An Introduction To The Circle Method
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An Introduction To The Circle Method
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-15
An Introduction To The Circle Method written by M. Ram Murty and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-15 with Mathematics categories.
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
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Author : Steven J. Miller
language : en
Publisher: Princeton University Press
Release Date : 2020-08-04
An Invitation To Modern Number Theory written by Steven J. Miller and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-04 with Mathematics categories.
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
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Author : Andrew Granville
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-08
Equidistribution In Number Theory An Introduction written by Andrew Granville and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-08 with Mathematics categories.
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.
A Course In Analytic Number Theory
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Author : Marius Overholt
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-30
A Course In Analytic Number Theory written by Marius Overholt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
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.
An Introduction To Mathematical Proofs
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2019-11-20
An Introduction To Mathematical Proofs written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.
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.
An Introduction To Analytical Fuzzy Plane Geometry
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Author : Debdas Ghosh
language : en
Publisher: Springer
Release Date : 2019-05-13
An Introduction To Analytical Fuzzy Plane Geometry written by Debdas Ghosh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-13 with Technology & Engineering categories.
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
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Author : Dr. A.R. Bapat
language : en
Publisher: Allied Publishers
Release Date : 2004-02-14
Engineering Graphics With An Introduction To Autocad written by Dr. A.R. Bapat and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-14 with Technology & Engineering categories.
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.
The Goldschmidt Two Circle Method
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Author : Charles Palache
language : en
Publisher:
Release Date : 1920
The Goldschmidt Two Circle Method written by Charles Palache and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1920 with categories.
An Introduction To Embankments For Small Earthfill Dams
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Author : J. Paul Guyer, P.E., R.A.
language : en
Publisher: Guyer Partners
Release Date : 2018-10-13
An Introduction To Embankments For Small Earthfill Dams written by J. Paul Guyer, P.E., R.A. and has been published by Guyer Partners this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-13 with Technology & Engineering categories.
Introductory technical guidance for civil engineers and construction managers interested in design and construction of small earthfill dams. Here is what is discussed: 1. FUNDAMENTAL CONSIDERATIONS 2. PORE WATER PRESSURE 3. SEEPAGE THROUGH EMBANKMENTS 4. STABILITY ANALYSES 5. EMBANKMENT DESIGN. 6. SEISMIC DESIGN.
Foundation Design Codes And Soil Investigation In View Of International Harmonization And Performance Based Design
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Author : Y. Honjo
language : en
Publisher: CRC Press
Release Date : 2002-01-01
Foundation Design Codes And Soil Investigation In View Of International Harmonization And Performance Based Design written by Y. Honjo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Technology & Engineering categories.
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.