Reading, Writing, and Proving [electronic resource] : A Closer Look at Mathematics / by Ulrich Daepp, Pamela Gorkin.

-Preface.-1. The How, When, and Why of Mathematics -- 2. Logically Speaking -- 3.Introducing the Contrapositive and Converse -- 4. Set Notation and Quantifiers -- 5. Proof Techniques -- 6. Sets -- 7. Operations on Sets -- 8. More on Operations on Sets -- 9. The Power Set and the Cartesian Product -- 10. Relations -- 11. Partitions -- 12. Order in the Reals -- 13. Consequences of the Completeness of (\Bbb R) -- 14. Functions, Domain, and Range.-15. Functions, One-to-One, and Onto -- 16. Inverses -- 17. Images and Inverse Images -- 18. Mathematical Induction -- 19. Sequences -- 20. Convergence of Sequences of Real Numbers -- 21. Equivalent Sets -- 22. Finite Sets and an Infinite Set -- 23. Countable and Uncountable Sets -- 24. The Cantor-Schrȵder-Bernstein Theorem -- 25. Metric Spaces -- 26. Getting to Know Open and Closed Sets -- 27. Modular Arithmetic -- 28. Fermats Little Theorem -- 29. Projects -- Appendix -- References -- Index.

Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based coursessuch ascalculus, 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 thatare required for success in navigatingadvanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and thevarious methods of proof, this textbook prepares students forfuturecourses byprovidinga strong foundationin the fields ofnumber 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 CantorSchrȵderBernstein 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: ǣThe bookǪemphasizes Pșlyas four-part framework for problem solving (from his book How to Solve It)Ǫ[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasizeǪThis book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutionsǪI was charmed by this book and found it quite enticing.ǥ Marcia G. Fung forMAA Reviews ǣǪ A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended.ǥ J. R. Burke, Gonzaga University for CHOICE Reviews

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