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Logic


A Field Guide to Lies: Critical Thinking in the Information Age

A Field Guide to Lies: Critical Thinking in the Information Age Lowest new price: $11.14
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Author: Daniel J. Levitin
Brand: Dutton Books

From The New York Times bestselling author of The Organized Mind and This is Your Brain on Music, a primer to the critical thinking that is more necessary now than ever.

We are bombarded with more information each day than our brains can process—especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them.

It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, distortions, and outright lies from reliable information? Levitin groups his field guide into two categories—statistical infomation and faulty arguments—ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning—not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some lying weasels in their tracks!

 

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  • Dutton Books

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Burn Math Class: And Reinvent Mathematics for Yourself

Burn Math Class: And Reinvent Mathematics for Yourself Lowest new price: $15.69
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Author: Jason Wilkes
Brand: Wilkes Jason

A manifesto for a mathematical revolution

Forget everything you've been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math--with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire.

Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically--and it becomes fun!

Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus.

Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

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  • Burn Math Class And Reinvent Mathematics for Yourself

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Category Theory (Oxford Logic Guides)

Category Theory (Oxford Logic Guides) Lowest new price: $43.11
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Author: Steve Awodey
Brand: imusti

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.

Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!

This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

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  • Oxford University Press USA

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Fundamentals of Mathematics

Fundamentals of Mathematics Lowest new price: $29.08
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Author: James Van Dyke
Brand: Brand: Cengage Learning

The FUNDAMENTALS OF MATHEMATICS, Tenth Edition, offers a comprehensive and objectives-based review of all basic mathematics concepts. The author helps learners by addressing three important needs: 1) establishing good study habits and overcoming math anxiety, 2) making the connections between mathematics and their modern, day-to-day activities, and 3) being paced and challenged according to their individual level of understanding. The clear exposition and the consistency of presentation make learning arithmetic accessible for all. Key concepts presented in section objectives--and further defined within the context of How and Why--provide a strong foundation for learning and lasting comprehension. With a predominant emphasis on problem-solving skills, concepts, and applications based on "real world" data (with some introductory algebra integrated throughout), this book is suitable for individual study or for a variety of course formats: lab, self-paced, lecture, group, or combined formats.

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  • Used Book in Good Condition

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The Unprovability of Consistency: An Essay in Modal Logic

The Unprovability of Consistency: An Essay in Modal Logic Lowest new price: $55.04
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Author: George Boolos
Brand: Boolos George

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.

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  • The Unprovability of Consistency An Essay in Modal Logic

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Category Theory in Context (Aurora: Dover Modern Math Originals)

Category Theory in Context (Aurora: Dover Modern Math Originals) Lowest new price: $15.94
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Author: Emily Riehl
Brand: Riehl Emily

Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.

Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. While the reader will be rewarded for familiarity with these background mathematical contexts, essential prerequisites are limited to basic set theory and logic.

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  • Category Theory in Context

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Code Warriors: NSA's Codebreakers and the Secret Intelligence War Against the Soviet Union

Code Warriors: NSA's Codebreakers and the Secret Intelligence War Against the Soviet Union Lowest new price: $6.98
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Author: Stephen Budiansky
Brand: Budiansky Stephen

A sweeping, in-depth history of NSA, whose famous “cult of silence” has left the agency shrouded in mystery for decades
 
The National Security Agency was born out of the legendary codebreaking programs of World War II that cracked the famed Enigma machine and other German and Japanese codes, thereby turning the tide of Allied victory. In the postwar years, as the United States developed a new enemy in the Soviet Union, our intelligence community found itself targeting not soldiers on the battlefield, but suspected spies, foreign leaders, and even American citizens. Throughout the second half of the twentieth century, NSA played a vital, often fraught and controversial role in the major events of the Cold War, from the Korean War to the Cuban Missile Crisis to Vietnam and beyond.

In Code Warriors, Stephen Budiansky—a longtime expert in cryptology—tells the fascinating story of how NSA came to be, from its roots in World War II through the fall of the Berlin Wall. Along the way, he guides us through the fascinating challenges faced by cryptanalysts, and how they broke some of the most complicated codes of the twentieth century. With access to new documents, Budiansky shows where the agency succeeded and failed during the Cold War, but his account also offers crucial perspective for assessing NSA today in the wake of the Edward Snowden revelations. Budiansky shows how NSA’s obsession with recording every bit of data and decoding every signal is far from a new development; throughout its history the depth and breadth of the agency’s reach has resulted in both remarkable successes and destructive failures.

Featuring a series of appendixes that explain the technical details of Soviet codes and how they were broken, this is a rich and riveting history of the underbelly of the Cold War, and an essential and timely read for all who seek to understand the origins of the modern NSA.


From the Hardcover edition.

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The Foundations of Mathematics

The Foundations of Mathematics Lowest new price: $18.69
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Author: Ian Stewart
Brand: Oxford University Press USA

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory.

The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.

This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups.

While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward.

This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

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  • Oxford University Press USA

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Introduction to Advanced Mathematics: A Guide to Understanding Proofs

Introduction to Advanced Mathematics: A Guide to Understanding Proofs Lowest new price: $41.30
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Author: Connie M. Campbell
Brand: Brand: Cengage Learning

This text offers a crucial primer on proofs and the language of mathematics. Brief and to the point, it lays out the fundamental ideas of abstract mathematics and proof techniques that students will need to master for other math courses. Campbell presents these concepts in plain English, with a focus on basic terminology and a conversational tone that draws natural parallels between the language of mathematics and the language students communicate in every day. The discussion highlights how symbols and expressions are the building blocks of statements and arguments, the meanings they convey, and why they are meaningful to mathematicians. In-class activities provide opportunities to practice mathematical reasoning in a live setting, and an ample number of homework exercises are included for self-study. This text is appropriate for a course in Foundations of Advanced Mathematics taken by students who've had a semester of calculus, and is designed to be accessible to students with a wide range of mathematical proficiency. It can also be used as a self-study reference, or as a supplement in other math courses where additional proofs practice is needed.

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  • Used Book in Good Condition

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On the Plurality of Worlds

On the Plurality of Worlds Lowest new price: $37.43
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Author: David K. Lewis
Brand: Brand: Wiley-Blackwell

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

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  • Used Book in Good Condition

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