How to Think About Analysis

Author: Lara Alcock
Publisher: OUP Oxford
ISBN: 0191035378
Category : Mathematics
Languages : en
Pages : 272

Book Description
Analysis (sometimes called Real Analysis or Advanced Calculus) 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. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

Intelligence Analysis

Author: Wayne Michael Hall
Publisher: Bloomsbury Publishing USA
ISBN: 0313382662
Category : Political Science
Languages : en
Pages : 458

Book Description
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

Author: Raffi Grinberg
Publisher: Princeton University Press
ISBN: 0691172935
Category : Mathematics
Languages : en
Pages : 200

Book Description
The essential "lifesaver" that every student of real analysis needs Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. The essential “lifesaver” companion for any course in real analysis Clear, humorous, and easy-to-read style Teaches students not just what the proofs are, but how to do them—in more than 40 worked-out examples Every new definition is accompanied by examples and important clarifications Features more than 20 “fill in the blanks” exercises to help internalize proof techniques Tried and tested in the classroom

Thinking Clearly with Data

Author: Ethan Bueno de Mesquita
Publisher: Princeton University Press
ISBN: 0691215014
Category : Social Science
Languages : en
Pages : 400

Book Description
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

Think Stats

Author: Allen B. Downey
Publisher: "O'Reilly Media, Inc."
ISBN: 1491907363
Category : Computers
Languages : en
Pages : 284

Book Description
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 Analysis

Author: Stephen Abbott
Publisher: Springer Science & Business Media
ISBN: 0387215069
Category : Mathematics
Languages : en
Pages : 269

Book Description
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Real Mathematical Analysis

Author: Charles Chapman Pugh
Publisher: Springer Science & Business Media
ISBN: 0387216847
Category : Mathematics
Languages : en
Pages : 445

Book Description
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising 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 it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Handbook of Language Analysis in Psychology

Author: Morteza Dehghani
Publisher: Guilford Publications
ISBN: 1462548431
Category : Social Science
Languages : en
Pages : 650

Book Description
Recent years have seen an explosion of interest in the use of computerized text analysis methods to address basic psychological questions. This comprehensive handbook brings together leading language analysis scholars to present foundational concepts and methods for investigating human thought, feeling, and behavior using language. Contributors work toward integrating psychological science and theory with natural language processing (NLP) and machine learning. Ethical issues in working with natural language data sets are discussed in depth. The volume showcases NLP-driven techniques and applications in areas including interpersonal relationships, personality, morality, deception, social biases, political psychology, psychopathology, and public health.

Why Nations Fail

Author: Daron Acemoglu
Publisher: Currency
ISBN: 0307719227
Category : Business & Economics
Languages : en
Pages : 546

Book Description
Brilliant and engagingly written, Why Nations Fail answers the question that has stumped the experts for centuries: Why are some nations rich and others poor, divided by wealth and poverty, health and sickness, food and famine? Is it culture, the weather, geography? Perhaps ignorance of what the right policies are? Simply, no. None of these factors is either definitive or destiny. Otherwise, how to explain why Botswana has become one of the fastest growing countries in the world, while other African nations, such as Zimbabwe, the Congo, and Sierra Leone, are mired in poverty and violence? Daron Acemoglu and James Robinson conclusively show that it is man-made political and economic institutions that underlie economic success (or lack of it). Korea, to take just one of their fascinating examples, is a remarkably homogeneous nation, yet the people of North Korea are among the poorest on earth while their brothers and sisters in South Korea are among the richest. The south forged a society that created incentives, rewarded innovation, and allowed everyone to participate in economic opportunities. The economic success thus spurred was sustained because the government became accountable and responsive to citizens and the great mass of people. Sadly, the people of the north have endured decades of famine, political repression, and very different economic institutions—with no end in sight. The differences between the Koreas is due to the politics that created these completely different institutional trajectories. Based on fifteen years of original research Acemoglu and Robinson marshall extraordinary historical evidence from the Roman Empire, the Mayan city-states, medieval Venice, the Soviet Union, Latin America, England, Europe, the United States, and Africa to build a new theory of political economy with great relevance for the big questions of today, including: - China has built an authoritarian growth machine. Will it continue to grow at such high speed and overwhelm the West? - Are America’s best days behind it? Are we moving from a virtuous circle in which efforts by elites to aggrandize power are resisted to a vicious one that enriches and empowers a small minority? - What is the most effective way to help move billions of people from the rut of poverty to prosperity? More philanthropy from the wealthy nations of the West? Or learning the hard-won lessons of Acemoglu and Robinson’s breakthrough ideas on the interplay between inclusive political and economic institutions? Why Nations Fail will change the way you look at—and understand—the world.

Introduction to Real Analysis

Author: William F. Trench
Publisher: Prentice Hall
ISBN: 9780130457868
Category : Applied mathematics
Languages : en
Pages : 0

Book Description
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.