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Topics From Arithmetic
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Book Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Book Synopsis Topics in Arithmetic by : Terence H. Murdock
Download or read book Topics in Arithmetic written by Terence H. Murdock and published by Xlibris Corporation. This book was released on 2013-08-30 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: With implicit emphasis on logic and reason, and supported by ample examples and illustrations, Topics in Arithmetic provides simple, clear instruction on the fundamental math needed for success in learning arithmetic. In six stand-alone studies, it augments standard classroom textbooks with engaging, enriching explanations of facets of math troubling to students. Following coverage of deductive logic and the development of numbers, and their expression as numerals, it explains the properties and rules of basic operations in arithmetic, and their use in forming algorithms. Beyond numerals, it illustrates extended arithmetic operations on fractions; and, with tabular examples, it clarifies the puzzling operations of raising powers, and calculating roots, with zero, negative and fractional exponents. Topics in Arithmetic presents technically challenging, essential features of arithmetic in simple terms from engaging perspectives. Students from middle school through college entry, their parents and math teachers will find the material in this book engrossing and enriching.
Book Synopsis Arithmetic for Teachers by : Gary R. Jensen
Download or read book Arithmetic for Teachers written by Gary R. Jensen and published by American Mathematical Soc.. This book was released on 2003-11-25 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent teaching of mathematics at the elementary school level requires that the teacher be an expert in school mathematics. This textbook for prospective teachers presents topics from the K-6 mathematics curriculum, but at a greater depth than is usually found in the classroom. The added knowledge that comes from this approach gives the teacher essential insight into how the topics interrelate and where difficulties might lie. With this deeper mathematical preparation, the teacher is better able to explain concepts, demonstrate computational procedures and lead students through problem-solving techniques. The primary focus is on the foundations of arithmetic, along with a selection of topics from geometry and a wide range of applications. The number line is used throughout to visualize concepts and to tie them to the solution of problems. The book emphasizes how to explain the concepts and how to explain problem solutions. This is a textbook for a college course in mathematics for prospective elementary school teachers. It will also be a resource for the instructors of such courses.
Book Synopsis All the Mathematics You Missed by : Thomas A. Garrity
Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Arithmetic written by Paul Lockhart and published by Harvard University Press. This book was released on 2019-07-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Lockhart reveals arithmetic not as the rote manipulation of numbers but as a set of ideas that exhibit the surprising behaviors usually reserved for higher branches of mathematics. In this entertaining survey, he explores the nature of counting and different number systems—Western and non-Western—and weighs the pluses and minuses of each.
Book Synopsis Analysis of Arithmetic for Mathematics Teaching by : Gaea Leinhardt
Download or read book Analysis of Arithmetic for Mathematics Teaching written by Gaea Leinhardt and published by Routledge. This book was released on 2020-11-25 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.
Book Synopsis Topics in Multiplicative Number Theory by : Hugh L. Montgomery
Download or read book Topics in Multiplicative Number Theory written by Hugh L. Montgomery and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Connecting Arithmetic to Algebra by : Susan Jo Russell
Download or read book Connecting Arithmetic to Algebra written by Susan Jo Russell and published by Heinemann Educational Books. This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Noncommutative Geometry, Arithmetic, and Related Topics by : Caterina Consani
Download or read book Noncommutative Geometry, Arithmetic, and Related Topics written by Caterina Consani and published by JHU Press. This book was released on 2011 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
Book Synopsis Topics in Mathematics for Elementary Teachers by : Sergei Abramovich
Download or read book Topics in Mathematics for Elementary Teachers written by Sergei Abramovich and published by IAP. This book was released on 2010-04-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects the author’s experience in teaching a mathematics content course for pre-service elementary teachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciences for the preparation of teachers demonstrating how abstract mathematical concepts can be motivated by concrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachers to grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts on higher levels of abstraction. A strong experiential component of the book made possible by the use of manipulative materials and digital technology such as spreadsheets, The Geometer’s Sketchpad, Graphing Calculator 3.5 (produced by Pacific Tech), and Kid Pix Studio Deluxe makes it possible to balance