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BT 34.016 514.330 Td /F1 28.5 Tf [(Algebra Serge Lang)] TJ ET
BT 34.016 460.106 Td /F1 14.2 Tf [(Thank you certainly much for downloading )] TJ ET
BT 304.880 460.106 Td /F1 14.2 Tf [(Algebra Serge Lang)] TJ ET
BT 431.619 460.106 Td /F1 14.2 Tf [(.Most likely you have knowledge that, people have look )] TJ ET
BT 34.016 442.707 Td /F1 14.2 Tf [(numerous times for their favorite books considering this Algebra Serge Lang, but stop happening in harmful downloads. )] TJ ET
BT 34.016 408.208 Td /F1 14.2 Tf [(Rather than enjoying a fine book when a cup of coffee in the afternoon, on the other hand they juggled like some harmful )] TJ ET
BT 34.016 390.809 Td /F1 14.2 Tf [(virus inside their computer. )] TJ ET
BT 208.236 390.809 Td /F1 14.2 Tf [(Algebra Serge Lang)] TJ ET
BT 334.976 390.809 Td /F1 14.2 Tf [( is easily reached in our digital library an online entrance to it is set as )] TJ ET
BT 34.016 373.409 Td /F1 14.2 Tf [(public correspondingly you can download it instantly. Our digital library saves in combined countries, allowing you to )] TJ ET
BT 34.016 356.010 Td /F1 14.2 Tf [(acquire the most less latency era to download any of our books considering this one. Merely said, the Algebra Serge Lang )] TJ ET
BT 34.016 338.611 Td /F1 14.2 Tf [(is universally compatible in imitation of any devices to read.)] TJ ET
BT 34.016 275.612 Td /F1 14.2 Tf [(Introduction to Algebraic and Abelian Functions)] TJ ET
BT 332.624 275.612 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 Introduction to Algebraic and Abelian Functions )] TJ ET
BT 34.016 258.212 Td /F1 14.2 Tf [(is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised )] TJ ET
BT 34.016 240.813 Td /F1 14.2 Tf [(edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout )] TJ ET
BT 34.016 223.414 Td /F1 14.2 Tf [(the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more )] TJ ET
BT 34.016 206.015 Td /F1 14.2 Tf [(advanced books listed in the bibliography.)] TJ ET
BT 34.016 188.615 Td /F1 14.2 Tf [(Algebraic Number Theory)] TJ ET
BT 196.352 188.615 Td /F1 14.2 Tf [( Serge Lang 2013-06-29 This is a second edition of Lang's well-known textbook. It covers all of )] TJ ET
BT 34.016 171.216 Td /F1 14.2 Tf [(the basic material of classical algebraic number theory, giving the student the background necessary for the study of )] TJ ET
BT 34.016 153.817 Td /F1 14.2 Tf [(further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great )] TJ ET
BT 34.016 136.418 Td /F1 14.2 Tf [(value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no )] TJ ET
BT 34.016 119.018 Td /F1 14.2 Tf [(exception."—-MATHEMATICAL REVIEWS)] TJ ET
BT 34.016 101.619 Td /F1 14.2 Tf [(Geometry)] TJ ET
BT 96.573 101.619 Td /F1 14.2 Tf [( Serge Lang 2013-04-17 At last: geometry in an exemplary, accessible and attractive form! The authors )] TJ ET
BT 34.016 84.220 Td /F1 14.2 Tf [(emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or )] TJ ET
BT 34.016 66.821 Td /F1 14.2 Tf [(classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(difference between important results and minor technical routines. Altogether, the text presents a coherent high school )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(curriculum for the geometry course, naturally backed by numerous examples and exercises.)] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Undergraduate Algebra)] TJ ET
BT 182.130 512.546 Td /F1 14.2 Tf [( Serge Lang 2013-06-29 The companion title, Linear Algebra, has sold over 8,000 copies The )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(including descriptions of the conjugation representation of the diagonal group)] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(Introduction to Algebraic Geometry)] TJ ET
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34.016 440.598 m 254.192 440.598 l S
BT 254.192 442.949 Td /F1 14.2 Tf [( Serge Lang 2019-03-20 Rapid, concise, self-contained introduction assumes only )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(familiarity with elementary algebra. Subjects include algebraic varieties; products, projections, and correspondences; )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(normal varieties; differential forms; theory of simple points; algebraic groups; more. 1958 edition.)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(Fundamentals of Diophantine Geometry)] TJ ET
BT 286.668 390.752 Td /F1 14.2 Tf [( S. Lang 2013-06-29 Diophantine problems represent some of the strongest )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields \(including the real and )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(complex numbers\) as representing a localization of the problems under consideration. We shall deal with global problems, )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(points.)] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(Topics in Cohomology of Groups)] TJ ET
BT 241.510 181.961 Td /F1 14.2 Tf [( Serge Lang 2006-11-14 The book is a mostly translated reprint of a report on )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(theory, following the cohomological approach. This report was first published \(in French\) by Benjamin. For this new )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(Except for this last item, which requires more substantial background in algebraic geometry and especially abelian )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(year graduate students.)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Algebra)] TJ ET
BT 83.121 60.166 Td /F1 14.2 Tf [( Serge Lang 2005-06-21 This book is intended as a basic text for a one year course in algebra at the graduate )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(which pervades some parts of algebra.")] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(Algebra: Chapter 0)] TJ ET
BT 153.616 460.349 Td /F1 14.2 Tf [( Paolo Aluffi 2009 Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(index and by hundreds of cross-references.)] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(Linear Algebra)] TJ ET
BT 126.683 268.957 Td /F1 14.2 Tf [( Serge Lang 1987-01-26 "Linear Algebra" is intended for a one-term course at the junior or senior level. It )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(has already had some exposure to the elementary theory of matrices, determinants and linear maps. However the book is )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(exercises have been added.)] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(Differential Manifolds)] TJ ET
