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This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
- Subjects:
- Mathematics and Statistics
- Keywords:
- MATLAB Textbooks Probabilities
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However, in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course. In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a discussion of the algebra of complex numbers (in particular complex numbers in polar form), the 2-dimensional real vector space R 2 sequences and series with focus on the arithmetic and geometric series (which are again examples of functions, though this is not emphasized), and finally the generalized binomial theorem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Precalculus Algebra Textbooks
- Resource Type:
- e-book
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e-book
A grasp of the logic and practice of science is essential to understand the rest of the world around us. To that end, the CMB3e iText (like earlier editions) remains focused on experimental support for what we know about cell and molecular biology, and on showing students the relationship of cell structure and function. Rather than trying to be a comprehensive reference book, CMB3e selectively details investigative questions, methods and experiments that lead to our understanding of cell biology. This focus is nowhere more obvious than in the chapter learning objectives and in external links to supplementary material. The Basic CMB3e version of the iText includes links to external web-sources as well as the author’s short, just-in-time YouTube VOPs (with edited, optional closed captions), all embedded in or near relevant text. Each video is identified with a descriptive title and video play and QR bar codes. The Learning objectives align with content and ask students to use new knowledge to make connections and deepen their understanding of concept and experiment. All external links are intended to expand or explain textual content and concepts and to engage student curiosity. Links to full VOP lectures are now at the back of the book. include optional edited closed captions. All images in the iText are by the author or are from public domain or Creative Commons (CC) licensed sources. For all externally sourced images, CC licenses are indicated with the image. Beyond the Basic CMB3e, the freely available Annotated CMB3e contains interactive links and formative assessments in the form of Challenge boxes. A CMB3e Sample Chapter and CMB3e iText for Instructors model additional interactive features, including short 25 Words or Less writing assignments that can be incorporated into almost any course management system, and all of which the author assigned as homework in his flipped, blended course. These assessments aim to reinforce writing as well as critical thinking skills. The CMB3e Sample Chapter is freely available for download; the CMB3e for Instructors version of the iText is available on request. My goal in writing this iText is to make the content engaging, free and comparable in accuracy and currency to commercial textbooks. I encourage instructors to use the interactive features of the iText (critical thought questions, YouTube videos, etc.) to challenge their students. With all of these enhancements, I encourage students to think about • how good and great experiments were inspired and designed, • how alternative experimental results were predicted, • how data was interpreted, and finally, • investigators (and we!) arrive at the most interesting “next questions”. The online iText is the most efficient way to access links and complete online assignments. Nevertheless, you can download, read, study, and access many links with a smart phone or tablet. And you can add your own annotations digitally, or write in the margins of a printout the old-fashioned way! Your instructor may provide additional instructions for using your iText.
- Subjects:
- Biology
- Keywords:
- Textbooks Cytology Molecular biology
- Resource Type:
- e-book
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e-book
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Mathematical analysis
- Resource Type:
- e-book
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e-book
Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra or basic math course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty. The first edition of Prealgebra by OpenStax is available in web view in the ancillaries.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks Arithmetic
- Resource Type:
- e-book
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e-book
College Algebra provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.College Algebraguides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.Algebra and Trigonometry guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Precalculus Algebra Textbooks
- Resource Type:
- e-book
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e-book
This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students' problem-solving and writing skills.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computer science -- Mathematics Textbooks Mathematics
- Resource Type:
- e-book
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e-book
The goals of this textbook are to help students acquire the technical skills of using software and managing a database, and develop research skills of collecting data, analyzing information and presenting results. We emphasize that the need to investigate the potential and practicality of GIS technologies in a typical planning setting and evaluate its possible applications. GIS may not be necessary (or useful) for every planning application, and we anticipate these readings to provide the necessary foundation for discerning its appropriate use. Therefore, this textbook attempts to facilitate spatial thinking focusing more on open-ended planning questions, which require judgment and exploration, while developing the analytical capacity for understanding a variety of local and regional planning challenges. While this textbook provides the background for understanding the concepts in GIS as applicable to urban and regional planning, it is best when accompanied by a hands-on tutorial, which will enable readers to develop an in-depth understanding of the specific planning applications of GIS. In the end of each chapter, we also provided several discussion questions, together with contextual applications through some web links.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Land Surveying and Geo-Informatics
- Keywords:
- Textbooks Geographic information systems
- Resource Type:
- e-book