informal and formal approaches to mathematics, allowing the teachers to learn how the two approaches complement each other. Classroom observations of the teachers’ learning mathematics as a combination of theory and experiment confirm that this approach elevates one’s mathematical understanding to a higher ground. The book not only shows the importance of mathematics content knowledge for teachers but better still, how this knowledge can be gradually developed in the context of exploring grade-appropriate activities and tasks and using computational and manipulative environments to support these explorations. Most of the chapters are motivated by a problem/activity typically found in the elementary mathematics curricula and/or standards (either National or New York State – the context in which the author prepares teachers). By exploring such problems in depth, the teachers can learn fundamental mathematical concepts and ideas hidden within a seemingly mundane problem/activity. The need to have experience in going beyond traditional expectations for learning is due to the constructivist orientation of contemporary mathematics pedagogy that encourages students to ask questions about mathematics they study. Each chapter includes an activity set that can be used for the development of the variety of assignments for the teachers. The material included in the book is original in terms of the approach used to teach mathematics to the teachers and it is based on a number of journal articles published by the author in the United States and elsewhere. Mathematics educators who are interested in integrating hands-on activities and digital technology into the teaching of mathematics will find this book useful. Mathematicians who teach mathematics to the teachers as part of their teaching load will be interested in the material included in the book as it connects childhood mathematics content and mathematics for the teachers.
Book Synopsis Bringing Out the Algebraic Character of Arithmetic by : Analúcia D. Schliemann
Download or read book Bringing Out the Algebraic Character of Arithmetic written by Analúcia D. Schliemann and published by Routledge. This book was released on 2006-08-29 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Study of Arithmetic Courses in the United States by : Lyman Henry Van Houten
Download or read book A Study of Arithmetic Courses in the United States written by Lyman Henry Van Houten and published by . This book was released on 1913 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Arithmetic for Teachers by : Gary R. Jensen
Download or read book Arithmetic for Teachers written by Gary R. Jensen and published by American Mathematical Soc.. This book was released on 2003 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent teaching of mathematics at the elementary school level requires that the teacher be an expert in school mathematics. This textbook for prospective teachers presents topics from the K-6 mathematics curriculum, but at a greater depth than is usually found in the classroom. The added knowledge that comes from this approach gives the teacher essential insight into how the topics interrelate and where difficulties might lie. With this deeper mathematical preparation, the teacher is better able to explain concepts, demonstrate computational procedures and lead students through problem-solving techniques. The primary focus is on the foundations of arithmetic, along with a selection of topics from geometry and a wide range of applications. The number line is used throughout to visualize concepts and to tie them to the solution of problems. The book emphasizes how to explain the concepts and how to explain problem solutions. This is a textbook for a college course in mathematics for prospective elementary school teachers. It will also be a resource for the instructors of such courses.
Book Synopsis Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts by : David C. Geary
Download or read book Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts written by David C. Geary and published by Academic Press. This book was released on 2017-08-01 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public
Download or read book Arithmetic written by K. K. SINGH and published by . This book was released on 2017-01-14 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Different Perspective on Math Education: -This book has been written based on my experience as an independent math tutor, and as a former institute's teacher of math. I changed careers from an unrelated industry to any institutions and traits in the whole life with my intent to independently self-publish the books on my own publication; my writing was not bound by the requirements or guidelines of any major publisher who would likely be uncomfortable with its non-mainstream, unique style. Because of my independence I am in a position in which I risk nothing by telling the unpleasant truth about why students struggle with math, as well as what can be done to improve the situation. This is not a generic textbook. Every word is based on the patterns that I have personally, repeatedly observed among many students of all ages.The Purpose of this Book In my independent tutoring work, I continually observe that that almost all of the difficulty that students have with math follows a distinct pattern. They all have very similar complaints, and they all get stuck in almost the exact same places. It is too consistent to be a coincidence. With that in mind, this book serves several