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Elements of Advanced Mathematics, Third Edition

2012-03-19 Mathematics
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Release : 2012-03-19
Genre : Mathematics
Kind : eBook
Book Rating : 340/5 ( reviews)

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Book Synopsis Elements of Advanced Mathematics, Third Edition by : Steven G. Krantz

Download or read book Elements of Advanced Mathematics, Third Edition written by Steven G. Krantz. This book was released on 2012-03-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Elements of Advanced Mathematics

2017-11-02 Mathematics
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Release : 2017-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 317/5 ( reviews)

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Book Synopsis The Elements of Advanced Mathematics by : Steven G. Krantz

Download or read book The Elements of Advanced Mathematics written by Steven G. Krantz. This book was released on 2017-11-02. Available in PDF, EPUB and Kindle. Book excerpt: The Elements of Advanced Mathematics, Fourth Edition is the latest edition of the author’s bestselling series of texts. Expanding on previous editions, the new Edition continues to provide students with a better understanding of proofs, a core concept for higher level mathematics. To meet the needs of instructors, the text is aligned directly with course requirements. The author connects computationally and theoretically based mathematics, helping students develop a foundation for higher level mathematics. To make the book more pertinent, the author removed obscure topics and included a chapter on elementary number theory. Students gain the momentum to further explore mathematics in the real world through an introduction to cryptography. These additions, along with new exercises and proof techniques, will provide readers with a strong and relevant command of mathematics. Presents a concise presentation of the material Covers logic, sets and moves to more advanced topics including topology Provides greater coverage of number theory and cryptography Streamlined to focus on the core of this course

The Elements of Advanced Mathematics

1995-03-01
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Release : 1995-03-01
Genre :
Kind : eBook
Book Rating : 943/5 ( reviews)

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Book Synopsis The Elements of Advanced Mathematics by : Steven George Krantz

Download or read book The Elements of Advanced Mathematics written by Steven George Krantz. This book was released on 1995-03-01. Available in PDF, EPUB and Kindle. Book excerpt: Clearly written & easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, & axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, & proofs. This text clearly identifies & explains the components & methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material.

Mathematical Proofs

2013 Proof theory
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Release : 2013
Genre : Proof theory
Kind : eBook
Book Rating : 094/5 ( reviews)

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Book Synopsis Mathematical Proofs by : Gary Chartrand

Download or read book Mathematical Proofs written by Gary Chartrand. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.

The Elements of Advanced Mathematics

2022-06-20 Mathematics
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Release : 2022-06-20
Genre : Mathematics
Kind : eBook
Book Rating : 312/5 ( reviews)

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Book Synopsis The Elements of Advanced Mathematics by : Steven G. Krantz

Download or read book The Elements of Advanced Mathematics written by Steven G. Krantz. This book was released on 2022-06-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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