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| examples of mathematical sentences: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| examples of mathematical sentences: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves. |
| examples of mathematical sentences: Fundamentals of Mathematics Denny Burzynski, Wade Ellis, 2008 Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject. |
| examples of mathematical sentences: The Simple Math of Writing Well Jennie Harrop, 2018-01-12 Writing guides abound, but The Simple Math of Writing Well is one of a kind. Readers will find its practical approach affirming, encouraging, and informative, and its focus on the basics of linguistic structure releases 21st-century writers to embrace the variety of mediums that define our internet-connected world. As Harrop reminds us in the opening chapters of her book, we write more today than ever before in history: texts, emails, letters, blogs, reports, social media posts, proposals, etc. The Simple Math of Writing Well is the first guide that directly addresses the importance of writing well in the Google age. |
| examples of mathematical sentences: A Spiral Workbook for Discrete Mathematics Harris Kwong, 2015-11-06 A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills. |
| examples of mathematical sentences: One Mathematical Cat, Please! Carol Jvf Burns, 2018-06-10 Want a fresh start on math? View it in a totally new way? Then read this little book. You'll learn that numbers have lots of different names, and math is the renaming tool. You'll learn that x is to math as cat is to English. It's an easy read. If you can add, subtract, multiply and divide with numbers like 1, 2, and 3, then you can read this book. Supplement any math class, 7th grade through college. Use for self-learners, home-schoolers, math lovers, math haters. Reviewers and users write: . . . wonderfully written and crafted with a care you rarely see . . . will do a great service to the mathematical educational world . . . the need for this book is immense . . . I found meat, potatoes, and pie on every page. It's all dessert. . . . never seen anything so supportive and affirming and reassuring and inspiring as the way you talk us through topics THIS IS GREAT!!!! . . . this is helping me get heads above the competition. You rock!!!! One Mathematical Cat drives me wild. An entire website (http: //www.onemathematicalcat.org) grew from this book: Algebra 1, Geometry, Algebra 2, Precalculus, Calculus. Free randomly-generated exercises. Free unlimited worksheets. Algebra Pinball. All the same style. All the same voice. All building on the ideas in this little book. Bound, printed copies are great for students: they can highlight, write margin notes, and do exercises right in the book. So, the next time you see x, maybe you'll think One Mathematical Cat, Please! and laugh! Enjoy! |
| examples of mathematical sentences: Teaching Elementary Mathematics to Struggling Learners Bradley S. Witzel, Mary E. Little, 2016-01-25 Packed with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention. |
| examples of mathematical sentences: Prealgebra 2e Lynn Marecek, Maryanne Anthony-Smith, Andrea Honeycutt Mathis, 2020-03-11 The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi. |
| examples of mathematical sentences: Mathematical Writing Franco Vivaldi, 2014-11-04 This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study. Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations. |
| examples of mathematical sentences: Division Word Problems , 2006 |
| examples of mathematical sentences: Mathematics: Operations & mathematical sentences (no. 437) John W. Ogle, 1970 |
| examples of mathematical sentences: One Mathematical Cat, Please! a First Course in Algebra Carol Jvf Burns, 2018-06-16 This is not just another algebra book. An entire website supports and extends this text. 400+ web exercises: unlimited, randomly-generated practice and worksheets. The book and website each stand alone as a learning environment; together, they're a dynamic duo. Visit http: //www.onemathematicalcat.org and go to Algebra I: then Geometry, Algebra II, Precalculus, and Calculus. While you're learning algebra, you'll also learn that numbers have lots of different names, and that math is the renaming tool. You'll learn that x is to math as cat is to English. The original cat book (One Mathematical Cat, Please! Ideas for anyone who wants to understand mathematics) is also available on Amazon. If you only need the math language ideas, get the original cat book. If you need Algebra too, get this book. The Algebra book has the original cat book embedded in it, so you don't need both! Reviewers and users write: ... wonderfully written and crafted with a care you rarely see ... will do a great service to the mathematical educational world ... the need for this book is immense ... I found meat, potatoes, and pie on every page. It's all dessert. ... never seen anything so supportive and affirming and reassuring and inspiring as the way you talk us through topics THIS IS GREAT!!!! ... this is helping me get heads above the competition. You rock!!!! OneMathematicalCat drives me wild. There are over 175 web exercises that go directly with this book at: http: //www.onemathematicalcat.org/algebra_book/online_problems/table_of_contents.htm All free. All agreeing perfectly with the text---same order of lessons, same notation, same writing style. Free randomly-generated exercises. Free unlimited worksheets/quizzes. Algebra Pinball. Never again will someone say they don't have enough practice. Bound, printed copies are great. You can highlight, write margin notes, and do exercises right in the book. So, the next time you see x, think One Mathematical Cat, Please! and laugh! Enjoy! |
