Introduction To Advanced Mathematics A Guide To Understanding Proofs
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Introduction To Advanced Mathematics A Guide To Understanding Proofs
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Author : Connie M. Campbell
language : en
Publisher: Cengage Learning
Release Date : 2011-01-01
Introduction To Advanced Mathematics A Guide To Understanding Proofs written by Connie M. Campbell and has been published by Cengage Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
This text offers a crucial primer on proofs and the language of mathematics. Brief and to the point, it lays out the fundamental ideas of abstract mathematics and proof techniques that students will need to master for other math courses. Campbell presents these concepts in plain English, with a focus on basic terminology and a conversational tone that draws natural parallels between the language of mathematics and the language students communicate in every day. The discussion highlights how symbols and expressions are the building blocks of statements and arguments, the meanings they convey, and why they are meaningful to mathematicians. In-class activities provide opportunities to practice mathematical reasoning in a live setting, and an ample number of homework exercises are included for self-study. This text is appropriate for a course in Foundations of Advanced Mathematics taken by students who've had a semester of calculus, and is designed to be accessible to students with a wide range of mathematical proficiency. It can also be used as a self-study reference, or as a supplement in other math courses where additional proofs practice is needed. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Introduction To Advanced Mathematics
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Author : William Barnier
language : en
Publisher:
Release Date : 1990-01
Introduction To Advanced Mathematics written by William Barnier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01 with Mathematics categories.
An exploration of the analytical tools of advanced math.
A Transition To Proof
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Author : Neil R. Nicholson
language : en
Publisher: CRC Press
Release Date : 2019-03-21
A Transition To Proof written by Neil R. Nicholson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Mathematics categories.
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
Introduction To Mathematical Proofs
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Author : Charles E. Roberts
language : en
Publisher:
Release Date : 2015
Introduction To Mathematical Proofs written by Charles E. Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Proofs And Ideas
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Author : B. Sethuraman
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-02
Proofs And Ideas written by B. Sethuraman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Mathematics categories.
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.
Introduction To Mathematical Proofs Second Edition
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Author : Charles Roberts
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2014-12-17
Introduction To Mathematical Proofs Second Edition written by Charles Roberts and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-17 with Mathematics categories.
Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.
Mathematical Proofs
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Author : Gary Chartrand
language : en
Publisher: Pearson
Release Date : 2013
Mathematical Proofs written by Gary Chartrand and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Proof theory categories.
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.
Mathematical Proofs
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Author : Gary Chartrand
language : en
Publisher: Pearson
Release Date : 2017-10-31
Mathematical Proofs written by Gary Chartrand and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with categories.
NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value; this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. For Books a la Carte editions that include MyLab(tm) or Mastering(tm), several versions may exist for each title -- including customized versions for individual schools -- and registrations are not transferable. In addition, you may need a Course ID, provided by your instructor, to register for and use MyLab or Mastering products. For courses in Transition to Advanced Mathematics or Introduction to Proof. Meticulously crafted, student-friendly text that helps build mathematical maturity Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity. They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs. 013484047X / 9780134840475 Chartrand/Polimeni/Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, Books a la Carte Edition, 4/e
Transition To Advanced Mathematics
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Author : Danilo R. Diedrichs
language : en
Publisher: CRC Press
Release Date : 2022-05-22
Transition To Advanced Mathematics written by Danilo R. Diedrichs and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-22 with Mathematics categories.
This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments Relations Part II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master’s degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).
Analysis With An Introduction To Proof
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Author : Steven R. Lay
language : en
Publisher: Pearson
Release Date : 2013-11-01
Analysis With An Introduction To Proof written by Steven R. Lay and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with categories.
Normal 0 false false false For courses in undergraduate Analysis and Transition to Advanced Mathematics. Analysis with an Introduction to Proof, Fifth Edition helps fill in the groundwork students need to succeed in real analysis--often considered the most difficult course in the undergraduate curriculum. By introducing logic and emphasizing the structure and nature of the arguments used, this text helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable, student-oriented, and teacher- friendly.