Elements of Advanced Mathematics, Third Edition - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Advanced Mathematics, Third Edition write by Steven G. Krantz. This book was released on 2012-03-19. Elements of Advanced Mathematics, Third Edition available in PDF, EPUB and Kindle. 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
The Elements of Advanced Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Elements of Advanced Mathematics write by Steven G. Krantz. This book was released on 2017-11-02. The Elements of Advanced Mathematics available in PDF, EPUB and Kindle. 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
The Elements of Advanced Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Elements of Advanced Mathematics write by Steven George Krantz. This book was released on 1995-03-01. The Elements of Advanced Mathematics available in PDF, EPUB and Kindle. 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.
The Elements of Advanced Mathematics, Second Edition
The Elements of Advanced Mathematics, Second Edition - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Elements of Advanced Mathematics, Second Edition write by Steven G. Krantz. This book was released on 2002-01-18. The Elements of Advanced Mathematics, Second Edition available in PDF, EPUB and Kindle. 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 set Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection Streamlined treatment of non-Euclidean geometry Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations More thorough treatment of the Axiom of Choice and its equivalents Additional material on Russell's paradox and related ideas Expanded treatment of group theory that helps students grasp the axiomatic method A wealth of added exercises
The Elements of Advanced Mathematics
The Elements of Advanced Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Elements of Advanced Mathematics write by Steven G. Krantz. This book was released on 2022-06-20. The Elements of Advanced Mathematics available in PDF, EPUB and Kindle. 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.
