*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:**6395

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# Search Results for: problems-and-theorems-in-analysis-volume-ii-theory-of-functions-zeros-polynomials-determinants-number-theory-geometry-classics-in-mathematics-v-2

*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:** 6395

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.

**Author**: Eberhard Freitag,Rolf Busam

**Publisher:** Springer Science & Business Media

**ISBN:** 3540308237

**Category:** Mathematics

**Page:** 552

**View:** 3185

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

**Author**: Feliks Ruvimovich Gantmakher

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821813768

**Category:** Mathematics

**Page:** 276

**View:** 9494

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.

**Author**: David Eisenbud,Joe Harris

**Publisher:** Springer Science & Business Media

**ISBN:** 0387226397

**Category:** Mathematics

**Page:** 300

**View:** 8192

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.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 535

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

**Publisher:** Springer Science & Business Media

**ISBN:** 0817647716

**Category:** Mathematics

**Page:** 523

**View:** 4716

"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
*L-Functions*

**Author**: Carlos J. Moreno

**Publisher:** American Mathematical Soc.

**ISBN:** 0821842668

**Category:** Mathematics

**Page:** 291

**View:** 4792

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.
*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:** 3744

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.

**Author**: Saugata Basu,Richard Pollack,Marie-Françoise Roy

**Publisher:** Springer Science & Business Media

**ISBN:** 3662053551

**Category:** Mathematics

**Page:** 602

**View:** 6067

In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
*Series · Integral Calculus · Theory of Functions*

**Author**: Georg Polya,Gabor Szegö

**Publisher:** Springer Science & Business Media

**ISBN:** 1475716400

**Category:** Mathematics

**Page:** 392

**View:** 6967

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.
*Revised*

**Author**: Lynn Harold Loomis,Shlomo Sternberg

**Publisher:** World Scientific Publishing Company

**ISBN:** 9814583952

**Category:** Mathematics

**Page:** 596

**View:** 2602

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

**Author**: Anthony W. Knapp

**Publisher:** Springer Science & Business Media

**ISBN:** 0817646132

**Category:** Mathematics

**Page:** 730

**View:** 2260

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
*A Guided Tour Through Real and Complex Geometry*

**Author**: Jürgen Richter-Gebert

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642172861

**Category:** Mathematics

**Page:** 571

**View:** 527

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.
*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:** 9700

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.

**Author**: David A.R. Wallace

**Publisher:** Springer Science & Business Media

**ISBN:** 1447104250

**Category:** Mathematics

**Page:** 248

**View:** 6496

This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.
*From the Training of the USA IMO Team*

**Author**: Titu Andreescu,Dorin Andrica,Zuming Feng

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817645618

**Category:** Mathematics

**Page:** 204

**View:** 3691

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 1618

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