Now in a new edition --the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of G del's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics."

On a chilly, gray autumn afternoon in 1984, a patrolman was dispatched to an inner-city tenement in Auburn, Maine to investigate the report of a possible fire. What he found inside the building's smoke-filled, second-story apartment was not a fire but something far more horrifying -- the charred body of a 4-year-old girl, Angela Palmer, who had been stuffed into the oven of a kitchen stove and cooked to death. The discovery traumatized the community and shocked the country. The ensuing murder prosecution of the youngster's mother, Cynthia Palmer, and her boyfriend, John Lane, cast a searching light into the shadows of a secret world in which children and women suffer violence and sexual predation at the hands of those who are supposed to love and protect them.

Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.

The forms and scope of logic rest on assumptions of how language and reasoning connect to experience. In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics. Chapters on propositional logic, parsing propositions, and meaning, truth and reference give a basis for criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples of formalizations of propositions and arguments illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, functions, and second-order logic. The chapter on second-order logic illustrates how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation, and supplemented by many exercises, this volume is suitable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formalizing reasoning.

If you're preparing for The American Institute of Professional Bookkeepers' (AIPB) bookkeeping certification test, you need an easy- to-follow test-preparation guide that gets you up to speed quickly in all of the bookkeeping basics, from setting up a company's books and recording transactions to managing employee payroll, handling government paperwork, and closing out the books. You need "Bookkeeping Workbook For Dummies."

With demonstration problems, complementary examples, and multiple-choice questions you'll find in this user-friendly primer, you'll sharpen your bookkeeping skills for the real world as you increase your ability to perform well on any test. Chapter quizzes let check your progress as you go, and step-by-step answers show you where you went wrong (or right) each problem. You'll feel your confidence --and competence--growing as you learn how to: Perform a wide variety of financial transactionsUse key concepts and skills with real-world bookkeeping problemsDesign a bookkeeping systemTrack day-to-day business operationsKeep journals for active accountsUse blank working papers and spread sheetsHandle cash entries and develop internal controlsCalculate and pay employee withholding taxesDepreciate assetsProve out your books at year's endPrepare tax returns as set up for a new year

Complete with Top Ten lists for managing cash, monitoring accounts, and finding additional helpful resources, "Bookkeeping Workbook For Dummies" is the test-prep guide you need to help you ace the certification test and speed your way into a successful and rewarding career.

Joyce L. Epstein is the leading authority on school, family, community partnerships Includes examples that illustrate how research-based approaches improve policies on partnerships, district leadership, and school programs of family and community involvement.

Joyce L. Epstein is the leading authority on school, family, community partnerships Includes examples that illustrate how research-based approaches improve policies on partnerships, district leadership, and school programs of family and community involvement.

Learn how to create culturally responsive, socially just school-family partnerships that positively impact student learning outcomes. Responding to the current rise in White supremacy in America, a surge in hate crimes against BIPOC students and families, and the gaping digital divide exposed by the COVID-19 pandemic, this book addresses the need for educators and schools to develop competency in working with diverse families and their communities. Chapters address misconceptions of school personnel that often result in microaggressions and miscommunications that impede fully including families in the education of their children. Exploring a wide range of sociocultural issues present in today's schools, readers will learn how to better work with military families during deployment, students with disabilities, families with various living arrangements, immigrant families, and religiously diverse students. The text features engaging, real-life scenarios and research-based practices designed to improve the academic success of all K-12 learners.Book Features: Innovative models for creating culturally responsive family and community engagement initiatives that focus on student success. Reflective questions to facilitate discussions in various professional development venues, including schools, university programs for teachers and administrators, and community organizations. Concrete examples of successful partnerships involving public schools, a higher education institution, and a public city library. An extensive list of resources for building better educational programs and communities.

This is a must-have, research-based guide for all schools serving culturally diverse elementary and middle grade students and their communities. It's filled with fun, practical, highly effective strategies for raising awareness and engaging all families in their children's education - a sure path toward increased student success! Get detailed examples and step-by-step guidelines for implementing successful... Multicultural Family Nights Workshops for Parents Curriculum Connections Much of the reproducible material is also provided in Spanish - giving educators an even broader reach!

