Synopses & Reviews
This text helps bridge computationally oriented mathematics with more theoretically oriented mathematics, preparing readers for more advanced courses that require understanding proofs. It covers logic, set theory, axiomatics, number systems, and reading, evaluating, and creating proofs. This third edition includes some of the more modern topics from theoretical computer science, such as the P/NP problem, Boolean algebra, and Church 's thesis. Along with new problems and examples, it also illustrates logic in action and discusses topics from the real number system and topology.
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.