purposes. The first is to explain very clearly why students struggle with math. This book has been written from a standpoint that acknowledges how hard math is for most students, but also maintains that there is a reason for why that is the case, and that there is a means of ending the struggle.This book serves as a carefully planned roadmap for self-studying and learning math. Topics that require extensive review and redundancy receive it, and those that do not are only covered in passing. The connection between topics and their dependence upon one another are very clearly highlighted. Nothing is presented in a vacuum. This is contrary to most commercial textbooks, test-prep books, and review books- which typically devote the same amount of space to every topic. There is no distinction between topics that most students find easy and ones that most students find difficult, nor is there a distinction between trivial topics and very significant ones that need to be repeatedly explained in many different ways, even at the risk of redundancy.While many math textbooks include embedded textboxes of "tips," I have yet to see a tip which reads "if you do not fully understand and master this essential concept, you will be absolutely sunk when you study later math."This book makes such statements where applicable and appropriate. They are not intended as threats, but indeed guarantees based on experience and observation.Finally, this book presents some important advice and suggestions for how to study and learn math, and how to improve scores on exams. They are based on my personnel experiences as clients. Most students never learn how to study effectively, and never learn how to evaluate their own readiness for exams. This book attempts to change that by presenting some ideas that are not commonly discussed elsewhere. How this Book is organized Chapter one of this book acknowledges the fact that most students find math to be extremely hard, and attempts to explain why that is the case, and what to do about it.Chapter Two through Eleven cover subject material starting with concepts in basic arithmetic and operations which are the foundation of all math students. It goes on to cover the basics of negative numbers, fractions, decimals, percents, probability, statistics, the metric system, and measurement. Chapter Twelve offers suggestions for how to study and learn math, and how to improve scores on exams. The book concludes with information about the companion website which provides additional help and information, as well as the means of asking one questions by e-mail at [email protected]
Book Synopsis Arithmetic and Pre-Algebra in 30 Days by : Reza Nazari
Download or read book Arithmetic and Pre-Algebra in 30 Days written by Reza Nazari and published by Reza Nazari. This book was released on 2018-07-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Best Book to Prepare for Arithmetic and Pre-Algebra Exam! The goal of this book is simple. It will help you incorporate the best method and the right strategies to prepare for the Arithmetic and Pre-Algebra exam FAST and EFFECTIVELY. Arithmetic and Pre-Algebra in 30 Days helps you learn all Math topics that you will need to prepare for the Arithmetic and Pre-Algebra exam. You only need to spend about 90-120 minutes daily in your 30-day period in order to ace the Arithmetic and Pre-Algebra exam. This book with more than 2,500 math questions is all you will ever need to fully prepare for the Arithmetic and Pre-Algebra. Arithmetic and Pre-Algebra in 30 Days provides students with the confidence and math skills they need to succeed on the Arithmetic and Pre-Algebra exams, providing a solid foundation of basic Math topics with abundant exercises for each topic. It is designed to address the needs of Arithmetic and Pre-Algebra takers who must have a working knowledge of basic Math. Whether you are intimidated by math, or even if you were the first to raise your hand in the Math classes, this book can help you accelerate the learning process and put you on the right track. Inside the pages of this comprehensive book, students can learn basic math operations in a structured manner with a complete study program to help them understand essential math skills. It also has many exciting features, including: Dynamic design and easy-to-follow activities Step-by-step guide for all Math topics Targeted, skill-building practices A fun, interactive and concrete learning process Math topics are grouped by category, so you can focus on the topics you struggle on All solutions for the exercises are included, so you will always find the answers Arithmetic and Pre-Algebra in 30 Days is for all Arithmetic and Pre-Algebra course takers. It is a breakthrough in Math learning - offering a winning formula and the most powerful methods for learning basic Math topics confidently. Each section offers step-by-step instruction and helpful hints, with a few topics being tackled each day. Effortlessly and confidently follow the step-by-step instructions in this book to prepare for the Arithmetic and Pre-Algebra in a short period of time. Arithmetic and Pre-Algebra in 30 Days is the only book you'll ever need to master Basic Math topics! It can be used as a self-study course - you do not need to work with a Math tutor. (It can also be used with a Math tutor). You'll be surprised how fast you master the Math topics covering on Arithmetic and Pre-Algebra. Ideal for self-study as well as for classroom usage. Published by: Effortless Math Education www.EffortlessMath.com