BT 167.054 129.763 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 The present volume supersedes my Introduction to Differentiable Manifolds )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(advanced calculus and the three great differential theories \(differential topology, differential geometry, ordinary differential )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(equations\), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(suitable differentiable maps in them \(immersions, embeddings, isomorphisms, etc.\). One may also use differentiable )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(structures on topological manifolds to determine the topological structure of the manifold \(e.g. it la Smale [26]\).)] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(Riemann-Roch Algebra)] TJ ET
BT 182.102 460.349 Td /F1 14.2 Tf [( William Fulton 2013-03-14 In various contexts of topology, algebraic geometry, and algebra \(e.g. )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(group representations\), one meets the following situation. One has two contravariant functors K and A from a certain )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(category to the category of rings, and a natural transformation p:K--+A of contravariant functors. The Chern character )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(being the central exam ple, we call the homomorphisms Px: K\(X\)--+ A\(X\) characters. Given f: X--+ Y, we denote the pull-)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(back homomorphisms by and fA: A\(Y\)--+ A\(X\). As functors to abelian groups, K and A may also be covariant, with push-)] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(forward homomorphisms and fA: A\(X\)--+ A\(Y\). Usually these maps do not commute with the character, but there is an )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(element r f E A\(X\) such that the following diagram is commutative: K\(X\)~A\(X\) fK j J~A K\(Y\) --p;-+ A\(Y\) The map in the top )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(line is p x multiplied by r f. When such commutativity holds, we say that Riemann-Roch holds for f. This type of formulation )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(was first given by Grothendieck, extending the work of Hirzebruch to such a relative, functorial setting. Since then viii )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(INTRODUCTION several other theorems of this Riemann-Roch type have appeared. Un derlying most of these there is a )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(basic structure having to do only with elementary algebra, independent of the geometry. One purpose of this monograph )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(is to describe this algebra independently of any context, so that it can serve axiomatically as the need arises.)] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(Introduction to Linear Algebra)] TJ ET
BT 220.947 251.558 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 This is a short text in linear algebra, intended for a one-term )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(while others are conceptual.)] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(Math!)] TJ ET
BT 69.655 147.162 Td /F1 14.2 Tf [( Serge Lang 2013-03-14 )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(Undergraduate Algebra)] TJ ET
BT 182.130 129.763 Td /F1 14.2 Tf [( Serge Lang 1987 )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(Calculus of Several Variables)] TJ ET
BT 220.121 112.364 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 This new, revised edition covers all of the basic topics in calculus of )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(inverse mapping theorem and its consequences. It includes many completely worked-out problems.)] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Solutions Manual for Lang’s Linear Algebra)] TJ ET
BT 306.476 529.946 Td /F1 14.2 Tf [( Rami Shakarchi 1996-08-09 This solutions manual for Lang’s Undergraduate )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Analysis provides worked-out solutions for all problems in the text. They include enough detail so that a student can fill in )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(the intervening details between any pair of steps.)] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Real and Functional Analysis)] TJ ET
BT 217.755 477.748 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 This book is meant as a text for a first-year graduate course in )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(exposition of material from later chapters.)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(SL2\(R\))] TJ ET
BT 79.145 390.752 Td /F1 14.2 Tf [( S. Lang 2012-12-06 SL2\(R\) gives the student an introduction to the infinite dimensional representation theory of )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(semisimple Lie groups by concentrating on one example - SL2\(R\). This field is of interest not only for its own sake, but for )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(and some differential equations.)] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(Algebra)] TJ ET
BT 83.121 286.356 Td /F1 14.2 Tf [( 1993 )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(A First Course in Calculus)] TJ ET
BT 198.717 268.957 Td /F1 14.2 Tf [( Serge Lang 2012-09-17 This fifth edition of Lang's book covers all the topics traditionally taught )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(previous editions.)] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(Abstract Algebra)] TJ ET
BT 139.352 181.961 Td /F1 14.2 Tf [( Paul B. Garrett 2007-09-25 Designed for an advanced undergraduate- or graduate-level course, Abstract )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(characterization of objects by universal mapping properties, rather than by constructions whose technical details are )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.)] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Complex Analysis)] TJ ET
