**Author**: Milo Beckman

**Publisher:** Penguin

**ISBN:** 1524745553

**Category : **Mathematics

**Languages : **en

**Pages : **225

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**Book Description**
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

**Author**: Milo Beckman

**Publisher:** Penguin

**ISBN:** 1524745553

**Category : **Mathematics

**Languages : **en

**Pages : **225

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**Book Description**
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

**Author**: Milo Beckman

**Publisher:** Penguin UK

**ISBN:** 0241507588

**Category : **Mathematics

**Languages : **en

**Pages : **224

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**Book Description**
'The whizz-kid making maths supercool. . . A brilliant book that takes everything we know (and fear) about maths out of the equation - starting with numbers' The Times 'A cheerful, chatty, and charming trip through the world of mathematics. . . Everyone should read this delightful book' Ian Stewart, author of Do Dice Play God? The only numbers in this book are the page numbers. The three main branches of abstract math - topology, analysis, and algebra - turn out to be surprisingly easy to grasp. Or at least, they are when our guide is a math prodigy. With forthright wit and warm charm, Milo Beckman upends the conventional approach to mathematics, inviting us to think creatively about shape and dimension, the infinite and the infinitesimal, symmetries, proofs, and all how all these concepts fit together. Why is there a million dollar prize for counting shapes? Is anything bigger than infinity? And how is the 'truth' of mathematics actually decided? A vivid and wholly original guide to the math that makes the world tick and the planets revolve, Math Without Numbers makes human and understandable the elevated and hypothetical, allowing us to clearly see abstract math for what it is: bizarre, beautiful, and head-scratchingly wonderful.

**Author**: Andrew Kravin

**Publisher:**
**ISBN:**
**Category : **
**Languages : **en

**Pages : **72

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**Book Description**

**Author**: Susan M. Brookhart

**Publisher:** ASCD

**ISBN:** 1416629890

**Category : **Education

**Languages : **en

**Pages : **136

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**Book Description**
Are you picking up all your students' work is trying to tell you? In this book, assessment expert Susan M. Brookhart and instructional coach Alice Oakley walk teachers through a better and more illuminating way to approach student work across grade levels and content areas. You’ll learn to view students' assignments not as a verdict on right or wrong but as a window into what students "got" and how they are thinking about it. The insight you'll gain will help you * Infer what students are thinking, * Provide effective feedback, * Decide on next instructional moves, and * Grow as a professional. Brookhart and Oakley then guide teachers through the next steps: clarify learning goals, increase the quality of classroom assessments, deepen your content and pedagogical knowledge, study student work with colleagues, and involve students in the formative learning cycle. The book's many authentic examples of student work and teacher insights, coaching tips, and reflection questions will help readers move from looking at student work for correctness to looking at student work as evidence of student thinking.

**Author**: Jeff Warren

**Publisher:** Xulon Press

**ISBN:** 1606474863

**Category : **Religion

**Languages : **en

**Pages : **196

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**Book Description**
Book Summary Forgiveness. It s the cry of the human heart and yet few of us ever really live in it. Instead we strive to establish our worth through our performance, the approval of others, the latest self-help plan, or even religion. Do you struggle to shake the mistakes of your past? Do thoughts of the future bring anxiety? Are you troubled by unwanted patterns that have developed in your life? Maybe you re convinced that God is somewhere in the mix but the often contradictory expressions of religion have left your head spinning and heart wanting. Perhaps you re weary of an us against them brand of Christianity. Could it be that Jesus Christ has been lost in a religion that bears His name? Live Forgiven offers real answers for real life from a fellow traveler. Liberating truths combined with practical application will help you discover the unexpected freedom and boundless joy of living forgiven. Everything is about to change as you discover the life you never thought possible.

**Author**: Andrea Cantini

**Publisher:** Springer Science & Business Media

**ISBN:** 9401721092

**Category : **Mathematics

**Languages : **en

**Pages : **284

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**Book Description**
The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies.

