The Elements of Advanced Mathematics

Steven G. Krantz

214 pages, parution le 07/03/2002 (2^eme édition)

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Résumé

The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs.New in the Second Edition:· Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science· A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor setú Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissectionú Streamlined treatment of non-Euclidean geometryú Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relationsú More thorough treatment of the Axiom of Choice and its equivalentsú Additional material on Russell's paradox and related ideasú Expanded treatment of group theory that helps students grasp the axiomatic methodú A wealth of added exercises

Contents

Basic logic
Methods of proof
Set theory
Relations and functions
Axioms of set theory, paradoxes, and rigor
Number systems
More on the real number system
Examples of axiomatic theories

Solutions to selected exercises
Bibliography
Index

L'auteur - Steven G. Krantz

Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned his PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA's Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations," "The Geometry of Domains in Space" (with Harold R. Parks), "Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem" (with Harold Parks). "Complex Analysis: The Geometric Viewpoint," and" A Panorama of Harmonic Analysis" (both for the MAA). He is also the author of over one-hundred research articles.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Steven G. Krantz
Parution	07/03/2002
Édition	2^eme édition
Nb. de pages	214
Format	16 x 24
Couverture	Broché
Poids	500g
Intérieur	Noir et Blanc
EAN13	9781584883036
ISBN13	978-1-58488-303-6