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BT 147.246 477.748 Td /F1 14.2 Tf [( Serge Lang 2013-06-29 The present book is meant as a text for a course on complex analysis at the )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(less advanced students. In some sense, I think the classical German prewar texts were the best \(Hurwitz-Courant, Knopp, )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(Bieberbach, etc. \) and I would recom mend to anyone to look through them. More recent texts have empha sized )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(systematic elementary development of formal and convergent power series was standard fare in the German texts, but )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(essentially decomposes into two parts.)] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(Real Analysis)] TJ ET
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BT 120.328 251.558 Td /F1 14.2 Tf [( Serge Lang 1983 )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(Algebra)] TJ ET
0.285 w 0 J [ ] 0 d
34.016 231.807 m 83.121 231.807 l S
BT 83.121 234.158 Td /F1 14.2 Tf [( Thomas W. Hungerford 2012-12-06 Finally a self-contained, one volume, graduate-level algebra text that is )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(exercises.)] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(Introduction to Algebraic Geometry)] TJ ET
BT 254.192 147.162 Td /F1 14.2 Tf [( Serge Lang 2019-03-20 Author Serge Lang defines algebraic geometry as the study )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(the theory of algebraic groups are featured.)] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Elements of Abstract Algebra)] TJ ET
0.285 w 0 J [ ] 0 d
34.016 475.397 m 218.553 475.397 l S
BT 218.553 477.748 Td /F1 14.2 Tf [( Allan Clark 2012-07-06 Lucid coverage of the major theories of abstract algebra, with helpful )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(Bibliography. Index. Includes 24 tables and figures.)] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(Linear Algebra and Geometry)] TJ ET
BT 220.933 425.550 Td /F1 14.2 Tf [( Igor R. Shafarevich 2012-08-23 This book on linear algebra and geometry is based on a )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-)] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(Euclidean geometry, topological properties of projective spaces, theory of quadrics \(in affine and projective spaces\), )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(decomposition of finite abelian groups, and finitely generated periodic modules \(similar to Jordan normal forms of linear )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(operators\). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.)] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(The Beauty of Doing Mathematics)] TJ ET
BT 248.649 268.957 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 If someone told you that mathematics is quite beautiful, you )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(might be surprised. But you should know that some people do mathematics all their lives, and create mathematics, just as )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(a composer creates music. Usually, every time a mathematician solves a problem, this gives rise to many oth ers, new )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(and just as beautiful as the one which was solved. Of course, often these problems are quite difficult, and as in other )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(disciplines can be understood only by those who have studied the subject with some depth, and know the subject well. In )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(1981, Jean Brette, who is responsible for the Mathematics Section of the Palais de la Decouverte \(Science Museum\) in )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Paris, invited me to give a conference at the Palais. I had never given such a conference before, to a non-mathematical )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(public. Here was a challenge: could I communicate to such a Saturday afternoon audience what it means to do )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(mathematics, and why one does mathematics? By "mathematics" I mean pure mathematics. This doesn't mean that pure )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(math is better than other types of math, but I and a number of others do pure mathematics, and it's about them that I am )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(now concerned. Math has a bad reputation, stemming from the most elementary levels. The word is in fact used in many )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(different contexts. First, I had to explain briefly these possible contexts, and the one with which I wanted to deal.)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Abelian Varieties)] TJ ET
BT 140.933 60.166 Td /F1 14.2 Tf [( Serge Lang 2019-02-13 A basic advanced text in its field, this monograph for undergraduates and )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(graduate students in mathematics requires some background in elementary qualitative algebraic geometry and the )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(elementary theory of algebraic groups. 1959 edition.)] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Introduction to Arakelov Theory)] TJ ET
BT 232.019 512.546 Td /F1 14.2 Tf [( Serge Lang 1988-11-09 Arakelov introduced a component at infinity in arithmetic )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(for second year graduate students and researchers in the field who want a systematic introduction to the subject. The )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(residue theorem, which forms the basis for the adjunction formula, is proved by a direct method due to Kunz and Waldi. )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(The Faltings Riemann-Roch theorem is proved without assumptions of semistability. An effort has been made to include )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(all necessary details, and as complete references as possible, especially to needed facts of analysis for Green's functions )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(and the Faltings metrics.)] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(Algebraic Structures)] TJ ET