| examples of mathematical sentences: Modern Mathematics Patrick Murphy, 2014-05-12 Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed. Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional statements; and biconditional sentences. Subsequent chapters focus on switching circuits; multibase arithmetic; finite systems; relations, vectors, and matrices; tessellations; and linear programming. The book concludes with an analysis of motion geometry and rubber sheet geometry, paying particular attention to radial enlargement and composite reflections as well as topological equivalence, networks for maps, and incidence matrices. This monograph is intended for students, parents, and teachers who are interested in modern mathematics. |
| examples of mathematical sentences: From Word to Sentence Joachim Lambek, 2008 |
| examples of mathematical sentences: A Concise Introduction to Logic Craig DeLancey, 2017-02-06 |
| examples of mathematical sentences: Prealgebra Lynn Marecek, MaryAnne Anthony-Smith, 2015-09-25 Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Prealgebra follows a nontraditional approach in its presentation of content. The beginning, in particular, is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.--BC Campus website. |
| examples of mathematical sentences: Fundamentals of Elementary Mathematics Merlyn J. Behr, Dale G. Jungst, 2014-05-10 Fundamentals of Elementary Mathematics provides an understanding of the fundamental aspects of elementary mathematics. This book presents the relevance of the mathematical concepts, which are also demonstrated in numerous exercises. Organized into 10 chapters, this book begins with an overview of the study of logic to understand the nature of mathematics. This text then discusses mathematics as a system of structure or as a collection of substructures. Other chapters consider the four essential components in a mathematical or logical system or structure, namely, undefined terms, defined terms, postulates, and theorems. This book discusses as well several principles used in numeration systems and provides examples of some numeration systems that are in use to illustrate these principles. The final chapter deals with the classification of certain mathematical systems as groups, fields, or rings to demonstrate some abstract mathematics. This book is a valuable resource for students and teachers in elementary mathematics. |
| examples of mathematical sentences: Writing Mathematical Papers in English Jerzy Trzeciak, 1995 |
| examples of mathematical sentences: How to Write Mathematics Norman Earl Steenrod, 1973-12-31 This classic guide contains four essays on writing mathematical books and papers at the research level and at the level of graduate texts. The authors are all well known for their writing skills, as well as their mathematical accomplishments. The first essay, by Steenrod, discusses writing books, either monographs or textbooks. He gives both general and specific advice, getting into such details as the need for a good introduction. The longest essay is by Halmos, and contains many of the pieces of his advice that are repeated even today: In order to say something well you must have something to say; write for someone; think about the alphabet. Halmos's advice is systematic and practical. Schiffer addresses the issue by examining four types of mathematical writing: research paper, monograph, survey, and textbook, and gives advice for each form of exposition. Dieudonne's contribution is mostly a commentary on the earlier essays, with clear statements of where he disagrees with his coauthors. The advice in this small book will be useful to mathematicians at all levels. |
| examples of mathematical sentences: Academic Language in Diverse Classrooms: Mathematics, Grades 3–5 Margo Gottlieb, Gisela Ernst-Slavit, 2013-02-27 Help your students unlock important mathematical concepts! If you’ve ever watched a student struggle with learning math concepts, you know that academic English can sometimes create stumbling blocks to understanding. To grasp complicated concepts, build skills, and demonstrate achievement, students need to master academic language in math. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning Each grade-specific chapter models the types of interactions and learning experiences that help students master both math content and academic language. This essential book shows you why mastery of academic language is the key to students’ academic success. With growing numbers of English Language Learners in our classrooms, teachers need to be able to help students as they learn academic vocabulary and concepts. This series offers teachers a practical support, complete with abundant rubrics and detailed plans for teaching math vocabulary! —Renee Peoples, Teacher Swain County Schools, Bryson City, NC |
| examples of mathematical sentences: Syntactic Structures Noam Chomsky, 2020-05-18 No detailed description available for Syntactic Structures. |