**Author**: Jeannie Oakes

**Publisher:** Routledge

**ISBN:** 1317250834

**Category : **Education

**Languages : **en

**Pages : **452

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**Book Description**
This is an up-to-the-moment, engaging, multicultural introduction to education and teaching and the challenges and opportunities they present. Together, the four authors bring a rich blend of theory and practical application to this groundbreaking text. Jeannie Oakes is a leading education researcher and former director of the UCLA teacher education program. Martin Lipton is an education writer and consultant and has taught in public schools for 31 years. Lauren Anderson and Jamy Stillman are former public school teachers, now working as teacher educators. This unique, comprehensive foundational text considers the values and politics that pervade the U.S. education system, explains the roots of conventional thinking about schooling and teaching, asks critical questions about how issues of power and privilege have shaped and continue to shape educational opportunity, and presents powerful examples of real teachers working for equity and justice. Taking the position that a hopeful, democratic future depends on ensuring that all students learn, the text pays particular attention to inequalities associated with race, social class, language, gender, and other social categories and explores teachers role in addressing them. The text provides a research-based and practical treatment of essential topics, and it situates those topics in relation to democratic values; issues of diversity; and cognitive, sociocultural, and constructivist perspectives on learning. The text shows how knowledge of education foundations and history can help teachers understand the organization of today s schools, the content of contemporary curriculum, and the methods of modern teaching. It likewise shows how teachers can use such knowledge when thinking about and responding to headline issues like charter schools, vouchers, standards, testing, and bilingual education, to name just a few. Central to this text is a belief that schools can and must be places of extraordinary educational quality and institutions in the service of social justice. Thus, the authors address head-on tensions between principles of democratic schooling and competition for always-scarce high-quality opportunities. Woven through the text are the voices of a diverse group of teachers, who share their analyses and personal anecdotes concerning what teaching to change the world means and involves. Click Here for Book Website Pedagogical Features: Digging Deeper sections referenced at the end of each chapter and featured online include supplementary readings and resources from scholars and practitioners who are addressing issues raised in the text. Instructor s Manual offers insights about how to teach course content in ways that are consistent with cognitive and sociocultural learning theories, culturally diverse pedagogy, and authentic assessment.New to this Edition: "

**Author**: William S. Veatch

**Publisher:** Createspace Independent Publishing Platform

**ISBN:** 9781539503392

**Category : **
**Languages : **en

**Pages : **354

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**Book Description**
Math Without Numbers - The Mathematics of Ideas. Volume 1 - Foundations. This Volume 1 in the "Math Without Numbers" series explores the nature of Ideas, from both a practical and an abstract mathematical point of view. The book demonstrates that mathematics can explain "how" we think, but cannot tell us "what" to think or how to act. The author applies principles of Set Theory to Ideas, and illustrates how Ideas form structures that are well-known in the field of Mathematics, including Partitions/Equivalence Classes, Groups, Boolean Algebras, Rings, Lattices, and Topologies. The book touches on Logic, Argumentation, and Debate, which are topics that will be explored in detail in Volumes 2 and 3. The discussion is original and accessible, and includes material appropriate for anyone with a background in basic high school math, as well as more advanced material for those looking for a challenge. The book begins at an introductory level, but proceeds to discuss more complex material for those interested in making language more precise and unambiguous. Much of the focus is on Lattices and Boolean Algebras/Rings, as applied to Ideas rather than numbers. There are many similarities to the relatively new field of mathematics called Formal Concept Analysis, although Math Without Numbers focuses on building a foundation in Set Theory and Logic. This book is intended for anyone interested in Set Theory, the Philosophy of Mathematics, the Philosophy of Language, Critical Thinking, Logic, and/or Artificial Intelligence. Those who like solving word puzzles will enjoy the Math Without Numbers series, which attempts to solve one of the greatest puzzles of all time: the Mathematics of Ideas.

**Author**: Paul A Wagner

**Publisher:** Rowman & Littlefield

**ISBN:** 1475862997

**Category : **
**Languages : **en

**Pages : **160

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**Book Description**
This book shows that engaging with the personality of math is an essential key to learning and teaching math.

**Author**: Joe C. Dixon

**Publisher:**
**ISBN:**
**Category : **Area studies

**Languages : **en

**Pages : **102

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**Book Description**