Passage To Abstract Mathematics

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Passage to Abstract Mathematics

Author : Mark E. Watkins
Publisher : Cognella Academic Publishing
ISBN 13 : 9781793530509
Total Pages : pages
Book Rating : 4.5/5 (35 download)

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Book Synopsis Passage to Abstract Mathematics by : Mark E. Watkins

Download or read book Passage to Abstract Mathematics written by Mark E. Watkins and published by Cognella Academic Publishing. This book was released on 2020-08-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Passage to Abstract Mathematics helps students progress from a facility with computational procedures to an understanding of abstract mathematical concepts. Students develop their ability in mathematical communication through reading proofs, constructing proofs, and writing proofs in correct mathematical language. Concise, practical, and highly valuable, the text is ideal for students who have taken lower-division mathematics courses and need the tools requisite to study more advanced, abstract mathematics. The text features material that instructors of upper-level courses in set theory, analysis, topology, and modern algebra presume students have already learned by the time they enter advanced courses. It places emphasis on complete and correct definitions, as well as expressing mathematics in correct syntax. The core material consists of the first five closely knit chapters: Logic, Numbers, Sets, Functions, and Induction. To support active and continuous learning, exercises are embedded within the text material immediately following a definition or theorem. The explanatory comments, hints to solutions, and thought-provoking questions that appear within brackets throughout the text all serve to deepen the student's understanding of the material. In the second edition, the chapter entitled Functions precedes the chapter entitled Induction, and select material has been clarified or corrected. Number theoretic digressions such as Euclid's Algorithm and the Chinese Remainder Theorem have been deleted.

Studyguide for Passage to Abstract Mathematics by Watkins, Mark E.

Author : Cram101 Textbook Reviews
Publisher : Cram101
ISBN 13 : 9781478482178
Total Pages : 114 pages
Book Rating : 4.4/5 (821 download)

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Book Synopsis Studyguide for Passage to Abstract Mathematics by Watkins, Mark E. by : Cram101 Textbook Reviews

Download or read book Studyguide for Passage to Abstract Mathematics by Watkins, Mark E. written by Cram101 Textbook Reviews and published by Cram101. This book was released on 2013-05 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Never HIGHLIGHT a Book Again Virtually all testable terms, concepts, persons, places, and events are included. Cram101 Textbook Outlines gives all of the outlines, highlights, notes for your textbook with optional online practice tests. Only Cram101 Outlines are Textbook Specific. Cram101 is NOT the Textbook. Accompanys: 9780521673761

Studyguide for Passage to Abstract Mathematics by Watkins, Mark E., ISBN 9780321738639

Author : Cram101 Textbook Reviews
Publisher : Cram101
ISBN 13 : 9781618300911
Total Pages : 152 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Studyguide for Passage to Abstract Mathematics by Watkins, Mark E., ISBN 9780321738639 by : Cram101 Textbook Reviews

Download or read book Studyguide for Passage to Abstract Mathematics by Watkins, Mark E., ISBN 9780321738639 written by Cram101 Textbook Reviews and published by Cram101. This book was released on 2012-08 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Never HIGHLIGHT a Book Again! Virtually all of the testable terms, concepts, persons, places, and events from the textbook are included. Cram101 Just the FACTS101 studyguides give all of the outlines, highlights, notes, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanys: 9780321738639 .

Proofs and Fundamentals

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
ISBN 13 : 1461221307
Total Pages : 434 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Proofs and Fundamentals by : Ethan D. Bloch

Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Bridge to Abstract Mathematics

Author : Ronald P. Morash
Publisher :
ISBN 13 :
Total Pages : 426 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Bridge to Abstract Mathematics by : Ronald P. Morash

Download or read book Bridge to Abstract Mathematics written by Ronald P. Morash and published by . This book was released on 1991 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content.

An Invitation to Abstract Mathematics

Author : Béla Bajnok
Publisher : Springer Nature
ISBN 13 : 3030561747
Total Pages : 443 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok

Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

Introductory Concepts for Abstract Mathematics

Author : Kenneth E. Hummel
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781584882268
Total Pages : pages
Book Rating : 4.8/5 (822 download)

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Book Synopsis Introductory Concepts for Abstract Mathematics by : Kenneth E. Hummel

Download or read book Introductory Concepts for Abstract Mathematics written by Kenneth E. Hummel and published by Chapman & Hall/CRC. This book was released on 2004-11-11 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A gap has long existed between basic calculus studies and those on abstract algebra and real analysis. The focus of calculus instruction has become more and more computational, leaving students ill-prepared for more advanced, abstract work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers span the chasm between calculus and more abstract courses. It teaches them to deal effectively with abstract ideas, to comprehend the logical structure of proofs, and to write mathematics using conventional terminology in an effective, logical, and understandable way. Copyright © Libri GmbH. All rights reserved.