| examples of mathematical sentences: What Your First Grader Needs to Know (Revised and Updated) E.D. Hirsch, Jr., 2014-08-26 Give your child a smart start with the revised and updated What Your First Grader Needs to Know What will your child be expected to learn in the first grade? How can you help him or her at home? How can teachers foster active, successful learning in the classroom? This book answers these all-important questions and more, offering the specific shared knowledge that hundreds of parents and teachers across the nation have agreed upon for American first graders. Featuring a new Introduction, filled with opportunities for reading aloud and fostering discussion, this first-grade volume of the acclaimed Core Knowledge Series presents the sort of knowledge and skills that should be at the core of a challenging first-grade education. Inside you’ll discover • Favorite poems—old and new, such as “The Owl and the Pussycat,” “Wynken, Blynken, and Nod,” and “Thirty Days Hath September” • Beloved stories—from many times and lands, including a selection of Aesop’s fables, “Hansel and Gretel,” “All Stories Are Anansi’s,” “The Tale of Peter Rabbit,” and more • Familiar sayings and phrases—such as “Do unto others as you would have them do unto you” and “Practice makes perfect” • World and American history and geography—take a trip down the Nile with King Tut and learn about the early days of our country, including the story of Jamestown, the Pilgrims, and the American Revolution • Visual arts—fun activities plus reproductions of masterworks by Leonardo da Vinci, Vincent van Gogh, Paul Cézanne, Georgia O’Keeffe, and others • Music—engaging introductions to great composers and music, including classical music, opera, and jazz, as well as a selection of favorite children’s songs • Math—a variety of activities to help your child learn to count, add and subtract, solve problems, recognize geometrical shapes and patterns, and learn about telling time • Science—interesting discussions of living things and their habitats, the human body, the states of matter, electricity, our solar system, and what’s inside the earth, plus stories of famous scientists such as Thomas Edison and Louis Pasteur |
| examples of mathematical sentences: Basic Language Of Mathematics Juan Jorge Schaffer, 2014-05-16 This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable.The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements. |
| examples of mathematical sentences: A Primer of Mathematical Writing Steven G. Krantz, 2017-11-07 This is the second edition of a book originally published in 1997. Today the internet virtually consumes all of our lives (especially the lives of writers). As both readers and writers, we are all aware of blogs, chat rooms, and preprint servers. There are now electronic-only journals and print-on-demand books, Open Access journals and joint research projects such as MathOverflow—not to mention a host of other new realities. It truly is a brave new world, one that can be overwhelming and confusing. The truly new feature of this second edition is an extensive discussion of technological developments. Similar to the first edition, Krantz's frank and straightforward approach makes this book particularly suitable as a textbook for an undergraduate course. |
| examples of mathematical sentences: A First Course in Mathematical Logic and Set Theory Michael L. O'Leary, 2015-09-14 A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis. |
| examples of mathematical sentences: Academic Language in Diverse Classrooms: Mathematics, Grades 68 Margo Gottlieb, Gisela Ernst-Slavit, 2013-05-09 Make every student fluent in the language of learning. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning |
| examples of mathematical sentences: Mathematics for Elementary School School Mathematics Study Group, 1963 |
| examples of mathematical sentences: The Cambridge Companion to Logical Empiricism Alan Richardson, Thomas Uebel, 2007-09-03 If there is a movement or school that epitomizes analytic philosophy in the middle of the twentieth century, it is logical empiricism. Logical empiricists created a scientifically and technically informed philosophy of science, established mathematical logic as a topic in and tool for philosophy, and initiated the project of formal semantics. Accounts of analytic philosophy written in the middle of the twentieth century gave logical empiricism a central place in the project. The second wave of interpretative accounts was constructed to show how philosophy should progress, or had progressed, beyond logical empiricism. The essays survey the formative stages of logical empiricism in central Europe and its acculturation in North America, discussing its main topics, and achievements and failures, in different areas of philosophy of science, and assessing its influence on philosophy, past, present, and future. |
| examples of mathematical sentences: Mathematical Mindsets Jo Boaler, 2015-10-12 Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age. |
| examples of mathematical sentences: The Princeton Companion to Mathematics Timothy Gowers, June Barrow-Green, Imre Leader, 2010-07-18 The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger |
