Pure and Applied Mathematics
Pure and Applied Mathematics ➤ ALGEBRa / COMBINATORICS ➤ LOGIc / SET THEORY ➤ NUMBER THEORY ➤ GEOMETRY / TOPOLOGY ➤ GROUPS AND REPRESENTATION THEORY ➤ ANALYSIS / OPERATOR THEORY ➤ PROBABILITY / STATISTICS / NUMERIcaL METHODS ➤ MaTHEMATIcaL PHYSICS / PHYSICS ➤ DIFFERENTIAL EQUATIONS / DYNAMIcaL SYSTEMS ➤ APPLIED MaTHEMATICS ➤ GENERAL INTEREST / REFERENCE / MaTH EDUcaTION www.birkhauser.com ALGEBRA / COMBINATORICS Cornerstones is a new Birkhäuser series that is comprised of textbooks focusing on “what students need to know” and Advanced Algebra “what faculty should teach” in various selected topics in pure ANTHONY W. KNAPP, State University of New York, Stony Brook, NY mathematics and related subjects. Basic Algebra and Advanced Algebra systematically develop Series Editors: concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together the two CHARLES L. EPSTEIN, University of Pennsylvania, Philadelphia, PA books give the reader a global view of algebra and its role in math- STEVEN G. KRANTZ, Washington University, St. Louis, MO ematics as a whole. Basic Algebra Key Topics and Features of Advanced Algebra: ANTHONY W. KNAPP, State University of • Topics build upon the linear algebra, group theory, factoriza- New York at Stony Brook, NY tions of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra Basic Algebra and Advanced Algebra systematically develop concepts and tools • Chapters on modern algebra treat various topics in commuta- in algebra that are vital to every mathema- tive and noncommutative algebra and povide introductions to tician, whether pure or applied,, aspiring the theory of associative algebras, homological algebras, alge- or established. Together, the two books braic number theory, and algebraic geometry give the reader a global view of algebra • Continues to carry on the three prominent themes recurring in and its role in mathematics as a whole.
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