applications to economics, computer science, biology, operations research, sociology, and numerous other areas. The book is designed for active student engagement with a geometric perspective in mind and is supported by a wealth of supplementary materials and interactive tools through Doenet, Sage, and Desmos. ... By leveraging geometric intuition as its foundation, the content progresses from geometry to linear algebra, proceeding from there to theory and computation through explorations and activities. This book is an excellent choice for instructors, students, and readers who wish to develop their own deep understanding and appreciation of linear optimization. - John A. Rock, Professor of Mathematics, Cal Poly Pomona

• Linear Optimization: A Geometric Inquiry Course is a great addition to the library of inquiry-based textbooks. The approach is consistent with the inquiry-based model of providing exploratory exercises for students to build a conceptual understanding before developing the more theoretical aspects. The main computational techniques are built through layers of activities that focus on building connections. The text includes a wide variety of computational tools including optimization tools in Sage and a pivoting tool in the exercises. The inclusion of Doenet interactives is very helpful for having students see the geometric side of linear optimization. Beyond the standard concepts of canonical and noncanonical optimization problems, the Simplex algorithm, and duality, the text includes a wide variety of applications including game theory, transportation problems, and network flows. - Jennifer Nordstrom, Professor of Mathematics, Linfield University

• I really liked how the textbook built up the ideas in a way that made the motivation behind each concept and theorem feel natural. The order that the material was presented in made sense, and it was clear why each new technique was introduced. I also appreciated that we often derived or proved results ourselves before seeing the formal version - it made everything fit together more logically and helped me actually understand why things work instead of just memorizing them. On top of that, the emphasis on the geometric perspective really deepened my understanding; seeing how the concepts connect visually made linear programming feel much more intuitive. - Lance Ding, Computer Science & Mathematics Student, Emory University

• I enjoyed the inquiry-based classroom experience - it transformed each class into an exciting research project. I felt a great sense of achievement when my peers and I collaborated to prove important theorems and explored how linear optimization applies to real-world scenarios. The excitement of discovery not only deepened my understanding of mathematics but also fostered lasting friendships and unforgettable memories. - Arthur Han, Mathematics & Physics Student, University of Michigan

Contact

Tien Chih is an assistant professor of mathematics at Oxford College of Emory University. Questions, feedback, suggestions, and anything else are always welcome:

Tien Chih, tienchih at emory.edu

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

© Tien Chih 2024 - 2025