The Resource Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin
Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin
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The item Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithmbased courses such as calculus, to theorem and proofbased courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the CantorSchröderBernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online. From the reviews of the First Edition: "The book ... emphasizes Pòlya's fourpart framework for problem solving (from his book How to Solve It) ... [it] contains more than enough material for a onesemester course, and is designed to give the instructor wide leeway in choosing topics to emphasize ... This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions ... I was charmed by this book and found it quite enticing."Marcia G. Fung for MAA Reviews " ... A book worthy of serious consideration for courses whose goal is to prepare students for upperdivision mathematics courses. Summing Up: Highly recommended."J.R. Burke, Gonzaga University for CHOICE Reviews
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (xiii, 376 pages).
 Contents

 ""Reading, Writing, and Proving""; ""Preface""; ""Contents""; ""Chapter 1: The How, When, and Why of Mathematics""; ""Solutions to Exercises""; ""Spotlight: George PÃ3lya""; ""Problems""; ""Tips on Doing Homework""; ""Chapter 2: Logically Speaking""; ""Solutions to Exercises""; ""Problems""; ""Chapter 3: Introducing the Contrapositive and Converse""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 4: Set Notation and Quantifiers""; ""Solutions to Exercises""; ""Problems""; ""Tips on Quantification""; ""Chapter 5: Proof Techniques""; ""Definitions""; ""Problems""
 ""Tips on Definitions""""Chapter 6: Sets""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Paradoxes""; ""Problems""; ""Chapter 7: Operations on Sets""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 8: More on Operations on Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 9: The Power Set and the Cartesian Product""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Writing Mathematics""; ""Chapter 10: Relations""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Reading Mathematics""
 ""Chapter 11: Partitions""""Definition""; ""Solutions to Exercises""; ""Problems""; ""Tips on Putting It All Together""; ""Chapter 12: Order in the Reals""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 13: Consequences of the Completeness of R""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips: You Solved It. Now What?""; ""Chapter 14: Functions, Domain, and Range""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Definition of Function""; ""Problems""; ""Chapter 15: Functions, OnetoOne, and Onto""; ""Definitions""
 ""Solutions to Exercises""""Problems""; ""Chapter 16: Inverses""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 17: Images and Inverse Images""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Minimum or Infimum?""; ""Problems""; ""Chapter 18: Mathematical Induction""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 19: Sequences""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 20: Convergence of Sequences of Real Numbers""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 21: Equivalent Sets""
 ""Definitions""""Solutions to Exercises""; ""Problems""; ""Chapter 22: Finite Sets and an Infinite Set""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 23: Countable and Uncountable Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 24: The Cantorâ€?SchrÃœderâ€?Bernstein Theorem""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Continuum Hypothesis""; ""Problems""; ""Chapter 25: Metric Spaces""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 26: Getting to Know Open and Closed Sets""; ""Definitions""
 Isbn
 9781441994790
 Label
 Reading, writing, and proving : a closer look at mathematics
 Title
 Reading, writing, and proving
 Title remainder
 a closer look at mathematics
 Statement of responsibility
 Ulrich Daepp, Pamela Gorkin
 Subject

 Mathematics  Study and teaching (Higher)
 Mathematics  Study and teaching (Higher)  United States
 Technical writing  Study and teaching (Higher)
 Technical writing  Study and teaching (Higher)
 Technical writing  Study and teaching (Higher)  United States
 United States
 United States
 Mathematics  Study and teaching (Higher)
 Language
 eng
 Summary
 Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithmbased courses such as calculus, to theorem and proofbased courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the CantorSchröderBernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online. From the reviews of the First Edition: "The book ... emphasizes Pòlya's fourpart framework for problem solving (from his book How to Solve It) ... [it] contains more than enough material for a onesemester course, and is designed to give the instructor wide leeway in choosing topics to emphasize ... This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions ... I was charmed by this book and found it quite enticing."Marcia G. Fung for MAA Reviews " ... A book worthy of serious consideration for courses whose goal is to prepare students for upperdivision mathematics courses. Summing Up: Highly recommended."J.R. Burke, Gonzaga University for CHOICE Reviews
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Daepp, Ulrich
 Dewey number
 371.3
 Index
 index present
 Language note
 English
 LC call number
 QA13
 LC item number
 .D34 2011
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Gorkin, Pamela
 Series statement
 Undergraduate texts in mathematics
 http://library.link/vocab/subjectName

