Algebraic Arithmetic

Author : Susan Jo Russell,Deborah Schifter,Virginia Bastable
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 50,9 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 : Analúcia D. Schliemann,David W. Carraher,Bárbara M. Brizuela
Publisher : Routledge
Page : 104 pages
File Size : 51,5 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 : Brian David Conrad
Publisher : American Mathematical Soc.
Page : 569 pages
File Size : 53,8 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 : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 54,5 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 : Bjorn Poonen,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,7 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 : 48,7 Mb
Release : 1897
Category : Arithmetic
ISBN : UCAL:$B306423

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An Algebraic Arithmetic by Silas Ellsworth Coleman Pdf

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 46,5 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 : Qing Liu,Reinie Erne
Publisher : Oxford University Press
Page : 593 pages
File Size : 48,8 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 : Eric Temple Bell
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 42,6 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 : Brian David Conrad
Publisher : American Mathematical Soc.
Page : 588 pages
File Size : 40,5 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821886916

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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 : 刘擎,Centre National de La Recherche Scientifique (Cnrs) Laboratoire de Theorie Des Nombres Et D'Algorithmique Arithmetique Qing Liu
Publisher : Oxford University Press on Demand
Page : 594 pages
File Size : 53,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780198502845

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Algebraic Geometry and Arithmetic Curves by 刘擎,Centre National de La Recherche Scientifique (Cnrs) Laboratoire de Theorie Des Nombres Et D'Algorithmique Arithmetique Qing Liu Pdf

This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text. - ;This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces b.

Author : International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002,International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002 : Universidad de Talca)
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 49,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834411

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Algebraic and Arithmetic Theory of Quadratic Forms by International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002,International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms (2002 : Universidad de Talca) Pdf

This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics.

Author : Wilfred W. J. Hulsbergen
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 40,5 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783663095057

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Conjectures in Arithmetic Algebraic Geometry by Wilfred W. J. Hulsbergen Pdf

In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.

Author : Analúcia D. Schliemann,David W. Carraher,Bárbara M. Brizuela
Publisher : Routledge
Page : 164 pages
File Size : 48,9 Mb
Release : 2006-08-29
Category : Education
ISBN : 9781136799624

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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 : Martin M. Zuckerman
Publisher : Rowman & Littlefield
Page : 308 pages
File Size : 50,6 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.