Advanced Topics in the Arithmetic of Elliptic Curves PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Advanced Topics in the Arithmetic of Elliptic Curves PDF full book. Access full book title Advanced Topics in the Arithmetic of Elliptic Curves by Joseph H. Silverman. Download full books in PDF and EPUB format.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1461208513
Category : Mathematics
Languages : en
Pages : 482
Get Book Here
Book Description
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.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1461208513
Category : Mathematics
Languages : en
Pages : 482
Get Book Here
Book Description
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.
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 1461221307
Category : Mathematics
Languages : en
Pages : 434
Get Book Here
Book Description
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
Author: Thomas A. Garrity
Publisher: 清华大学出版社有限公司
ISBN: 9787302090854
Category : Mathematics
Languages : en
Pages : 380
Get Book Here
Book Description
Author: Gaea Leinhardt
Publisher: Psychology Press
ISBN: 9780805809299
Category : Education
Languages : en
Pages : 472
Get Book Here
Book Description
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.
Author: Terence H. Murdock
Publisher: Xlibris Corporation
ISBN: 1483670457
Category : Mathematics
Languages : en
Pages : 229
Get Book Here
Book Description
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.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1475719205
Category : Mathematics
Languages : en
Pages : 414
Get Book Here
Book Description
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.
Author: Hugh L. Montgomery
Publisher: Springer
ISBN: 354036935X
Category : Mathematics
Languages : en
Pages : 187
Get Book Here
Book Description
Author: Susan Jo Russell
Publisher: Heinemann Educational Books
ISBN: 9780325041919
Category : Education
Languages : en
Pages : 0
Get Book Here
Book Description
"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: Caterina Consani
Publisher: JHU Press
ISBN: 1421403528
Category : Mathematics
Languages : en
Pages : 324
Get Book Here
Book Description
Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
Author: Emil Grosswald
Publisher: Springer Science & Business Media
ISBN: 0817648380
Category : Mathematics
Languages : en
Pages : 336
Get Book Here
Book Description
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.