 Mathematics
 Technical writing
 Mathematics
 Technical writing
 United States
 Label
 Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 ""Reading, Writing, and Proving""; ""Preface""; ""Contents""; ""Chapter 1: The How, When, and Why of Mathematics""; ""Solutions to Exercises""; ""Spotlight: George PÃ3lya""; ""Problems""; ""Tips on Doing Homework""; ""Chapter 2: Logically Speaking""; ""Solutions to Exercises""; ""Problems""; ""Chapter 3: Introducing the Contrapositive and Converse""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 4: Set Notation and Quantifiers""; ""Solutions to Exercises""; ""Problems""; ""Tips on Quantification""; ""Chapter 5: Proof Techniques""; ""Definitions""; ""Problems""
 ""Tips on Definitions""""Chapter 6: Sets""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Paradoxes""; ""Problems""; ""Chapter 7: Operations on Sets""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 8: More on Operations on Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 9: The Power Set and the Cartesian Product""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Writing Mathematics""; ""Chapter 10: Relations""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Reading Mathematics""
 ""Chapter 11: Partitions""""Definition""; ""Solutions to Exercises""; ""Problems""; ""Tips on Putting It All Together""; ""Chapter 12: Order in the Reals""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 13: Consequences of the Completeness of R""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips: You Solved It. Now What?""; ""Chapter 14: Functions, Domain, and Range""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Definition of Function""; ""Problems""; ""Chapter 15: Functions, OnetoOne, and Onto""; ""Definitions""
 ""Solutions to Exercises""""Problems""; ""Chapter 16: Inverses""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 17: Images and Inverse Images""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Minimum or Infimum?""; ""Problems""; ""Chapter 18: Mathematical Induction""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 19: Sequences""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 20: Convergence of Sequences of Real Numbers""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 21: Equivalent Sets""
 ""Definitions""""Solutions to Exercises""; ""Problems""; ""Chapter 22: Finite Sets and an Infinite Set""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 23: Countable and Uncountable Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 24: The Cantorâ€?SchrÃœderâ€?Bernstein Theorem""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Continuum Hypothesis""; ""Problems""; ""Chapter 25: Metric Spaces""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 26: Getting to Know Open and Closed Sets""; ""Definitions""
 Control code
 745005676
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xiii, 376 pages).
 Form of item
 online
 Isbn
 9781441994790
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781441994790
 http://library.link/vocab/ext/overdrive/overdriveId
 9781441994783
 Specific material designation
 remote
 System control number
 (OCoLC)745005676
 Label
 Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 ""Reading, Writing, and Proving""; ""Preface""; ""Contents""; ""Chapter 1: The How, When, and Why of Mathematics""; ""Solutions to Exercises""; ""Spotlight: George PÃ3lya""; ""Problems""; ""Tips on Doing Homework""; ""Chapter 2: Logically Speaking""; ""Solutions to Exercises""; ""Problems""; ""Chapter 3: Introducing the Contrapositive and Converse""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 4: Set Notation and Quantifiers""; ""Solutions to Exercises""; ""Problems""; ""Tips on Quantification""; ""Chapter 5: Proof Techniques""; ""Definitions""; ""Problems""
 ""Tips on Definitions""""Chapter 6: Sets""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Paradoxes""; ""Problems""; ""Chapter 7: Operations on Sets""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 8: More on Operations on Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 9: The Power Set and the Cartesian Product""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Writing Mathematics""; ""Chapter 10: Relations""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips on Reading Mathematics""
 ""Chapter 11: Partitions""""Definition""; ""Solutions to Exercises""; ""Problems""; ""Tips on Putting It All Together""; ""Chapter 12: Order in the Reals""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 13: Consequences of the Completeness of R""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Tips: You Solved It. Now What?""; ""Chapter 14: Functions, Domain, and Range""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Definition of Function""; ""Problems""; ""Chapter 15: Functions, OnetoOne, and Onto""; ""Definitions""
 ""Solutions to Exercises""""Problems""; ""Chapter 16: Inverses""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 17: Images and Inverse Images""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: Minimum or Infimum?""; ""Problems""; ""Chapter 18: Mathematical Induction""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 19: Sequences""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 20: Convergence of Sequences of Real Numbers""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 21: Equivalent Sets""
 ""Definitions""""Solutions to Exercises""; ""Problems""; ""Chapter 22: Finite Sets and an Infinite Set""; ""Definition""; ""Solutions to Exercises""; ""Problems""; ""Chapter 23: Countable and Uncountable Sets""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 24: The Cantorâ€?SchrÃœderâ€?Bernstein Theorem""; ""Definitions""; ""Solutions to Exercises""; ""Spotlight: The Continuum Hypothesis""; ""Problems""; ""Chapter 25: Metric Spaces""; ""Definitions""; ""Solutions to Exercises""; ""Problems""; ""Chapter 26: Getting to Know Open and Closed Sets""; ""Definitions""
 Control code
 745005676
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xiii, 376 pages).
 Form of item
 online
 Isbn
 9781441994790
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781441994790
 http://library.link/vocab/ext/overdrive/overdriveId
 9781441994783
 Specific material designation
 remote
 System control number
 (OCoLC)745005676
Subject
 Mathematics  Study and teaching (Higher)
 Mathematics  Study and teaching (Higher)  United States
 Technical writing  Study and teaching (Higher)
 Technical writing  Study and teaching (Higher)
 Technical writing  Study and teaching (Higher)  United States
 United States
 United States
 Mathematics  Study and teaching (Higher)
Member of
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