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This 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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Combinatorial analysis
- Resource Type:
- e-book
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e-book
Unlike some other textbooks, this one does not follow a top-down narrative. Rather it has the flow of a conversation, with backtracking. We will often build up programs incrementally, just as a pair of programmers would. We will include mistakes, not because I don't know the answer, but because this is the best way for you to learn. Including mistakes makes it impossible for you to read passively: you must instead engage with the material, because you can never be sure of the veracity of what you're reading. At the end, you'll always get to the right answer. However, this non-linear path is more frustrating in the short term (you will often be tempted to say, “Just tell me the answer, already!”), and it makes the book a poor reference guide (you can't open up to a random page and be sure what it says is correct). However, that feeling of frustration is the sensation of learning. I don't know of a way around it. At various points you will encounter this: ExerciseThis is an exercise. Do try it. This is a traditional textbook exercise. It's something you need to do on your own. If you're using this book as part of a course, this may very well have been assigned as homework. In contrast, you will also find exercise-like questions that look like this: Do Now!There's an activity here! Do you see it? When you get to one of these, stop. Read, think, and formulate an answer before you proceed. You must do this because this is actually an exercise, but the answer is already in the book—most often in the text immediately following (i.e., in the part you're reading right now)—or is something you can determine for yourself by running a program. If you just read on, you'll see the answer without having thought about it (or not see it at all, if the instructions are to run a program), so you will get to neither (a) test your knowledge, nor (b) improve your intuitions. In other words, these are additional, explicit attempts to encourage active learning. Ultimately, however, I can only encourage it; it's up to you to practice it. The main programming language used in this book is Racket. Like with all operating systems, however, Racket actually supports a host of programming languages, so you must tell Racket which language you're programming in. This textbook has been used in classes at: Brown University, Cal Poly, Columbus State University, Northeastern University, NYU, Reed College, UC-San Diego, UC-Santa Cruz, University of Rhode Island, University of Utah, Westmont College, Williams College, Worcester Polytechnic Institute.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Programming languages (Electronic computers) Textbooks
- Resource Type:
- e-book
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e-book
Welcome to the exciting world of technical theatre. Studying this topic can lead to many different careers in several different sectors of the economy. The general skills needed for any of the careers or sectors have many things in common. Workers need to be dead-line oriented, as most productions have firm timelines that cannot be altered. Critical thinking and analysis are much needed skills. Almost every project in the field is unique and technicians and designers alike must discover the best way of reaching a project’s goal. Creative problem solving is trait successful practitioners have in common. With every project being unique, there are no guaranteed solutions to the problems that are presented. Technicians draw on their vast experience of what worked in the past that can be adapted to be a solution to the current problems. Clear communication and collaboration round out the necessary skills. No technical theatre project is ever handled by one person on their own. Collaboration with many people is the norm, and successful collaboration requires clear written and verbal communication skills.
