Download or read book An Introduction to the Circle Method written by M. Ram Murty and published by American Mathematical Society. This book was released on 2023-06-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2020-08-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Circle Packing written by Kenneth Stephenson and published by Cambridge University Press. This book was released on 2005-04-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Download or read book The Circle Way written by Christina Baldwin and published by Berrett-Koehler Publishers. This book was released on 2010-03 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Hardy Littlewood Method written by R. C. Vaughan and published by Cambridge University Press. This book was released on 1981-07-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Little Book of Circle Processes written by Kay Pranis and published by Simon and Schuster. This book was released on 2015-01-27 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Around the Unit Circle written by James McKee and published by Springer Nature. This book was released on 2021-12-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Equidistribution in Number Theory An Introduction written by Andrew Granville and published by Springer Science & Business Media. This book was released on 2007-04-08 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Course in Analytic Number Theory written by Marius Overholt and published by American Mathematical Soc.. This book was released on 2014-12-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Decade of the Berkeley Math Circle written by Zvezdelina Stankova and published by American Mathematical Soc.. This book was released on 2008-11-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematicians have been drawn to mathematics through their experience with math circles: extracurricular programs exposing teenage students to advanced mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics. Founded in 1998, the Berkeley Math Circle (BMC) is a pioneering model of a U.S. math circle, aspiring to prepare our best young minds for their future roles as mathematics leaders. Over the last decade, 50 instructors--from university professors to high school teachers to business tycoons--have shared their passion for mathematics by delivering more than 320 BMC sessions full of mathematical challenges and wonders. Based on a dozen of these sessions, this book encompasses a wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik's cube and abstract algebra; from number theory to mass point theory; from complex numbers to game theory via invariants and monovariants. The treatments of these subjects encompass every significant method of proof and emphasize ways of thinking and reasoning via 100 problem solving techniques. Also featured are 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions. The book presents possible paths to studying mathematics and inevitably falling in love with it, via teaching two important skills: thinking creatively while still ``obeying the rules,'' and making connections between problems, ideas, and theories. The book encourages you to apply the newly acquired knowledge to problems and guides you along the way, but rarely gives you ready answers. ``Learning from our own mistakes'' often occurs through discussions of non-proofs and common problem solving pitfalls. The reader has to commit to mastering the new theories and techniques by ``getting your hands dirty'' with the problems, going back and reviewing necessary problem solving techniques and theory, and persistently moving forward in the book. The mathematical world is huge: you'll never know everything, but you'll learn where to find things, how to connect and use them. The rewards will be substantial. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Download or read book Cubic Forms and the Circle Method written by Tim Browning and published by Springer Nature. This book was released on 2021-11-19 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Analytical Fuzzy Plane Geometry written by Debdas Ghosh and published by Springer. This book was released on 2019-05-13 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Mathematical Proofs written by Nicholas A. Loehr and published by CRC Press. This book was released on 2019-11-20 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Engineering Graphics with an Introduction to AutoCAD written by Dr. A.R. Bapat and published by Allied Publishers. This book was released on 2004-02-14 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Flexibility of Group Actions on the Circle written by Sang-hyun Kim and published by Springer. This book was released on 2019-01-02 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.

Download or read book Decode and Conquer written by Lewis C. Lin and published by . This book was released on 2013-11-28 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Land that Dream Product Manager Job...TODAYSeeking a product management position?Get Decode and Conquer, the world's first book on preparing you for the product management (PM) interview. Author and professional interview coach, Lewis C. Lin provides you with an industry insider's perspective on how to conquer the most difficult PM interview questions. Decode and Conquer reveals: Frameworks for tackling product design and metrics questions, including the CIRCLES Method(tm), AARM Method(tm), and DIGS Method(tm) Biggest mistakes PM candidates make at the interview and how to avoid them Insider tips on just what interviewers are looking for and how to answer so they can't say NO to hiring you Sample answers for the most important PM interview questions Questions and answers covered in the book include: Design a new iPad app for Google Spreadsheet. Brainstorm as many algorithms as possible for recommending Twitter followers. You're the CEO of the Yellow Cab taxi service. How do you respond to Uber? You're part of the Google Search web spam team. How would you detect duplicate websites? The billboard industry is under monetized. How can Google create a new product or offering to address this? Get the Book that's Recommended by Executives from Google, Amazon, Microsoft, Oracle & VMWare...TODAY

Download or read book An Introduction to Sieve Methods and Their Applications written by Alina Carmen Cojocaru and published by Cambridge University Press. This book was released on 2005-12-08 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.