An Introduction To The Circle Method

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An Introduction to the Circle Method

M. Ram Murty,Kaneenika Sinha
An Introduction to the Circle Method Book PDF

Author : M. Ram Murty,Kaneenika Sinha
Publisher : American Mathematical Society
Page : 280 pages
File Size : 48,6 Mb
Release : 2023-06-15
Category : Mathematics
ISBN : 9781470472030

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An Introduction to the Circle Method by M. Ram Murty,Kaneenika Sinha Pdf

The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see important breakthroughs. This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. The authors' goal is to show the students the elegance of the circle method and at the same time give a complete solution of the famous Waring problem as an illustration of the method. The first half of this book is a curated introduction to elementary number theory with an emphasis on topics needed for the second half. The second half showcases the two most “classic” applications of the circle method, to Waring's problem (following Hardy–Littlewood–Hua) and to Goldbach's conjectures (following Vinogradov, with improvements by Vaughan). This text is suitable for a one-semester undergraduate course or for independent study and will be a great entry point into this fascinating area of research.

An Invitation to Modern Number Theory

Steven J. Miller,Ramin Takloo-Bighash
An Invitation to Modern Number Theory Book PDF

Author : Steven J. Miller,Ramin Takloo-Bighash
Publisher : Princeton University Press
Page : 128 pages
File Size : 49,8 Mb
Release : 2020-08-04
Category : Mathematics
ISBN : 9780691215976

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An Invitation to Modern Number Theory by Steven J. Miller,Ramin Takloo-Bighash Pdf

In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Equidistribution in Number Theory, An Introduction

Andrew Granville,Zeév Rudnick
Equidistribution in Number Theory An Introduction Book PDF

Author : Andrew Granville,Zeév Rudnick
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 54,7 Mb
Release : 2007-04-08
Category : Mathematics
ISBN : 9781402054044

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Equidistribution in Number Theory, An Introduction by Andrew Granville,Zeév Rudnick Pdf

This set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields who reveal fascinating links between seemingly disparate areas.

The Hardy-Littlewood Method

R. C. Vaughan
The Hardy Littlewood Method Book PDF

Author : R. C. Vaughan
Publisher : Cambridge University Press
Page : 184 pages
File Size : 46,9 Mb
Release : 1981-07-30
Category : Mathematics
ISBN : 0521234395

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The Hardy-Littlewood Method by R. C. Vaughan Pdf

The Hardy-Littlewood method is a means of estimating the number of integer solutions of equations and was first applied to Waring's problem on representations of integers by sums of powers. This introduction to the method deals with its classical forms and outlines some of the more recent developments. Now in its second edition it has been fully updated; the author has made extensive revisions and added a new chapter to take account of major advances by Vaughan and Wooley. The reader is expected to be familiar with elementary number theory and postgraduate students should find it of great use as an advanced textbook. It will also be indispensable to all lecturers and research workers interested in number theory.

The Circle Way

Christina Baldwin,Ann Linnea
The Circle Way Book PDF

Author : Christina Baldwin,Ann Linnea
Publisher : Berrett-Koehler Publishers
Page : 241 pages
File Size : 47,7 Mb
Release : 2010-03
Category : Business & Economics
ISBN : 9781605092584

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The Circle Way by Christina Baldwin,Ann Linnea Pdf

Meetings in the round have become the preferred tool for moving individual commitment into group action. This book lays out the structure of circle conversation, based on the original work of the authors who have standardized the essential elements that constitute circle practice.

Introduction to Circle Packing

Kenneth Stephenson
Introduction to Circle Packing Book PDF

Author : Kenneth Stephenson
Publisher : Cambridge University Press
Page : 380 pages
File Size : 40,6 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 0521823560

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Introduction to Circle Packing by Kenneth Stephenson Pdf

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A Course in Analytic Number Theory

Marius Overholt
A Course in Analytic Number Theory Book PDF

Author : Marius Overholt
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 42,5 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062

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A Course in Analytic Number Theory by Marius Overholt Pdf

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Cubic Forms and the Circle Method

Tim Browning
Cubic Forms and the Circle Method Book PDF

Author : Tim Browning
Publisher : Springer Nature
Page : 175 pages
File Size : 45,7 Mb
Release : 2021-11-19
Category : Mathematics
ISBN : 9783030868727

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Cubic Forms and the Circle Method by Tim Browning Pdf

The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

An Introduction to Mathematical Proofs

Nicholas A. Loehr
An Introduction to Mathematical Proofs Book PDF

Author : Nicholas A. Loehr
Publisher : CRC Press
Page : 483 pages
File Size : 50,6 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9781000709803

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An Introduction to Mathematical Proofs by Nicholas A. Loehr Pdf

An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.

Around the Unit Circle

James McKee,Chris Smyth
Around the Unit Circle Book PDF

Author : James McKee,Chris Smyth
Publisher : Springer Nature
Page : 444 pages
File Size : 48,8 Mb
Release : 2021-12-08
Category : Mathematics
ISBN : 9783030800314

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Around the Unit Circle by James McKee,Chris Smyth Pdf

Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.

