his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.

Widespread media reports of local teacher shortages have become a hot topic in education since the summer of 2015. After years of teacher layoffs, districts began hiring again as the economy recovered from the Great Recession. Many were surprised to find they had serious difficulty finding qualified teachers for their positions, especially in fields like mathematics, science, special education, and bilingual education/English language development. A number of states greatly expanded emergency permits to allow hiring of untrained teachers to meet these demands—which is the classic definition of shortage. To date, however, there has not yet been a detailed national analysis of the sources and extent of these shortages, and the prognosis for the future.

This textbook is designed for beginning-intermediate English language learners. It is composed of 7 chapters, each of which covers specific speaking and listening learning objectives and includes dialogues, interviews, discussions and conversation activities. Each chapter includes listening and speaking components such as dialogues, interviews, discussions and conversation activities. Each chapter also focuses on 10 target words from the New General Service List of English vocabulary. The textbook includes an audio component that consists of recorded conversations of native and non-native English speakers, as well as links to additional listening resources on the web.

An overview of some communication basics, including three common communication models: Action, Interactive, and Transactional.

Communication in the Real World: An Introduction to Communication Studies overviews the time-tested conceptual foundations of the field, while incorporating the latest research and cutting-edge applications of these basics. Each chapter will include timely, concrete, and real-life examples of communication concepts in action. A key feature of this book is the integration of content regarding diversity and organizational communication in each chapter through examples and/or discrete sub-sections. Discussions of diversity are not relegated to feature boxes. Also integrated into the content are examples that are inclusive in terms of race, gender, sexuality, ability, age, marital status, religion, and other diverse identity characteristics.

Overview of Communism and Marxist-Leninist states. For extra coverage of the Cold War outside the scope of the AP course, click here. Created by Sal Khan.

This reader is an Open Educational Resource, meant to accompany a graduate or higher-level undergraduate university course in climate change resilience, adaptation, and/or planning. While the material is geared toward students in urban and regional planning, it may also be of interest to students of urban studies, public health, geography, political science, sociology, risk management, and others.

The introductions in this anthology are meant to be just that: a basic overview of what students need to know before they begin reading, with topics that students can research further. An open access literature textbook cannot be a history book at the same time, but history is the great companion of literature: The more history students know, the easier it is for them to interpret literature.

It is common to use GDP as a measure of economic welfare or standard of living in a nation. When comparing the GDP of different nations for this purpose, two issues immediately arise. First, the GDP of a country is measured in its own currency: the United States uses the U.S. dollar; Canada, the Canadian dollar; most countries of Western Europe, the euro; Japan, the yen; Mexico, the peso; and so on. Thus, comparing GDP between two countries requires converting to a common currency. A second issue is that countries have very different numbers of people. For instance, the United States has a much larger economy than Mexico or Canada, but it also has roughly three times as many people as Mexico and nine times as many people as Canada. So, if we are trying to compare standards of living across countries, we need to divide GDP by population.

This textbook is designed for the novice learner who is seeking to develop a foundationalunderstanding of the complete subjective health assessment in the context of health and illness. The textbook deconstructs the categories of the complete subjective health assessment, providing learners with explanations and examples of what constitutes relevant subjective data. This textbook provides an opportunity to learn how to respond to normal, abnormal, and critical findings when completing a complete subjective health assessment

This Composition Reader is an edited, curated collection of OER material for you to use as you see fit in your course.  It consists of personal essays, literature, video and audio files, web writing, and long-form journalism.

Composition Reading Bank is a repository of links to freely available texts that replaces a traditional reader for Composition courses.

This Reading Bank is meant to be an ongoing collaborative project; users should contact Nick Lakostik at nlakosti@cscc.edu if they have ideas for freely accessible texts that would be good additions to the Reading Bank. A summary of what the text is about and how it is or could be useful in your Composition course would also be appreciated. Please also send information about broken links to the same email address.

A link to this resource on the Columbus State Community College Library's web page is:

https://library.cscc.edu/compreadingbank

Except where otherwise indicated, the Composition Reading Bank by Rachel Brooks-Pannell, Shawn Casey, Rebecca Fleming, and Nick Lakostik at Columbus State Community College is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. This license does not extend to the contents of external web pages.

A rubric designed by educators from Lawrence Public Schools to be used in its annual review process of openly licensed educational resources.

This online textbook addresses the population of individuals with disabilities that experience complex lifelong needs across multiple areas in their lives. Drs. Sennott and Loman drafted this book (along with the help from some friends) with the hope of providing pertinent, practical, and current resources to future special educators who plan to serve individuals with complex disabilities.

The Compromise of 1850 was a series of acts that dealt with issues related to slavery and territorial expansion. This guide contains Library of Congress digital materials, external websites, and a print bibliography.

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

The sixth edition, first published as an ebook, and this seventh edition carry forward the philosophy and structure of the earlier editions. This book is not a comprehensive treatise on the subject of civil procedure, yet it provides a mixture of expository text, cases, and self-testing questions in nearly all of the major areas of the subject.

This open textbook aims to fill the gap between the open-source implementations and the open-source network specifications by providing a detailed but pedagogical description of the key principles that guide the operation of the Internet.

Suppose you want to build a computer network, one that has the potential to grow to global proportions and to support applications as diverse as teleconferencing, video on demand, electronic commerce, distributed computing, and digital libraries. What available technologies would serve as the underlying building blocks, and what kind of software architecture would you design to integrate these building blocks into an effective communication service? Answering this question is the overriding goal of this book—to describe the available building materials and then to show how they can be used to construct a network from the ground up.

This textbook covers the traditional introductory Computer Science I topics but takes a unique approach. Topics are covered in a language-agnostic manner in the first part with supplemental parts that cover the same concepts in a specific language. The current version covers C, Java, and PHP. This textbook as been used in several Computer Science I sections over multiple years at the University of Nebraska-Lincoln.