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Think DSP is an introduction to Digital Signal Processing in Python. The premise of this book (and the other books in the Think X series) is that if you know how to program, you can use that skill to learn other things. The author is writing this book because he thinks the conventional approach to digital signal processing is backward: most books (and the classes that use them) present the material bottom-up, starting with mathematical abstractions like phasors.
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This book is about complexity science, data structures and algorithms, intermediate programming in Python, and the philosophy of science: Data structures and algorithms: A data structure is a collection that contains data elements organized in a way that supports particular operations. For example, a dictionary organizes key-value pairs in a way that provides fast mapping from keys to values, but mapping from values to keys is generally slower. An algorithm is a mechanical process for performing a computation. Designing efficient programs often involves the co-evolution of data structures and the algorithms that use them. For example, the first few chapters are about graphs, a data structure that is a good implementation of a graph---nested dictionaries---and several graph algorithms that use this data structure. Python programming: This book picks up where Think Python leaves off. I assume that you have read that book or have equivalent knowledge of Python. As always, I will try to emphasize fundmental ideas that apply to programming in many languages, but along the way you will learn some useful features that are specific to Python. Computational modeling: A model is a simplified description of a system that is useful for simulation or analysis. Computational models are designed to take advantage of cheap, fast computation. Philosophy of science: The models and results in this book raise a number of questions relevant to the philosophy of science, including the nature of scientific laws, theory choice, realism and instrumentalism, holism and reductionism, and Bayesian epistemology. This book focuses on discrete models, which include graphs, cellular automata, and agent-based models. They are often characterized by structure, rules and transitions rather than by equations. They tend to be more abstract than continuous models; in some cases there is no direct correspondence between the model and a physical system. Complexity science is an interdisciplinary field---at the intersection of mathematics, computer science and physics---that focuses on these kinds of models. That's what this book is about.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Computational complexity Textbooks Python (Computer program language)
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- e-book
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Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Mathematics and Statistics
- Keywords:
- Python (Computer program language) Textbooks Bayesian statistical decision theory
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- e-book
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e-book
Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Mathematics and Statistics
- Keywords:
- Statistics -- Computer programs Textbooks
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- e-book
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e-book
Think Java is a hands-on introduction to computer science and programming used by many universities and high schools around the world. Its conciseness, emphasis on vocabulary, and informal tone make it particularly appealing for readers with little or no experience. The book starts with the most basic programming concepts and gradually works its way to advanced object-oriented techniques. In this fully updated and expanded edition, authors Allen Downey and Chris Mayfield introduce programming as a means for solving interesting problems. Each chapter presents material for one week of a college course and includes exercises to help you practice what you’ve learned. Along the way, you’ll see nearly every topic required for the AP Computer Science A exam and Java SE Programmer I certification.
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This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting. This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Mathematics and Statistics
- Keywords:
- Fourier transformations Textbooks
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- e-book
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e-book
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
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- 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
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- 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
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- e-book
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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