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Author: Lara Alcock
Publisher: OUP Oxford
ISBN: 0191035378
Category : Mathematics
Languages : en
Pages : 272
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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.
Author: Lara Alcock
Publisher: OUP Oxford
ISBN: 0191035378
Category : Mathematics
Languages : en
Pages : 272
Get Book
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.
Author: Wayne Michael Hall
Publisher: Bloomsbury Publishing USA
ISBN:
Category : Political Science
Languages : en
Pages : 675
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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.
Author: Raffi Grinberg
Publisher: Princeton University Press
ISBN: 0691172935
Category : Mathematics
Languages : en
Pages : 200
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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
Author: Ethan Bueno de Mesquita
Publisher: Princeton University Press
ISBN: 0691215014
Category : Social Science
Languages : en
Pages : 400
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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
Author: Allen B. Downey
Publisher: "O'Reilly Media, Inc."
ISBN: 1491907363
Category : Computers
Languages : en
Pages : 284
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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
Author: Charles Chapman Pugh
Publisher: Springer Science & Business Media
ISBN: 0387216847
Category : Mathematics
Languages : en
Pages : 445
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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.
Author: Lara Alcock
Publisher: Oxford University Press, USA
ISBN: 0198723539
Category : Mathematics
Languages : en
Pages : 265
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Book Description
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.
Author: William F. Trench
Publisher: Prentice Hall
ISBN: 9780130457868
Category : Applied mathematics
Languages : en
Pages : 0
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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.
Author: Tom Chatfield
Publisher: SAGE
ISBN: 1526418770
Category : Philosophy
Languages : en
Pages : 329
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Book Description
Shortlisted for the British Book Design and Production Awards 2018, Educational Books category Do you need to demonstrate a good argument or find more evidence? Are you mystified by your tutor′s comment ′critical analysis needed′? What does it really mean to think well - and how do you learn to do it? Critical thinking is a set of techniques. You just need to learn them. So here’s your personal toolkit for demystifying critical engagement. I’ll show you how to sharpen your critical thinking by developing and practicing this set of skills, so you can... Spot an argument and get why reasoning matters Sniff out errors and evaluate evidence Understand and account for bias Become a savvy user of technology Develop clear, confident critical writing. Designed to work seamlessly with a power pack of digital resources and exercises, you′ll find practical and effective tools to think and write critically in an information-saturated age. No matter whether you′re launching on your first degree or arriving as an international or mature student, Critical Thinking gives you the skills, insights and confidence to succeed. In your critical thinking toolkit Watch the 10 commandments videos – life rules to change how you think Smart Study boxes share excellent tips to whip your work into shape BuzzFeed quizzes to test what (you think) you know Space to scribble! Journal your thoughts, questions, eureka moments as you go Chat more online with #TalkCriticalThinking
Author: Ray Bradbury
Publisher: Simon and Schuster
ISBN: 0743247221
Category : Fiction
Languages : en
Pages : 217
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Book Description
Set in the future when "firemen" burn books forbidden by the totalitarian "brave new world" regime.
