Coverart for item
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

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
Creator
Contributor
Subject
Language
eng
Summary
Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based 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 Cantor-Schröder-Bernstein 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 four-part framework for problem solving (from his book How to Solve It) ... [it] contains more than enough material for a one-semester 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 upper-division mathematics courses. Summing Up: Highly recommended."--J.R. Burke, Gonzaga University for CHOICE Reviews
Member of
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
Instantiates
Publication
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, One-to-One, 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
10.1007/978-1-4419-9479-0
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4419-9478-3
Specific material designation
remote
System control number
(OCoLC)745005676
Label
Reading, writing, and proving : a closer look at mathematics, Ulrich Daepp, Pamela Gorkin
Publication
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, One-to-One, 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
10.1007/978-1-4419-9479-0
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4419-9478-3
Specific material designation
remote
System control number
(OCoLC)745005676

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      38.944491 -92.326012
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