This book adapts material from several open-source textbooks and lecture notes. Every source listed here uses a license that is compatible with the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license under which this book is distributed. Each entry records the original author, source URL, original license, and how the material was used. Modifications to all adapted material were made by Robert Hildebrand and other contributors to this book.
A First Course in Linear Algebra
Author:
Ken Kuttler, with adaptations by Lyryx Learning
Source:
License:
Creative Commons Attribution 4.0 International (CC BY 4.0)
Local copy:
external-sources/aFirstCourseLinearAlgebra/
Used in:
Appendix on Linear Algebra (vectors, dot product, cross product, projections, Gram–Schmidt, planes, parametric lines). The book also reuses Lyryx’s chapter and theorem formatting templates.
Compatibility:
CC BY 4.0 material may be incorporated into a CC BY-SA 4.0 work with attribution. The adapted material here is relicensed under CC BY-SA 4.0 as part of this book.
Foundations of Applied Mathematics: Volume 2 – Algorithms, Approximation, and Optimization
Authors:
Jeffrey Humpherys, Tyler Jarvis, and contributors at Brigham Young University (full contributor list at the source repository below; a compact acknowledgment appears in the back matter)
Source:
License:
Creative Commons Attribution 3.0 United States License (CC BY 3.0 US)
Local copy:
external-sources/foundationsAppliedMathematicsLabs/
Used in:
Selected sections, code formatting templates, and references to associated lab code throughout the book.
Compatibility:
CC BY 3.0 permits adaptation under any compatible license; the adapter’s license here is CC BY-SA 4.0. Attribution is retained for all adapted material.
Linear Inequalities and Linear Programming
Author:
Kevin Cheung, Carleton University
Source:
License:
Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
Local copy:
external-sources/lineqlpbook/
Used in:
Substantial portions of Part I (Linear Programming): notation, basic feasible solutions, the Fundamental Theorem of LP, Farkas’ lemma, complementary slackness, duality, the Fourier–Motzkin elimination method, and the graphical example. License is documented via headers in every .tex source file.
Compatibility:
CC BY-SA 4.0 source content is directly compatible with CC BY-SA 4.0 adaptation; no version transition.
Optimization Notes (Linear Programming Notes)
Author:
Douglas Bish, Virginia Tech
License:
Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
Local copy:
external-sources/Opt_Notes/
Used in:
Substantial portions of Part I (Linear Programming), including modeling, the simplex method exposition, and sensitivity analysis. License is documented in external-sources/Opt_Notes/README.md.
Compatibility:
CC BY-SA 4.0 source content is directly compatible with CC BY-SA 4.0 adaptation.
Math in Society, Graph Theory chapter
Author:
David Lippman, Pierce College Ft. Steilacoom
Source:
License:
Creative Commons Attribution-ShareAlike 3.0 United States (CC BY-SA 3.0)
Used in:
The Graph Algorithms chapter (Book 1): the lawn inspector and Königsberg motivating examples, the basic graph definitions, the Dijkstra and minimum cost spanning tree worked examples, and many of the chapter exercises, all with edits and additions.
Compatibility:
CC BY-SA 3.0 material may be adapted and redistributed under CC BY-SA 4.0, which Creative Commons lists as a compatible later license version for adaptations. Attribution is retained here and in the chapter source file.
Applied Finite Mathematics, Chapter 1: Linear Equations
Authors:
Rupinder Sekhon and Roberta Bloom
Source:
License:
Creative Commons Attribution 4.0 International (CC BY 4.0), via LibreTexts
Local copy:
external-sources/applied-finite-mathematics/ (with LICENSE file)
Used in:
Appendix A (Linear Equations), including text and figures adapted from LibreTexts Chapter 1.
Compatibility:
CC BY 4.0 material may be incorporated into a CC BY-SA 4.0 work with attribution. A visible attribution paragraph appears at the start of the appendix chapter.
Bridges of Königsberg. The historical engraving of the seven bridges (used in the Graph Theory chapter) is in the public domain. The line-drawing variant included here is by Bogdan Giusca (Wikipedia user Bogdang) and is licensed under Creative Commons Attribution-ShareAlike 3.0 (CC BY-SA 3.0). Source: https://commons.wikimedia.org/wiki/File:Konigsberg_bridges.png.
All other figures. All TikZ figures, plots, and diagrams in this book are original works by Robert Hildebrand and contributors, created specifically for this text. Earlier versions of some Wikipedia-derived figures (e.g., generic linear-programming and integer-programming illustrations) have been replaced with original TikZ versions. The four multi-objective optimization figures in Chapter 13 are original works by Robert Hildebrand.
We thank Laurent Poirrier and Diego Moran for contributing notes on linear and integer programming, and Jamie Fravel for editing, contributing chapters, and contributing example code. We also thank Irma Adams for researching and writing the “pioneer spotlight” biographical sidebars that appear throughout the book (including the profiles of George Dantzig and other founders of the field). Joshua Emmanuel provided early guidance on graphical-method exposition during course development; the current text on the graphical method is original to this book.
| Source license | Compatibility | Mechanism |
| CC BY-SA 4.0 | Direct | Same license; attribution retained |
| CC BY 4.0 | Direct | Adapted into CC BY-SA 4.0 with attribution |
| CC BY 3.0 US | Indirect | Adapter’s-license provision permits CC BY-SA 4.0 |
| Public Domain | Direct | No restriction; attribution provided |
The full text of the CC BY-SA 4.0 license under which this book is distributed is available at https://creativecommons.org/licenses/by-sa/4.0/ and in the file LICENSE-Content in the book’s source repository. Code released with this book is licensed separately under the MIT License, with text in LICENSE-Code.