Host family reading nights at your school These events promote literacy outside of the classroom and encourage families to get involved in their children s achievement. They also build relationships among educators, families, and community partners. This practical book is full of step-by-step guidelines and reproducible activities to help you bring family reading nights to life in your own school or district.

Special Features:

• The book is organized by month of the school year, so you can quickly find activities that meet your needs
• Each activity is easy to implement and includes a page of instructions for teacher-leaders and an activity page for families
• An appendix provides all of the forms you need to get your Family Reading Night started, including invitations and registration sheets
• All of the family activities can be photocopied or downloaded for free from our website, www.routledge.com/books/details/9781138021471, so that you can print and distribute them during your event

This enhanced second edition includes connections to the Common Core State Standards for reading. It also features a special new appendix with all of the family activities translated into Spanish, to help more families get involved "

Host family reading nights at your school These events promote literacy outside of the classroom and encourage families to get involved in their children s achievement. They also build relationships among educators, families, and community partners. This practical book is full of step-by-step guidelines and reproducible activities to help you bring family reading nights to life in your own school or district.

Special Features:

• The book is organized by month of the school year, so you can quickly find activities that meet your needs
• Each activity is easy to implement and includes a page of instructions for teacher-leaders and an activity page for families
• An appendix provides all of the forms you need to get your Family Reading Night started, including invitations and registration sheets
• All of the family activities can be photocopied or downloaded for free from our website, www.routledge.com/books/details/9781138021471, so that you can print and distribute them during your event

This enhanced second edition includes connections to the Common Core State Standards for reading. It also features a special new appendix with all of the family activities translated into Spanish, to help more families get involved "

This is a must-have, research-based guide for all schools serving culturally diverse elementary and middle grade students and their communities. It's filled with fun, practical, highly effective strategies for raising awareness and engaging all families in their children's education - a sure path toward increased student success! Get detailed examples and step-by-step guidelines for implementing successful... Multicultural Family Nights Workshops for Parents Curriculum Connections Much of the reproducible material is also provided in Spanish - giving educators an even broader reach!

Manage the art of bookkeeping Do you need to get up and running on bookkeeping basics and the latest tools and technology used in the field? You've come to the right place! Bookkeeping All-In-One For Dummies is your go-to guide for all things bookkeeping. Bringing you accessible information on the new technologies and programs, it cuts through confusing jargon and gives you friendly instruction you can use right away. Inside, you'll learn how to keep track of transactions, unravel up-to-date tax information, recognize your assets, and so much more. Covers all the new techniques and programs in the bookkeeping field Shows you how to manage assets and liabilities Explains how to track business transactions accurately with ledgers and journals Helps you make sense of accounting and bookkeeping basics Get all the info you need to jumpstart your career as a bookkeeper!

Your personal roadmap to becoming fluent in financial reports At first glance, the data in financial reports might seem confusing or overwhelming. But, with the right guide at your side, you can learn to translate even the thickest and most complex financial reports into plain English. In Reading Financial Reports For Dummies, you'll move step-by-step through each phase of interpreting and understanding the data in a financial report, learning the key accounting and business fundamentals as you go. The book includes clear explanations of basic and advanced topics in finance, from the difference between private and public companies to cash flow analysis. In this book, you'll also find: Full coverage of how to analyze annual reports, including their balance sheets, income statements, statements of cash flow, and consolidated statements Real-world case studies and financial statement examples from companies like Mattel and Hasbro Strategies for analyzing financial reports to reveal opportunities for operations optimization Reading Financial Reports For Dummies is a can't-miss resource for early-career investors, traders, brokers, and business leaders looking to improve their financial literacy with a reliable, accurate, and easy-to-follow financial handbook.

Financial statements hold the key to a company's fiscal health--so learn to read them

In order to gauge a company's health--as well as the competition's--managers must know how to properly read and understand financial statements. "The Business Owner's Guide to Reading and Understanding Financial Statements" will introduce managers and business owners to various types of financial statements and explain why they are important. Serving as a desktop reference, especially for managers without a strong background in finance, this book will discuss the difference between internal and external financial statements and explain how they can be used for financial decision-making in order to avoid common missteps.