An Introduction to Analytical Fuzzy Plane Geometry

Debdas Ghosh,Debjani Chakraborty
An Introduction to Analytical Fuzzy Plane Geometry Book PDF

Author : Debdas Ghosh,Debjani Chakraborty
Publisher : Springer
Page : 206 pages
File Size : 54,6 Mb
Release : 2019-05-13
Category : Technology & Engineering
ISBN : 9783030157227

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An Introduction to Analytical Fuzzy Plane Geometry by Debdas Ghosh,Debjani Chakraborty Pdf

This book offers a rigorous mathematical analysis of fuzzy geometrical ideas. It demonstrates the use of fuzzy points for interpreting an imprecise location and for representing an imprecise line by a fuzzy line. Further, it shows that a fuzzy circle can be used to represent a circle when its description is not known precisely, and that fuzzy conic sections can be used to describe imprecise conic sections. Moreover, it discusses fundamental notions on fuzzy geometry, including the concepts of fuzzy line segment and fuzzy distance, as well as key fuzzy operations, and includes several diagrams and numerical illustrations to make the topic more understandable. The book fills an important gap in the literature, providing the first comprehensive reference guide on the fuzzy mathematics of imprecise image subsets and imprecise geometrical objects. Mainly intended for researchers active in fuzzy optimization, it also includes chapters relevant for those working on fuzzy image processing and pattern recognition. Furthermore, it is a valuable resource for beginners interested in basic operations on fuzzy numbers, and can be used in university courses on fuzzy geometry, dealing with imprecise locations, imprecise lines, imprecise circles, and imprecise conic sections.

Engineering Graphics with an Introduction to AutoCAD

Dr. A.R. Bapat
Engineering Graphics with an Introduction to AutoCAD Book PDF

Author : Dr. A.R. Bapat
Publisher : Allied Publishers
Page : 538 pages
File Size : 41,6 Mb
Release : 2004-02-14
Category : Technology & Engineering
ISBN : 9788177646429

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Engineering Graphics with an Introduction to AutoCAD by Dr. A.R. Bapat Pdf

Although the world of drawing has changed from graphite technology (i.e. conventional pencils, drawing paper, instruments and associated skills) to graphic technology (i.e. computer assisted drawing and drafting), the basics of the subject are equally important in either of the approaches. The teaching-learning process for engineering drawing calls for more imaginative thinking on the part of the student than may be needed for learning other subjects and ingenious ways for the teacher for communicating with the students so as to develop a scheme that enables a student to translate 3D visualization into a 2D graphic representation on a drawing in an easy manner. Learning engineering drawing is thus learning a new language for effective communication and uniform understanding between people dealing with physical objects. The book also includes a chapter on AutoCAD which will serve as a good course material to students and teachers of engineering drawing. The language used for presentation has been simple, since the focus is the first year students just entering the engineering discipline. The CD enclosed with the book contains “Power point presentations on Conversion of Orthographic view to Isometric and Conversion of Pictorial view to Orthographic Projections” to facilitate students as well as the teachers.

Little Book of Circle Processes

Kay Pranis
Little Book of Circle Processes Book PDF

Author : Kay Pranis
Publisher : Simon and Schuster
Page : 76 pages
File Size : 42,6 Mb
Release : 2015-01-27
Category : Law
ISBN : 9781680990416

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Little Book of Circle Processes by Kay Pranis Pdf

Our ancestors gathered around a fire in a circle, families gather around their kitchen tables in circles, and now we are gathering in circles as communities to solve problems. The practice draws on the ancient Native American tradition of a talking piece. Peacemaking Circles are used in neighborhoods to provide support for those harmed by crime and to decide sentences for those who commit crime, in schools to create positive classroom climates and resolve behavior problems, in the workplace to deal with conflict, and in social services to develop more organic support systems for people struggling to get their lives together. A title in The Little Books of Justice and Peacebuilding Series.

Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance Based Design

Y. Honjo,O. Kusakabe,K. Matsui,M. Koda,G. Pokharel
Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance Based Design Book PDF

Author : Y. Honjo,O. Kusakabe,K. Matsui,M. Koda,G. Pokharel
Publisher : CRC Press
Page : 474 pages
File Size : 42,6 Mb
Release : 2002-01-01
Category : Technology & Engineering
ISBN : 9058093816

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Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance Based Design by Y. Honjo,O. Kusakabe,K. Matsui,M. Koda,G. Pokharel Pdf

The contributions contained in these proceedings are divided into three main sections: theme lectures presented during the pre-workshop lecture series; keynote lectures and other contributed papers; and a translation of the Japanese geotechnical design code.

Classroom Literature Circles for Primary Grades, Grades K - 2

Elizabeth Suarez Aguerre
Classroom Literature Circles for Primary Grades Grades K 2 Book PDF

Author : Elizabeth Suarez Aguerre
Publisher : Carson-Dellosa Publishing
Page : 80 pages
File Size : 47,6 Mb
Release : 2008-08-26
Category : Juvenile Nonfiction
ISBN : 9781604183979

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Classroom Literature Circles for Primary Grades, Grades K - 2 by Elizabeth Suarez Aguerre Pdf

Develop readers in grades K–2 who discuss, respond to, and think about literature using Classroom Literature Circles for Primary Grades. This 80-page book gives a glimpse into classrooms that use literature circles and includes tips for setting up groups, choosing literature, finding enough books, and teaching students how to be active participants in the literature circle process. It also includes reproducible role sheets that are adjusted for different learning levels, advice about literature circles and classroom management, and a FAQs section.