| examples of mathematical sentences: Prospects for Meaning Richard Schantz, 2012-07-30 Original papers by leading international authors address the most important problem in the philosophy of language, the question of how to assess the prospects of developing a tenable theory of meaning, given the influential sceptical attacks mounted against the concept of meaning by Willard Van Quine and Saul Kripke and their adherents in particular. Thus the texts attempt to answer the fundamental questions – of whether there are meanings, and, if there are, of what they are and of the form a serious philosophical theory of meaning should take. |
| examples of mathematical sentences: A Student's Guide to the Study, Practice, and Tools of Modern Mathematics Donald Bindner, Martin Erickson, 2010-11-29 A Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R. Along with a color insert, the text include |
| examples of mathematical sentences: Research in Collegiate Mathematics Education VII Fernando Hitt, Derek Allan Holton, Patrick W. Thompson, 2010-03-05 The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use. |
| examples of mathematical sentences: Economics as Literature William Henderson, 2006-06-07 A rich vein of economics writings which runs through the nineteenth century and beyond is now largely ignored because its authors were women or because they favoured literary over scientific forms. Economics as Literature re-examines some of the most interesting texts from within this tradition. The works considered include: *stories (eg by Maria Edgeworth and Harriet Martineau) *dialogues (eg by Jane Marcet and Thomas de Quincey) *'imaginative' writing (eg from Ruskin and Francis Edgeworth) *Keynes' General Theory which is locked within a nineteenth century 'tradition' of uniting science and art. |
| examples of mathematical sentences: Deflating Existential Consequence Jody Azzouni, 2004-01-08 If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything that our theories quantify. Escaping metaphysical straitjackets (such as the correspondence theory of truth), while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time. |
| examples of mathematical sentences: Truth: The Basics Jc Beall, Ben Middleton, 2023-12-04 Truth: The Basics is a concise and engaging introduction to philosophical theories about the nature of truth. The two authors – leading philosophers in this field – build the book around a single question: what, if anything, is common to all truths, which makes them true? The book explores five important answers (‘theories’) to the given question: correspondence, semantic, verifiability, transparency, and plurality. For each given theory, the following questions are addressed: • What is the theory’s answer to the central question? • What is the basic motivation behind that answer? • What is a precise argument for that answer? • What are the biggest objections to that answer? • What are a few good resources for understanding more about the theory? An additional chapter provides an extensive introduction to the notorious liar paradox. Truth: The Basics is an ideal starting point for anyone seeking a lively and accessible introduction to the rich and complex philosophical study of truth. Key Features: |
| examples of mathematical sentences: Helping Children Learn Mathematics Robert Reys, Mary Lindquist, Diana V. Lambdin, Nancy L. Smith, Anna Rogers, Audrey Cooke, Sue Bennett, Bronwyn Ewing, John West, 2020-01-21 The third edition of Reys’ Helping Children Learn Mathematics is a practical resource for undergraduate students of primary school teaching. Rich in ideas, tools and stimulation for lessons during teaching rounds or in the classroom, this edition continues to provide a clear understanding of how to navigate the Australian Curriculum, with detailed coverage on how to effectively use Information and Communications Technology (ICT) in the classroom. This is a full colour printed textbook with an interactive ebook code included. Great self-study features include: auto-graded in-situ knowledge check questions, video of teachers demonstrating how different maths topics can be taught in the classroom and animated, branched chain scenarios are in the e-text. |
| examples of mathematical sentences: MATHEMATICS FOR ELEMENTARY TEACHERS. (PRODUCT ID 23864410). MICHELLE. MANES, 2018 |
| examples of mathematical sentences: An Introduction to Abstract Mathematics Robert J. Bond, William J. Keane, 2007-08-24 Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments. |
| examples of mathematical sentences: A History of Mathematical Notations Florian Cajori, 2013-09-26 This classic study notes the origin of a mathematical symbol, the competition it encountered, its spread among writers in different countries, its rise to popularity, and its eventual decline or ultimate survival. 1929 edition. |
Examples - Apache ECharts
Apache ECharts，一款基于JavaScript的数据可视化图表库，提供直观，生动，可交互，可个性化定制的数据可视化图表。
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Apache ECharts
ECharts: A Declarative Framework for Rapid Construction of Web-based Visualization. 如果您在科研项目、产品、学术论文、技术报告、新闻报告、教育、专利以及其他相关活动中使用了 …
Events - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Examples - Apache ECharts
Apache ECharts，一款基于JavaScript的数据可视化图表库，提供直观，生动，可交互，可个性化定制的数据可视化图表。
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Apache ECharts
ECharts: A Declarative Framework for Rapid Construction of Web-based Visualization. 如果您在科研项目、产品、学术论文、技术报告、新闻报告、教育、专利以及其他相关活动中使用了 …
Events - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
