How To Think About Analysis
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How To Think About Analysis
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Author : Lara Alcock
language : en
Publisher:
Release Date : 2014
How To Think About Analysis written by Lara Alcock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Juvenile Nonfiction categories.
Analysis is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared.
Intelligence Analysis
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Author : Wayne Michael Hall
language : en
Publisher: Bloomsbury Publishing USA
Release Date : 2009-12-22
Intelligence Analysis written by Wayne Michael Hall and has been published by Bloomsbury Publishing USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-22 with Political Science categories.
This book offers a vast conceptual and theoretical exploration of the ways intelligence analysis must change in order to succeed against today's most dangerous combatants and most complex irregular theatres of conflict. Intelligence Analysis: How to Think in Complex Environments fills a void in the existing literature on contemporary warfare by examining the theoretical and conceptual foundations of effective modern intelligence analysis—the type of analysis needed to support military operations in modern, complex operational environments. This volume is an expert guide for rethinking intelligence analysis and understanding the true nature of the operational environment, adversaries, and most importantly, the populace. Intelligence Analysis proposes substantive improvements in the way the U.S. national security system interprets intelligence, drawing on the groundbreaking work of theorists ranging from Carl von Clauswitz and Sun Tzu to M. Mitchell Waldrop, General David Petraeus, Richards Heuer, Jr., Orson Scott Card, and others. The new ideas presented here will help the nation to amass a formidable, cumulative intelligence power, with distinct advantages over any and all adversaries of the future regardless of the level of war or type of operational environment.
The Real Analysis Lifesaver
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Author : Raffi Grinberg
language : en
Publisher: Princeton Lifesaver Study Guides
Release Date : 2017
The Real Analysis Lifesaver written by Raffi Grinberg and has been published by Princeton Lifesaver Study Guides this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Functions of real variables categories.
Cover -- Title -- Copyright -- CONTENTS -- Preliminaries -- 1 Introduction -- 2 Basic Math and Logic* -- 3 Set Theory* -- Real Numbers -- 4 Least Upper Bounds* -- 5 The Real Field* -- 6 Complex Numbers and Euclidean Spaces -- Topology -- 7 Bijections -- 8 Countability -- 9 Topological Definitions* -- 10 Closed and Open Sets* -- 11 Compact Sets* -- 12 The Heine-Borel Theorem* -- 13 Perfect and Connected Sets -- Sequences -- 14 Convergence* -- 15 Limits and Subsequences* -- 16 Cauchy and Monotonic Sequences* -- 17 Subsequential Limits -- 18 Special Sequences -- 19 Series* -- 20 Conclusion -- Acknowledgments -- Bibliography -- Index
Understanding Analysis
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Author : Stephen Abbott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Understanding Analysis written by Stephen Abbott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible without it.
Thinking Clearly With Data
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Author : Ethan Bueno de Mesquita
language : en
Publisher: Princeton University Press
Release Date : 2021-11-16
Thinking Clearly With Data written by Ethan Bueno de Mesquita and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Social Science categories.
An engaging introduction to data science that emphasizes critical thinking over statistical techniques An introduction to data science or statistics shouldn’t involve proving complex theorems or memorizing obscure terms and formulas, but that is exactly what most introductory quantitative textbooks emphasize. In contrast, Thinking Clearly with Data focuses, first and foremost, on critical thinking and conceptual understanding in order to teach students how to be better consumers and analysts of the kinds of quantitative information and arguments that they will encounter throughout their lives. Among much else, the book teaches how to assess whether an observed relationship in data reflects a genuine relationship in the world and, if so, whether it is causal; how to make the most informative comparisons for answering questions; what questions to ask others who are making arguments using quantitative evidence; which statistics are particularly informative or misleading; how quantitative evidence should and shouldn’t influence decision-making; and how to make better decisions by using moral values as well as data. Filled with real-world examples, the book shows how its thinking tools apply to problems in a wide variety of subjects, including elections, civil conflict, crime, terrorism, financial crises, health care, sports, music, and space travel. Above all else, Thinking Clearly with Data demonstrates why, despite the many benefits of our data-driven age, data can never be a substitute for thinking. An ideal textbook for introductory quantitative methods courses in data science, statistics, political science, economics, psychology, sociology, public policy, and other fields Introduces the basic toolkit of data analysis—including sampling, hypothesis testing, Bayesian inference, regression, experiments, instrumental variables, differences in differences, and regression discontinuity Uses real-world examples and data from a wide variety of subjects Includes practice questions and data exercises
Real Mathematical Analysis
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Author : Charles Chapman Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Real Mathematical Analysis written by Charles Chapman Pugh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Mathematics categories.
Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .
Think Stats
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Author : Allen B. Downey
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2014-10-16
Think Stats written by Allen B. Downey and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Computers categories.
If you know how to program, you have the skills to turn data into knowledge, using tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. By working with a single case study throughout this thoroughly revised book, you’ll learn the entire process of exploratory data analysis—from collecting data and generating statistics to identifying patterns and testing hypotheses. You’ll explore distributions, rules of probability, visualization, and many other tools and concepts. New chapters on regression, time series analysis, survival analysis, and analytic methods will enrich your discoveries. Develop an understanding of probability and statistics by writing and testing code Run experiments to test statistical behavior, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Import data from most sources with Python, rather than rely on data that’s cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data
Understanding The Mathematical Way Of Thinking The Registers Of Semiotic Representations
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Author : Raymond Duval
language : en
Publisher: Springer
Release Date : 2018-08-12
Understanding The Mathematical Way Of Thinking The Registers Of Semiotic Representations written by Raymond Duval and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-12 with Education categories.
In this book, Raymond Duval shows how his theory of registers of semiotic representation can be used as a tool to analyze the cognitive processes through which students develop mathematical thinking. To Duval, the analysis of mathematical knowledge is in its essence the analysis of the cognitive synergy between different kinds of semiotic representation registers, because the mathematical way of thinking and working is based on transformations of semiotic representations into others. Based on this assumption, he proposes the use of semiotics to identify and develop the specific cognitive processes required to the acquisition of mathematical knowledge. In this volume he presents a method to do so, addressing the following questions: • How to situate the registers of representation regarding the other semiotic “theories” • Why use a semio-cognitive analysis of the mathematical activity to teach mathematics • How to distinguish the different types of registers • How to organize learning tasks and activities which take into account the registers of representation • How to make an analysis of the students’ production in terms of registers Building upon the contributions he first presented in his classic book Sémiosis et pensée humaine, in this volume Duval focuses less on theoretical issues and more on how his theory can be used both as a tool for analysis and a working method to help mathematics teachers apply semiotics to their everyday work. He also dedicates a complete chapter to show how his theory can be applied as a new strategy to teach geometry. “Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations is an essential work for mathematics educators and mathematics teachers who look for an introduction to Raymond Duval’s cognitive theory of semiotic registers of representation, making it possible for them to see and teach mathematics with fresh eyes.” Professor Tânia M. M. Campos, PHD.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
The Convenient Setting Of Global Analysis
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Author : Andreas Kriegl
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-15
The Convenient Setting Of Global Analysis written by Andreas Kriegl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-15 with Mathematics categories.
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.