An Algebraic Arithmetic

Author : Susan Jo Russell,Deborah Schifter,Virginia Bastable
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 43,6 Mb
Release : 2011
Category : Education
ISBN : 0325041911

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Connecting Arithmetic to Algebra by Susan Jo Russell,Deborah Schifter,Virginia Bastable Pdf

"To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.

Author : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 47,6 Mb
Release : 2010-04-11
Category : Mathematics
ISBN : 9780817647476

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Algebra, Arithmetic, and Geometry by Yuri Tschinkel,Yuri Zarhin Pdf

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

Author : Analúcia D. Schliemann,David W. Carraher,Bárbara M. Brizuela
Publisher : Routledge
Page : 104 pages
File Size : 45,9 Mb
Release : 2006-08-29
Category : Education
ISBN : 9781136799617

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Bringing Out the Algebraic Character of Arithmetic by Analúcia D. Schliemann,David W. Carraher,Bárbara M. Brizuela Pdf

Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes downloadable resources with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.

Author : Eric Temple Bell
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 47,7 Mb
Release : 1927-12-31
Category : Mathematics
ISBN : 9780821846018

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Algebraic Arithmetic by Eric Temple Bell Pdf

The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bocher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, elliptic and theta functions, Bernoulli numbers and functions, and the foundations of mathematics.

Author : Rosanne Proga
Publisher : Brooks/Cole
Page : 650 pages
File Size : 41,8 Mb
Release : 1986
Category : Mathematics
ISBN : 0871509075

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Arithmetic and Algebra by Rosanne Proga Pdf

This book uses a practical approach to arithmetic and beginning algebra and assumes no prior knowledge of mathematics. By thoroughly explaining various mathematical techniques, Proga helps students understand why a technique works so they'll remember how to use it. Well-known for its flexibility and complete coverage of arithmetic and algebra topics, Proga's text is perfectly suited for a combination arithmetic-elementary algebra course, for either an arithmetic or an algebra course, or for a two-term course sequence.

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 52,8 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 0306110369

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Arithmetic of Algebraic Curves by Serguei A. Stepanov Pdf

Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.

Author : Martin M. Zuckerman
Publisher : Rowman & Littlefield
Page : 308 pages
File Size : 48,6 Mb
Release : 1984-06
Category : Electronic
ISBN : 0912675020

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Arithmetic with an Introduction to Algebra by Martin M. Zuckerman Pdf

This book covers the basic topics in arithmetic and algebra with which every college student should be thoroughly familiar. It is written with the student in mind, in a style and at a level appropriate for student understanding.

Author : Bjorn Poonen,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681708

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Arithmetic of Higher-Dimensional Algebraic Varieties by Bjorn Poonen,Yuri Tschinkel Pdf

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

Author : Silas Ellsworth Coleman
Publisher : Unknown
Page : 178 pages
File Size : 52,9 Mb
Release : 1897
Category : Arithmetic
ISBN : UCAL:$B306423

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An Algebraic Arithmetic by Silas Ellsworth Coleman Pdf

Author : S. E. Coleman
Publisher : Forgotten Books
Page : 172 pages
File Size : 44,9 Mb
Release : 2017-11-05
Category : Mathematics
ISBN : 0260296813

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An Algebraic Arithmetic by S. E. Coleman Pdf

Excerpt from An Algebraic Arithmetic: An Exposition of the Theory, and Practice of Advanced Arithmetic The introduction of elementary algebra into the schools is of more doubtful value for two principal reasons. The conceptions of geometry can be represented by fig ures and objects, and are therefore readily grasped by the child, but those of algebra can be so represented only to a very limited degree; and, for the most part, are abstractions the nature of which the child comprehends with difficulty. Moreover, the time that can be allotted to the subject in the grammar school is barely sufficient to carry the pupil over the essentially uninteresting details of algebraic manipulation that necessarily precede any but the Simplest applications of the science. But while the wisdom of introducing elementary algebra into the schools may, for these and minor reasons, be seriously questioned, the experience of several years as a teacher has led the author to the conclusion that the application of certain algebraic conceptions to arithmetic would contribute largely toward the rational presentation of the subject, thus increasing its disciplinary value, and at the same time preparing the way for a natural transi tion to the algebra of the high school. These conceptions are the use of letters as the general representatives of (positive) numbers and of the equation to express their relations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Brian David Conrad
Publisher : American Mathematical Soc.
Page : 569 pages
File Size : 46,7 Mb
Release : 2008
Category : Mathematics
ISBN : 0821844482

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Arithmetic Algebraic Geometry by Brian David Conrad Pdf

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Author : Qing Liu,Reinie Erne
Publisher : Oxford University Press
Page : 593 pages
File Size : 52,8 Mb
Release : 2006-06-29
Category : Mathematics
ISBN : 9780191547805

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Algebraic Geometry and Arithmetic Curves by Qing Liu,Reinie Erne Pdf

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Author : Bradley S. Witzel
Publisher : Council For Exceptional Children
Page : 200 pages
File Size : 55,5 Mb
Release : 2015-11-15
Category : Education
ISBN : 9780865865082

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Bridging the Gap Between Arithmetic & Algebra by Bradley S. Witzel Pdf

Although two federal panels have concluded that all students can learn mathematics and most can succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students … and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, the book is an essential reference for mathematics teachers and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra. Audiences: General education (mathematics) teachers, special education teachers, administrators, teacher educators.

Author : John Derbyshire
Publisher : National Academies Press
Page : 390 pages
File Size : 44,8 Mb
Release : 2006-05-02
Category : Science
ISBN : 9780309164801

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Unknown Quantity by John Derbyshire Pdf

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 49,6 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780821846483

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Quadratic Forms -- Algebra, Arithmetic, and Geometry by Ricardo Baeza Pdf

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.