Elements of Advanced Mathematics, Third Edition (Textbooks in Mathematics) - Hardcover

Krantz, Steven G.

Hardcover

ISBN 10: 1439898340 ISBN 13: 9781439898345

Publisher: Chapman and Hall/CRC, 2012

Synopsis

For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant.

This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques.

Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.

About this title

Review:

... one of the difficulties that students have with university mathematics is being able to relate it to what they’ve done at school. In this respect, the work on logic, sets, proof, relations and functions plays an essential bridging role. But another problem to be addressed is to re-present mathematics as a way of knowing―rather than a static body of formalised knowledge. In this book, Steven Krantz tackles this anomaly by including many open-ended problems in the rich collections of exercises. ... The new chapters on theoretical computer science are concisely lucid, and I learned much by reading them. ... this book engages the reader in really meaningful aspects of mathematics: it is well organized and is written with accuracy. ... it is recommended as a possible course text for those who are planning to teach a foundation course.
―P.N. Ruane, MAA Reviews, July 2012

Retains the content and character of previous editions while making the material more up-to-date and significant. ... gives readers the background, tools, and skills necessary in more advanced mathematical work.
― L'Enseignement Mathematique, 2012

About the Author:

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis, Missouri. He has published over 150 papers and nearly 70 books and has been an editor of several journals. He earned a Ph.D. in mathematics from Princeton University. His research interests include complex variables, harmonic analysis, partial differential equations, geometry, interpolation of operators, and real analysis.

About this edition

• Publisher: Chapman and Hall/CRC
• Publication date: 2012
• ISBN 10: 1439898340
• ISBN 13: 9781439898345
• Binding: Hardcover
• Edition number: 3
• Number of pages: 367