
The Elements of Advanced Mathematics
Steven G. Krantz(Author)
Chapman & Hall/CRC (Publisher)
5th Edition
Published on 26. August 2024
Book
Paperback/Softback
312 pages
978-1-032-10279-5 (ISBN)
Description
This book has enjoyed considerable use and appreciation during its first four editions. With hundreds of students having learned out of early editions, the author continues to find ways to modernize and maintain a unique presentation.
What sets the book apart is the excellent writing style, exposition, and unique and thorough sets of exercises. This edition offers a more instructive preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.
As would be expected in a fifth edition, the overall content and structure of the book are sound.
This new edition offers a more organized treatment of axiomatics. Throughout the book, there is a more careful and detailed treatment of the axioms of set theory. The rules of inference are more carefully elucidated.
Additional new features include:
An emphasis on the art of proof.
Enhanced number theory chapter presents some easily accessible but still-unsolved problems. These include the Goldbach conjecture, the twin prime conjecture, and so forth.
The discussion of equivalence relations is revised to present reflexivity, symmetry, and transitivity before we define equivalence relations.
The discussion of the RSA cryptosystem in Chapter 8 is expanded.
The author introduces groups much earlier. Coverage of group theory, formerly in Chapter 11, has been moved up; this is an incisive example of an axiomatic theory.
Recognizing new ideas, the author has enhanced the overall presentation to create a fifth edition of this classic and widely-used textbook.
What sets the book apart is the excellent writing style, exposition, and unique and thorough sets of exercises. This edition offers a more instructive preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.
As would be expected in a fifth edition, the overall content and structure of the book are sound.
This new edition offers a more organized treatment of axiomatics. Throughout the book, there is a more careful and detailed treatment of the axioms of set theory. The rules of inference are more carefully elucidated.
Additional new features include:
An emphasis on the art of proof.
Enhanced number theory chapter presents some easily accessible but still-unsolved problems. These include the Goldbach conjecture, the twin prime conjecture, and so forth.
The discussion of equivalence relations is revised to present reflexivity, symmetry, and transitivity before we define equivalence relations.
The discussion of the RSA cryptosystem in Chapter 8 is expanded.
The author introduces groups much earlier. Coverage of group theory, formerly in Chapter 11, has been moved up; this is an incisive example of an axiomatic theory.
Recognizing new ideas, the author has enhanced the overall presentation to create a fifth edition of this classic and widely-used textbook.
Reviews / Votes
The great strength of the book overall and of the chapters I read is a very accessible writing style, and extremely good exercises. The mix of discussion of advanced topics alongside the presentation of more elementary material is excellent. This is a product of having a highly accomplished and knowledgeable mathematician writing a textbook intended for not-so-advanced students.--David Walnut, George Washington UniversityMore details
Series
Edition
5th edition
Language
English
Place of publication
Boca Raton
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Undergraduate Advanced
Illustrations
36 s/w Abbildungen, 36 s/w Zeichnungen, 1 s/w Tabelle
1 Tables, black and white; 36 Line drawings, black and white; 36 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 17 mm
Weight
477 gr
ISBN-13
978-1-032-10279-5 (9781032102795)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Steven G. Krantz
The Elements of Advanced Mathematics
Book
06/2022
5th Edition
Chapman & Hall/CRC
€133.70
Shipment within 10-20 days

Steven G. Krantz
The Elements of Advanced Mathematics
E-Book
06/2022
5th Edition
Chapman & Hall/CRC
€78.99
Available for download

Steven G. Krantz
The Elements of Advanced Mathematics
E-Book
06/2022
5th Edition
Chapman & Hall/CRC
€78.99
Available for download
Person
Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 130 books and more than 250 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.
Content
1. Basic Logic 2. Methods of Proof 3. Set Theory 4. Relations and Functions 5. Group Theory 6. Number Systems 7. More on the Real Number System 8. A Glimpse of Topology 9. Elementary Number Theory 10. Zero-Knowledge Proofs and Cryptography
11. An Example of an Axiomatic Theory
11. An Example of an Axiomatic Theory