BT 162.308 355.953 Td /F1 14.2 Tf [( Serge Lang 1967 )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(Cyclotomic Fields I and II)] TJ ET
BT 193.188 338.554 Td /F1 14.2 Tf [( Serge Lang 2012-12-06 Kummer's work on cyclotomic fields paved the way for the development )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(In the mid 1950's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(rationals. Finally, in the late 1960's, Iwasawa [Iw 11] made the fundamental discovery that there was a close connection )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(between his work on towers of cyclotomic fields and these p-adic L-functions of Leopoldt - Kubota.)] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(Complex Multiplication)] TJ ET
BT 176.544 112.364 Td /F1 14.2 Tf [( S. Lang 2012-12-06 The small book by Shimura-Taniyama on the subject of complex multi is a )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(classic. It gives the results obtained by them \(and some by Weil\) plication in the higher dimensional case, generalizing in a )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(non-trivial way the method of Deuring for elliptic curves, by reduction mod p. Partly through the work of Shimura himself )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(\(cf. [Sh 1] [Sh 2], and [Sh 5]\), and some others \(Serre, Tate, Kubota, Ribet, Deligne etc.\) it is possible today to make a )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(more snappy and extensive presentation of the fundamental results than was possible in 1961. Several persons have )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(found my lecture notes on this subject useful to them, and so I have decided to publish this short book to make them more )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(widely available. Readers acquainted with the standard theory of abelian varieties, and who wish to get rapidly an idea of )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(the fundamental facts of complex multi plication, are advised to look first at the two main theorems, Chapter 3, §6 and )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Chapter 4, §1, as well as the rest of Chapter 4. The applications of Chapter 6 could also be profitably read early. I am )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(much indebted to N. Schappacher for a careful reading of the manu script resulting in a number of useful suggestions. S. )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(LANG Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive Definite Involutions . . . 6 2. CM Types and )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(Subfields. . . . . 8 3. Application to Abelian Manifolds. 4. Construction of Abelian Manifolds with CM 14 21 5. Reflex of a )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(CM Type . . . . .)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(Algebra)] TJ ET
BT 83.121 390.752 Td /F1 14.2 Tf [( Serge Lang 2012-11-10 This book is intended as a basic text for a one year course in algebra at the graduate )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(which pervades some parts of algebra.")] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(Basic Mathematics)] TJ ET
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BT 153.587 286.356 Td /F1 14.2 Tf [( Serge Lang 1988-01 )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(Algebraic Geometry)] TJ ET
BT 159.929 268.957 Td /F1 14.2 Tf [( Solomon Lefschetz 2015-12-08 The first application of modern algebraic techniques to a )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(comprehensive selection of classical geometric problems. Written with spirit and originality, this is a valuable book for )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(anyone interested in the subject from other than the purely algebraic point of view. Originally published in 1953. The )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(University Press since its founding in 1905.)] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(Algebra)] TJ ET
BT 83.121 129.763 Td /F1 14.2 Tf [( Serge A. Lang 1993 This basic text for a one-year course in algebra at the graduate level thoroughly prepares )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(students to handle the algebra they will use in all of mathematics. The author assumes that students have a basic )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(familiarity with the language of mathematics "i.e.: sets and mapping, integers, and rational numbers." The text was )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(thoroughly revised and enhanced in response to reviewers' comments and suggestions. Designed to improve students' )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(retention and comprehension, the text is divided into four parts. The first introduces the basic notions of algebra. The )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(second covers the direction of algebraic equations, including the Galois theory, and the final two parts cover the direction )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(of linear and multilinear algebra.)] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Algebra)] TJ ET
BT 83.121 512.546 Td /F1 14.2 Tf [( Serge Lang 1978 )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(Algebraic Number Theory)] TJ ET
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BT 196.352 495.147 Td /F1 14.2 Tf [( Ian Stewart 1979-05-31 The title of this book may be read in two ways. One is 'algebraic )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(proper coverage of either topic would require more space than is available, and demand more of the reader than we wish )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(axiomatization of mathematics has led to enormous organizational and conceptual gains.)] TJ ET
BT 36.266 258.861 Td /F1 8.0 Tf [(algebra-serge-lang)] TJ ET
BT 579.288 259.068 Td /F1 8.0 Tf [(Downloaded from )] TJ ET
BT 644.200 258.861 Td /F1 8.0 Tf [(cowa.org.nz)] TJ ET
BT 687.328 259.068 Td /F1 8.0 Tf [( on September 28, 2022 by guest)] TJ ET
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