Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.

Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.
Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom’s MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book’s source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book.

Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics.

This resource is intended for biomechanics evaluation. It may be disseminated in any number of ways, including blackboard, canvas, or through print. Required materials:Computer; Kinovea download (free ware); Markers for analysis;  Iphone or camcorder with tripod; squat bar, with or without weight.All authors: Dr. Jennifer J. Brown1, Dr. Resa Chandler2, Dr. Vanessa Fiaud3, and Dr. Cortney Armitano-Lago4Acknowledgements: Keeley Weber1, Kali Flanigan1, Naomi Lockamy1, Sierra Dietrich2, Brooklyn Lester2Elizabeth City State University1, Western Carolina University2, West Texas A&M University3, and UNC School of Medicine, Thurston Arthritis Research Center4

This resource is intended for biomechanics evaluation. It may be disseminated in any number of ways, including blackboard, canvas, or through print. Required materials:Desktop/laptop computer; Kinovea download (free ware); Markers for analysis;  Iphone or camcorder with tripod; Vertec or adapt to s. jump test All authors: Dr. Jennifer J. Brown1, Dr. Resa Chandler2, Dr. Vanessa Fiaud3, and Dr. Cortney Armitano-Lago4 Acknowledgements: Keeley Weber1, Kali Flanigan1, Naomi Lockamy1, Sierra Dietrich2, Brooklyn Lester2 Elizabeth City State University1, Western Carolina University2, West Texas A&M University3, and UNC School of Medicine, Thurston Arthritis Research Center4

In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked.

The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.

To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.

Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.

To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.

Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

An Instructor's Guide is available to any instructor who uses the text.

Applied ecology is a framework for the application of knowledge about ecosystems so that actions can be taken to create a better balance and harmony between people and nature in order to reduce human impact on other beings and their habitats.

About this book
Origin story
I (Erin) began this book project after participating in the Open Pedagogy Incubator hosted by the NC State University Libraries in 2020, with the goal of making my course materials – and information about Applied Ecology – more broadly accessible to students, educators, and the general public. Rather than impose my sole voice, perspective, and biases, I restructured my course assignments to enable student creation of the content you will encounter in this book. The assignments are open-ended and open-world, motivating students to collaborate with each other and to seek knowledge beyond the classroom, and thus embody core characteristics of the discipline of Applied Ecology as well as Open Education and Universal Design for Learning. I hope that by centering student voices and by highlighting diverse scientists, research systems and ecosystems, this work empowers the reader and highlights the relevance of Applied Ecology in our everyday lives.

Intended use
This book is formatted to provide information about key ecological principles, concepts, and processes, explored and applied across various contexts. The text can be used as a foundational or supplementary text for ecology courses, or as a standalone reference for students in formal academic settings or beyond.

The Vocabulary terms at the beginning of each chapter are listed in the order that students will encounter them while reading the blog-style summary for that chapter. The Glossary lists all terms in the entire book in alphabetical order, for quick reference as needed.

We have provided an appendix with skeletal outlines that students can use to guide their notetaking. I also intend to compile a companion volume for educators, containing templates for each assignment used to guide the student works presented here.

Accessibility
We use sans-serif fonts to facilitate readability in digital format and by readers who are neurodivergent. We also support screen readership through alt-text images.

László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course “Applied Geometric Algebra” taught by Professor Tisza in the Spring of 1976.
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza’s attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, ‘77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

The structure of the human body is usually considered in courses in gross anatomy. These courses typically consist of lectures by the faculty, readings in assigned textbooks and the study of photographs and illustrations in human anatomy atlases. However, as student’s progress through the curriculum and move into the more clinical or practice oriented phases, many discover that the anatomical knowledge they actually need is somewhat different from the kind they possess. What many encounter is difficulty in applying their knowledge to a clinical setting.

Applied Human Anatomy was created to better integrate material that is more often than not treated separately in contemporary health care curricula. It is hoped that through this integration students will develop a deeper and more lasting knowledge and understanding of human anatomy as they are likely to need it in the evaluation and management of patients.

A print version is available for purchase on Amazon.

This 155-page manual is comprised of two types of learning activities: 1) free response fill-in-the blank questions focused of the facts and principles of neuroanatomy and neurophysiology that underpin the neurologic examination and specifically developed exercises that demonstrate how the facts and principles are related to the particular tests and procedures that comprise the neurologic examination. Free response questions form the bulk of the Neuroscience Review section of each chapter and are intended as a review of information previously or concurrently being learned regarding the structure, function and organization of the nervous system. Some questions focus on anatomical or physiological facts and relationships that help explain why certain techniques are performed as they are, such as why non-nociceptive tactile stimuli are required in order to activate nerve impulse transmission in the lemniscal system. Other questions are intended to revisit facts and concepts that are needed to properly interpret the elicited findings. 2) The Application Exercises of each chapter are designed to demonstrate how neuroanatomical and neurophysiological information is used in the design of particular clinical tests of neurologic function. The application exercises are also intended to help users learn how to perform and become comfortable with the various clinical maneuvers and tests that comprise the routine neurologic examination. An important outcome of performing these exercises is that, as a member of a learning group, each individual has the opportunity to experience the neurologic examination from the point of view of the subject (patient)—an experience that arguably provides insight and understanding that can be gained in no other way.

This free electrical engineering/technology textbook provides a series of chapters covering electricity and electronics. The information provided is great for students, makers, and professionals who are looking for an application-centric coverage of this field.

I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; we’ll learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options.

The primary learning objective of this textbook is to introduce the reader to the fundamental statistical methods and basic analytical procedures associated with processing data in regard to healthcare research. It is intended that by working through the applications and practice problems, readers should be able to understand and apply some of the methods for developing, implementing, and applying healthcare statistic principles in research.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"For an anesthesiologist, medically induced transitions between conscious and unconscious brain states are just part of the daily routine. But precisely how general anesthetics produce a state of unconsciousness isn’t all that clear. That’s because researchers are missing a key piece to the puzzle: no one has been able to definitively pinpoint exactly where consciousness comes from. The prevailing idea is that there’s no single “seat” of consciousness – it’s more the product of multiple interactions occurring throughout the brain. A recent review article published in the journal Anesthesiology argues that, because of this global network property, the field of network science could provide the framework needed to more comprehensively understand the biological basis of consciousness…and by extension the principles underlying anesthetic-induced unconsciousness..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

Using the Hardy-Weinberg equation to calculate allele and genotype frequencies. Created by Sal Khan.

This text is a complete team-based and project-based learning course focused on the application of the World Health Organization’s International Classification of Functioning, Disability and Health (ICF) to unique groups of program clients and patients. It is designed to engage undergraduate students in exploration of the different facets of the ICF, in how the ICF differs from medical and social models because of these facets, and how each applies to, and ensures, an awareness of all of the ways in which health affects and is affected by peoples’ characteristics and environments. The text includes readings, digital links, readiness assurance elements, and guidelines for individual and team deliverables, but can also be used as a stand-alone text to provide a rich constructivist approach to understanding the structure of the ICF and how to use it for problem solving and decision-making with a patient/client population.

It is the author’s intention that the text be used as suits the instructor, and modified to fit the pre-professional or paraprofessional healthcare students being taught, so while case study examples for rehabilitation are include, the text will lend itself to any patient or client group.