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040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a511 _bLOZ-N
100			_aLozano-Robledo, Álvaro
245			_aNumber theory and geometry : _ban introduction to arithmetic geometry
260			_aIndia : _bUniversities Press, _c2025.
300			_axv, 488 pages ; _c27 cm.
490			_aPure and applied undergraduate texts ; _v35
490			_aThe Sally series
504			_aIncludes bibliographical references and index.
520			_aGeometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
521			_aReadership: Undergraduate and graduate students interested in learning and teaching.
650			_aArithmetical algebraic geometry
650			_aNumber theory
650			_aDiophantine geometry _xArithmetic problems
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/amstext-35-toc.pdf?_gl=1*1ljqigr*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAwNDYzMjQkbzEkZzEkdDE3NTAwNTA5NDUkajQ4JGwwJGgw
856			_3Reviews _uhttps://www.goodreads.com/book/show/44696676-number-theory-and-geometry?ref=nav_sb_ss_1_13#CommunityReviews
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