Elements of Advanced Mathematics, Third Edition

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Author :
Publisher : CRC Press
ISBN 13 : 1439898340
Total Pages : 368 pages
Book Rating : 4.4/5 (398 download)

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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 and published by CRC Press. This book was released on 2012-03-19 with total page 368 pages. 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

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Author :
Publisher : CRC Press
ISBN 13 : 1351378317
Total Pages : 390 pages
Book Rating : 4.3/5 (513 download)

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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 and published by CRC Press. This book was released on 2017-11-02 with total page 390 pages. 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

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Author :
Publisher : CRC Press
ISBN 13 : 9780849384943
Total Pages : 81 pages
Book Rating : 4.3/5 (849 download)

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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 and published by CRC Press. This book was released on 1995-03-01 with total page 81 pages. 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

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Author :
Publisher : Pearson Educacion
ISBN 13 : 9780321782519
Total Pages : 400 pages
Book Rating : 4.7/5 (825 download)

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Book Synopsis Mathematical Proofs by : Gary Chartrand

Download or read book Mathematical Proofs written by Gary Chartrand and published by Pearson Educacion. This book was released on 2013 with total page 400 pages. 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, Second Edition

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Author :
Publisher : CRC Press
ISBN 13 : 9781584883036
Total Pages : 240 pages
Book Rating : 4.8/5 (83 download)

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

Download or read book The Elements of Advanced Mathematics, Second Edition written by Steven G. Krantz and published by CRC Press. This book was released on 2002-01-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author :
Publisher : CRC Press
ISBN 13 : 1000593282
Total Pages : 312 pages
Book Rating : 4.0/5 (5 download)

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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 and published by CRC Press. This book was released on 2022-06-20 with total page 312 pages. 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.

Advanced Mathematics

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119563534
Total Pages : 556 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Advanced Mathematics by : Stanley J. Farlow

Download or read book Advanced Mathematics written by Stanley J. Farlow and published by John Wiley & Sons. This book was released on 2019-10-02 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.

Mathematical Proofs: A Transition to Advanced Mathematics

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Author :
Publisher : Pearson Higher Ed
ISBN 13 : 1292052341
Total Pages : 422 pages
Book Rating : 4.2/5 (92 download)

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Book Synopsis Mathematical Proofs: A Transition to Advanced Mathematics by : Gary Chartrand

Download or read book Mathematical Proofs: A Transition to Advanced Mathematics written by Gary Chartrand and published by Pearson Higher Ed. This book was released on 2013-10-03 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book 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. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

A Transition to Advanced Mathematics

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Author :
Publisher : Cengage Learning
ISBN 13 : 9780495562023
Total Pages : 416 pages
Book Rating : 4.5/5 (62 download)

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Book Synopsis A Transition to Advanced Mathematics by : Douglas Smith

Download or read book A Transition to Advanced Mathematics written by Douglas Smith and published by Cengage Learning. This book was released on 2010-06-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Fundamentals of Advanced Mathematics V3

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Publisher : Elsevier
ISBN 13 : 0081023863
Total Pages : 424 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics V3 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics V3 written by Henri Bourles and published by Elsevier. This book was released on 2019-10-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems. Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems Provides theory as well as practical information

Book of Proof

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Publisher :
ISBN 13 : 9780989472111
Total Pages : 314 pages
Book Rating : 4.4/5 (721 download)

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Book Synopsis Book of Proof by : Richard H. Hammack

Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Elements of Mathematics

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Publisher : Princeton University Press
ISBN 13 : 0691178542
Total Pages : 440 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Elements of Mathematics by : John Stillwell

Download or read book Elements of Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2017-11-07 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting look at the world of elementary mathematics Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

Elements of Abstract Algebra

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Publisher : Courier Corporation
ISBN 13 : 0486140350
Total Pages : 224 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Elements of Abstract Algebra by : Allan Clark

Download or read book Elements of Abstract Algebra written by Allan Clark and published by Courier Corporation. This book was released on 2012-07-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

A Transition to Proof

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Author :
Publisher : CRC Press
ISBN 13 : 0429535473
Total Pages : 323 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis A Transition to Proof by : Neil R. Nicholson

Download or read book A Transition to Proof written by Neil R. Nicholson and published by CRC Press. This book was released on 2019-03-21 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

Advanced Calculus

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Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

The Mathematical Theory of Finite Element Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 1475736584
Total Pages : 369 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Mathematical Theory of Finite Element Methods by : Susanne Brenner

Download or read book The Mathematical Theory of Finite Element Methods written by Susanne Brenner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

The Elements of Advanced Mathematics

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Publisher :
ISBN 13 : 9781315275796
Total Pages : 214 pages
Book Rating : 4.2/5 (757 download)

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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 and published by . This book was released on 2002 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: