Algebra, Arithmetic and Geometry with Applications

Algebra, Arithmetic and Geometry with Applications PDF

Author: Chris Christensen

Publisher: Springer Science & Business Media

Published: 2011-06-27

Total Pages: 778

ISBN-13: 3642184871

DOWNLOAD EBOOK →

Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty-five of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. Sessions were held on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by expert authors.

Algebra & Geometry

Algebra & Geometry PDF

Author: Mark V. Lawson

Publisher: CRC Press

Published: 2016-11-25

Total Pages: 383

ISBN-13: 1482246503

DOWNLOAD EBOOK →

Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra

Algebraic Geometry and Arithmetic Curves

Algebraic Geometry and Arithmetic Curves PDF

Author: Qing Liu

Publisher: Oxford University Press

Published: 2006-06-29

Total Pages: 593

ISBN-13: 0191547808

DOWNLOAD EBOOK →

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Arithmetic Algebraic Geometry

Arithmetic Algebraic Geometry PDF

Author: Brian David Conrad

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 569

ISBN-13: 9780821844489

DOWNLOAD EBOOK →

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Geometry, Algebra, Number Theory, and Their Information Technology Applications

Geometry, Algebra, Number Theory, and Their Information Technology Applications PDF

Author: Amir Akbary

Publisher: Springer

Published: 2018-09-18

Total Pages: 528

ISBN-13: 3319973797

DOWNLOAD EBOOK →

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Number Theory and Geometry: An Introduction to Arithmetic Geometry PDF

Author: Álvaro Lozano-Robledo

Publisher: American Mathematical Soc.

Published: 2019-03-21

Total Pages: 488

ISBN-13: 147045016X

DOWNLOAD EBOOK →

Geometry 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.

Arithmetic Algebraic Geometry

Arithmetic Algebraic Geometry PDF

Author: G., van der Geer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 450

ISBN-13: 1461204577

DOWNLOAD EBOOK →

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Basic Math, Algebra, and Geometry with Applications

Basic Math, Algebra, and Geometry with Applications PDF

Author: Cheryl S. Cleaves

Publisher: Prentice Hall

Published: 2003-07-24

Total Pages: 0

ISBN-13: 9780131844414

DOWNLOAD EBOOK →

"Basic Math, Algebra and Geometry with Applications" provides a spiral approach to developing concepts that enables readers to become familiar with concepts and computations before being asked to progress to the more abstract concept using variables as bases and other types of numbers as exponents. The clear concise language makes it easy to read and examples have line-by-line explanatory comments for each step of the example so readers can easily follow the steps illustrated. The volume provides detailed explanations of whole numbers and decimals, integers, fractions, percents, measurement, area, perimeter, and volume, interpreting and analyzing data, linear equations, powers and polynomials, roots and radicals, formulas and applications, quadratic and higher-degree equations, exponential and logarithmic equations, graphing functions and slope and distance. For nurses, dietitians, job trainers, home schooling professionals and more.

Lanterna Rally - Theme by Grace Themes