Whether you're planning for major capital projects or simply managing the fiscal aspects of your department, this nontechnical, results-driven guide will arm you with the fundamentals to: Understand the budget process and why it is importantManage assets and track inventoryGauge profitabilityMonitor success throughout the year using internal reportingSet prices and make key cost decisions

Financial statements are essential to determining a company's fiscal health. Understand where your company stands so that you can make informed decisions about its future.

The fast and easy way to master the art of bookkeeping If you're a business owner or an employee who manages finances, the latest edition of Bookkeeping For Dummies is for you. This handy guide gives you clear and concise information on how to keep track of accounts, prepare balance sheets, organize ledgers or journals, create financial statements, and so much more. Packed with the most up-to-date bookkeeping practices, tax information, and small-business laws, Bookkeeping For Dummies is an accessible, invaluable resource you'll turn to again and again. Accurate and complete bookkeeping is crucial to any -business owner but jumping in headfirst without knowing your accounts from your balance sheets can confuse even the most astute businessperson. That's where Bookkeeping For Dummies helps! Written in the familiar and friendly tone that has defined the For Dummies brand for more than twenty years, this clear and comprehensive guide covers everything you'll encounter as you set out to tackle your company's books, ensuring you're on the right track and saving you tons of headaches along the way. So what are you waiting for? It's time to hit the books! * Offers easy-to-follow instructions to keep track of your business' financial well-being * Covers managing assets and liabilities * Includes updated QuickBooks screenshots and Excel spreadsheets * Provides guidance on producing balance sheets and creating financial statements Whether you're just starting out with bookkeeping or a bookkeeper who needs to brush up on your skills Bookkeeping For Dummies sets you up for success.

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of logic as the art of reasoning well, yet each essay is designed so that it may be read independently. The topic of this volume is prescriptive reasoning. Descriptive claims say how the world is, was, or will be; prescriptive claims say how the world should be. We have fairly clear rules for reasoning with descriptive claims. The goal of the first essay, "Reasoning with Prescriptive Claims," is to clarify how to reason with prescriptive ones. The first step in doing so is to justify our viewing prescriptions as true or false. That justification is part of a general approach to reasoning in which many kinds of personal evaluations are taken to be true-false divisions. That view has been implicit if not explicit in analyses of reasoning from formal logic through argument analysis. in "Truth and Reasoning" I set out reasons for adopting that methodology. Theories, too, seem to be descriptive or prescriptive. Some say how the world is, others how the world should be. Yet, as shown in "Prescriptive Theories?," on close examination the distinction evaporates. Unless, that is, one says that certain theories about values use an entirely different notion of truth than is used in science and is codified in our usual methods of reasoning. Absent that, there seems to be no justification for constructing and evaluating what are typically thought of as prescriptive theories differently from descriptive ones. Many discussions of how to evaluate prescriptive claims are given in terms of what is rational or irrational to do. In the final essay, "Rationality," what we mean by the idea of someone being rational is investigated and the limitations of that label in evaluating reasoning or actions is shown.

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process.

Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Holder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations."

The easy way to get a handle on bookkeeping Accurate and complete bookkeeping is crucial to any business owner, but it's also important to those who work with the business, such as investors, financial institutions, and employees. Bookkeeping For Dummies provides the easy and painless way to master this critical skill. You'll get clear and concise information on keeping track of transactions, figuring out balance sheets, keeping ledgers or journals, creating financial statements, and operating accounts for businesses, along with practices and examples to hone your skills. Plus, the bonus CD includes samples of bookkeeping forms, working papers, letters, resources, and spreadsheets. * Keeping track of transactions * Figuring out the balance sheet * Keeping a ledger and journal * Creating financial statements * Operating accounts for businesses * Recognizing assets and liabilities * Up-to-date tax information * Changes in small business regulations * Additional and complementary examples * Demonstration problems * True/false and multiple-choice questions and scenarios Whether you're a professional or a student looking to expand your skills, Bookkeeping Kit For Dummies is a one-stop resource for anyone interested in this ever-growing occupation.

In "Classical Mathematical Logic," Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations.

The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference.

"Classical Mathematical Logic" presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.