- Subjects:
- Performing Arts
- Keywords:
- Theaters--Stage-setting scenery Stage management Theater -- Production direction Textbooks
- Resource Type:
- e-book
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e-book
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Mathematical analysis
- Resource Type:
- e-book
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e-book
In this book, you will learn about all three kinds of interaction. In all three cases, interesting software techniques are needed in order to bring the computations into contact, yet keep them suffciently at arm's length that they don't compromise each other's reliability. The exciting challenge, then, is supporting controlled interaction. This includes support for computations that share a single computer and interact with one another, as your email and word processing programs do. It also includes support for data storage and network communication. This book describes how all these kinds of support are provided both by operating systems and by additional software layered on top of operating systems, which is known as middleware. Chapter 1 provides an overview of the text as a whole, explaining what an operating system is, what middleware is, and what sorts of support these systems provide for controlled interaction. The next nine chapters work through the varieties of controlled interac- tion that are exemplified by the scenario at the beginning of the preface: in- teraction between concurrent computations on the same system (as between your email program and your word processor), interaction across time (as between your word processor before your trip and your word processor after your trip), and interaction across space (as between your email program and your service provider's email server). The first of these three topics is controlled interaction between computa- tions operating at one time on a particular computer. Before such interaction can make sense, you need to understand how it is that a single computer can be running more than one program, such as an email program in one window and a word processing program in another. Therefore, Chapter 2 explains the fundamental mechanism for dividing a computer's attention between concurrent computations, known as threads. Chapter 3 continues with the related topic of scheduling. That is, if the computer is dividing its time between computations, it needs to decide which ones to work on at any moment. With concurrent computations explained, Chapter 4 introduces con- trolled interactions between them by explaining synchronization, which is control over the threads' relative timing. For example, this chapter explains how, when your email program sends a document to your word processor, the word processor can be constrained to read the document only after the email program writes it. One particularly important form of synchroniza- tion, atomic transactions, is the topic of Chapter 5. Atomic transactions are groups of operations that take place as an indivisible unit; they are most commonly supported by middleware, though they are also playing an increasing role in operating systems. Other than synchronization, the main way that operating systems con- trol the interaction between computations is by controlling their access to memory. Chapter 6 explains how this is achieved using the technique known as virtual memory. That chapter also explains the many other objectives this same technique can serve. Virtual memory serves as the foundation for Chapter 7's topic, which is processes. A process is the fundamental unit of computation for protected access, just as a thread is the fundamental unit of computation for concurrency. A process is a group of threads that share a protection environment; in particular, they share the same access to virtual memory. The next three chapters move outside the limitations of a single com- puter operating in a single session. First, consider the document stored before a trip and available again after it. Chapter 8 explains persistent storage mechanisms, focusing particularly on the file storage that operat- ing systems provide. Second, consider the interaction between your email program and your service provider's email server. Chapter 9 provides an overview of networking, including the services that operating systems make available to programs such as the email client and server. Chapter 10 ex- tends this discussion into the more sophisticated forms of support provided by communication middleware, such as messaging systems, RMI, and web services. Finally, Chapter 11 focuses on security. Because security is a pervasive issue, the preceding ten chapters all provide some information on it as well. Specifically, the final section of each chapter points out ways in which se- curity relates to that chapter's particular topic. However, even with that coverage distributed throughout the book, a chapter specifically on security is needed, primarily to elevate it out of technical particulars and talk about general principles and the human and organizational context surrounding the computer technology. The best way to use these chapters is in consecutive order. However, Chapter 5 can be omitted with only minor harm to Chapters 8 and 10, and Chapter 9 can be omitted if students are already suffciently familiar with networking.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Operating systems (Computers) Computer software -- Development Middleware Textbooks
- Resource Type:
- e-book
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e-book
This book is written both for practitioners and business students. Managers wishing to understand how electronic commerce is revolutionizing business will find that our comprehensive coverage of essential business issues (e.g., pricing and distribution) answers many of their questions. Advanced business students (junior, seniors, and graduate students) will find that the blend of academic structure and practical examples provides an engaging formula for learning. The book's title reflects some key themes that we develop. First, we are primarily concerned with electronic commerce, which we define as using technology (e.g., the Internet) to communicate or transact with stakeholders (e.g., customers). Second, we discuss how organizations must change in order to take advantage of electronic commerce opportunities. In this sense, our book offers the strategic perspective (i.e., the best way to operate a successful business in the 21st century). Third, with the growing importance of the Internet and related technologies, organizations must take electronic commerce into account when they are creating strategic plans. Thus, electronic commerce is a strategic perspective that all firms must adopt, both in the present and in the future. In other words, an organization that does not explicitly consider electronic commerce as a strategic imperative is probably making a crucial error. Here, we focus primarily on the opportunities and tactics that can lead to success in the electronic marketplace.
- Subjects:
- E-Commerce
- Keywords:
- Electronic commerce Internet marketing Textbooks
- Resource Type:
- e-book