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Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Mathematical analysis
- Resource Type:
- e-book
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e-book
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Boundary value problems Differential equations Partial
- Resource Type:
- e-book
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e-book
Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages, and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Textbooks Computer science
- 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
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. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes atCasper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computer science -- Mathematics Textbooks Mathematics
- Resource Type:
- e-book
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e-book
An introductory coverage of algorithms and data structures with application to graphics and geometry.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Textbooks Data structures (Computer science) Algorithms
- Resource Type:
- e-book
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e-book
Programming Fundamentals - A Modular Structured Approach using C++ is written by Kenneth Leroy Busbee, a faculty member at Houston Community College in Houston, Texas. The materials used in this textbook/collection were developed by the author and others as independent modules for publication within the Connexions environment. Programming fundamentals are often divided into three college courses: Modular/Structured, Object Oriented and Data Structures. This textbook/collection covers the first of those three courses. The learning modules of this textbook/collection were written as standalone modules. Students using a collection of modules as a textbook will usually view it contents by reading the modules sequentially as presented by the author of the collection. The learning modules of this textbook/collection were, for the most part, written without consideration of a speci??c programming language. In many cases the C++ language is discussed as part of the explanation of the concept. Often the examples used for C++ are exactly the same for the Java programming language. However, some modules were written speci??cally for the C++ programming language. This could not beavoided as the C++ language is used in conjunction with this textbook/collection by the author in teaching college courses.
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e-book
In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level. Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. Shafer and Zhang believe that the students in this course are best served by a focus on that core material and not by an exposure to a plethora of peripheral topics. Therefore in writing Introduction to Statistics they have sought to present only the core concepts and use a wide-ranging set of exercises for each concept to drive comprehension. As a result Introduction to Statistics is a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better-focused presentation of the central material. You will not only appreciate the depth and breadth of exercises in Introduction to Statistics, but you will also like the close attention to detail that Shafer and Zhang have paid to the student and instructor solutions manuals. This is one of few books on the market where the textbook authors have written the solutions manuals to maintain the integrity of the material. In addition, in order to facilitate the use of technology with the book the authors included “large data set exercises,” where appropriate, that refer to large data sets that are available on the web, and for which use of statistical software is necessary.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Statistics
- Resource Type:
- e-book
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e-book
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines. Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book