An Introduction to Abstract Mathematics

Author : Robert J. Bond
Publisher : Waveland Press
ISBN 13 : 1478608056
Total Pages : 344 pages
Book Rating : 4.4/5 (786 download)

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Book Synopsis An Introduction to Abstract Mathematics by : Robert J. Bond

Download or read book An Introduction to Abstract Mathematics written by Robert J. Bond and published by Waveland Press. This book was released on 2007-08-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.

The Joy of Abstraction

Author : Eugenia Cheng
Publisher : Cambridge University Press
ISBN 13 : 1108477224
Total Pages : 439 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis The Joy of Abstraction by : Eugenia Cheng

Download or read book The Joy of Abstraction written by Eugenia Cheng and published by Cambridge University Press. This book was released on 2022-10-13 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely accessible introduction to abstract mathematics and category theory written by popular science author of How to Bake Pi.

Chapter Zero

Author : Carol Schumacher
Publisher :
ISBN 13 : 9780134995403
Total Pages : pages
Book Rating : 4.9/5 (954 download)

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Book Synopsis Chapter Zero by : Carol Schumacher

Download or read book Chapter Zero written by Carol Schumacher and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Principles of Mathematics

Author : Bertrand Russell
Publisher : W. W. Norton & Company
ISBN 13 : 9780393314045
Total Pages : 580 pages
Book Rating : 4.3/5 (14 download)

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Book Synopsis The Principles of Mathematics by : Bertrand Russell

Download or read book The Principles of Mathematics written by Bertrand Russell and published by W. W. Norton & Company. This book was released on 1996 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.

A Gateway to Abstract Mathematics

Author : George Hiram Shortley
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (959 download)

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Book Synopsis A Gateway to Abstract Mathematics by : George Hiram Shortley

Download or read book A Gateway to Abstract Mathematics written by George Hiram Shortley and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Writing

Author : Donald E. Knuth
Publisher : Cambridge University Press
ISBN 13 : 9780883850633
Total Pages : 132 pages
Book Rating : 4.8/5 (56 download)

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Book Synopsis Mathematical Writing by : Donald E. Knuth

Download or read book Mathematical Writing written by Donald E. Knuth and published by Cambridge University Press. This book was released on 1989 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will help those wishing to teach a course in technical writing, or who wish to write themselves.

A Passage to Infinity

Author : George Gheverghese Joseph
Publisher : SAGE Publications Pvt. Limited
ISBN 13 : 9788132101680
Total Pages : 0 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis A Passage to Infinity by : George Gheverghese Joseph

Download or read book A Passage to Infinity written by George Gheverghese Joseph and published by SAGE Publications Pvt. Limited. This book was released on 2009-12-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book traces the first faltering steps taken in the mathematical theorization of infinity which marks the emergence of modern mathematics. It analyzes the part played by Indian mathematics through the Kerala conduit, which is an important but neglected part of the history of mathematics.

Sets for Mathematics

Author : F. William Lawvere
Publisher : Cambridge University Press
ISBN 13 : 9780521010603
Total Pages : 280 pages
Book Rating : 4.0/5 (16 download)

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Book Synopsis Sets for Mathematics by : F. William Lawvere

Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

A Transition to Abstract Mathematics

Author : Randall Maddox
Publisher : Academic Press
ISBN 13 : 0080922716
Total Pages : 379 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis A Transition to Abstract Mathematics by : Randall Maddox

Download or read book A Transition to Abstract Mathematics written by Randall Maddox and published by Academic Press. This book was released on 2008-10-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. A Transition to Abstract Mathematics teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point.Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction Explains identification of techniques and how they are applied in the specific problem Illustrates how to read written proofs with many step by step examples Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter

Proofs and Ideas

Author : B. Sethuraman
Publisher : American Mathematical Society
ISBN 13 : 1470465140
Total Pages : 334 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Proofs and Ideas by : B. Sethuraman

Download or read book Proofs and Ideas written by B. Sethuraman and published by American Mathematical Society. This book was released on 2021-12-02 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts. The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine. This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.