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Algebra
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Serge A Lang
From April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books: "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has ...
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Undergraduate Analysis
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This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier ...
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Linear algebra
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is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and ...
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Complex Analysis
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Serge Lang
This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs ...
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A first course in calculus
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Serge A Lang
This is the fifth edition of Lang's calculus book. It covers all of the topics traditionally taught in the first-year calculus sequence. The book consists of five parts: Review of Basic Material, Differention and Elementary Functions, Integration, Taylor's Formula and Series and Functions of Several Variables. Each section of "A First Course in ...
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Introduction to Linear Algebra
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Serge A Lang
This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian ...
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Analysis One
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Real Analysis
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Algebraic Number Theory
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Serge Lang
Covers the basic material of classical algebraic number theory. This book gives the student the background useful for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms.
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The Beauty of Doing Mathematics: Three Public Dialogues
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Serge A Lang
This book contains the faithful transcriptions of these three mathematical dialogues. Lang's foal was to communicate something of the true nature and beauty of mathematical thought and, as one can see from the enthusiasm of audience, he was quite successful. The three topics (Prime Numbers, Diophantine Equations, and Great Problems in the Geometry ...
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Cyclotomic fields II
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Analysis Two
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Differential Manifolds
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Serge A Lang
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