Problems and Theorems in Analysis II

Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

Author: George Polya,Gabor Szegö

Publisher: Springer Science & Business Media

ISBN: 9783540636861

Category: Mathematics

Page: 392

View: 5221

Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.

Problems and Theorems in Analysis

Series · Integral Calculus · Theory of Functions

Author: Georg Polya,Gabor Szegö

Publisher: Springer Science & Business Media

ISBN: 1475716400

Category: Mathematics

Page: 392

View: 1576

The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924. We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published in this work have given rise to extensive research. To include all such developments would have changed the character of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion and scrupulous conscientiousness with which they attacked their far from easy task.

Complex Analysis

Author: Eberhard Freitag,Rolf Busam

Publisher: Springer Science & Business Media

ISBN: 3540308237

Category: Mathematics

Page: 552

View: 9063

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

Advanced Analytic Number Theory

L-Functions

Author: Carlos J. Moreno

Publisher: American Mathematical Soc.

ISBN: 0821842668

Category: Mathematics

Page: 291

View: 710

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. The present book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

The Theory of Matrices

Author: Feliks Ruvimovich Gantmakher

Publisher: American Mathematical Soc.

ISBN: 9780821813768

Category: Mathematics

Page: 276

View: 3809

This treatise, by one of Russia's leading mathematicians, gives in easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, electrical engineering, etc. The individual chapters have been kept as far as possible independent of each other, so that the reader acquainted with the contents of Chapter 1 can proceed immediately to the chapters of special interest. Much of the material has been available until now only in the periodical literature.

Discriminants, Resultants, and Multidimensional Determinants

Author: Israel M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

Publisher: Springer Science & Business Media

ISBN: 0817647716

Category: Mathematics

Page: 523

View: 9833

"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews

Applications of the Theory of Matrices

Author: F. R. Gantmacher,J.L. Brenner

Publisher: Courier Corporation

ISBN: 0486445542

Category: Mathematics

Page: 317

View: 8187

The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3733

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,

Author: Emil Artin

Publisher: Courier Corporation

ISBN: 048615825X

Category: Mathematics

Page: 86

View: 3957

Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Problem-Solving Through Problems

Author: Loren C. Larson

Publisher: Springer Science & Business Media

ISBN: 1461254981

Category: Mathematics

Page: 352

View: 5988

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Random Polynomials

Probability and Mathematical Statistics: A Series of Monographs and Textbooks

Author: A. T. Bharucha-Reid,M. Sambandham

Publisher: Academic Press

ISBN: 148319146X

Category: Mathematics

Page: 222

View: 554

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.

Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry

Author: Jürgen Richter-Gebert

Publisher: Springer Science & Business Media

ISBN: 9783642172861

Category: Mathematics

Page: 571

View: 4561

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Numerically Solving Polynomial Systems with Bertini

Author: Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler

Publisher: SIAM

ISBN: 1611972698

Category: Science

Page: 352

View: 5997

This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Proofs from THE BOOK

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer

ISBN: 3662572656

Category: Mathematics

Page: 326

View: 2659

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" “... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.” From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011

The Geometry of Schemes

Author: David Eisenbud,Joe Harris

Publisher: Springer Science & Business Media

ISBN: 0387226397

Category: Mathematics

Page: 300

View: 2720

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Principia Mathematica

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 4435