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" Reading, writing, and proving : "
Ulrich Daepp, Pamela Gorkin.
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BL
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| Record Number
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809583
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b623599
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| Main Entry
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Daepp, Ulrich.
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| Title & Author
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Reading, writing, and proving : : a closer look at mathematics /\ Ulrich Daepp, Pamela Gorkin.
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| Edition Statement
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2nd ed.
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| Publication Statement
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New York :: Springer,, ©2011.
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| Series Statement
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Undergraduate texts in mathematics
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| Page. NO
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1 online resource (xiii, 376 pages)
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| ISBN
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9781441994790
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: 1441994793
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: 1441994785
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: 9781441994783
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9781441994783
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Reading, Writing, and Proving -- Preface -- Contents -- Chapter 1: The How, When, and Why of Mathematics -- Solutions to Exercises -- Spotlight: George Pólya -- 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
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Tips on DefinitionsChapter 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
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Chapter 11: PartitionsDefinition -- 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
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Solutions to ExercisesProblems -- 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
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DefinitionsSolutions 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 Cantor�SchrÜder�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
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| Abstract
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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.
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| Subject
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Mathematics-- Study and teaching (Higher)-- United States.
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Technical writing-- Study and teaching (Higher)-- United States.
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Mathematics-- Study and teaching (Higher)
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Technical writing-- Study and teaching (Higher)
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United States.
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| Dewey Classification
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371.3
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| LC Classification
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QA13.D34 2011
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| Added Entry
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Gorkin, Pamela.
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