00000cmm a22000004a 4500 UP-99796217611212510 Buklod 20241007114355.0 m go j cr |n |||auu|a 241007s2011 xxu o j | eng d 9781441994790 (eBook) 1441994793 (eBook) (iLib)UPD-00215704299 DLC eng DMLR rda eng DMLUC QA 13 D34 2011eb Daepp, Ulrich author. Reading, writing, and proving a closer look at mathematics [electronic resource] by Ulrich Daepp, Pamela Gorkin. New York, NY Springer New York 2011. 1 online resource text rdacontent computer rdamedia online resource rdacarrier Undergraduate texts in mathematics 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-Schröder-Bernstein Theorem -- 25. Metric Spaces -- 26. Getting to Know Open and Closed Sets -- 27. Modular Arithmetic -- 28. Fermat?s Little Theorem -- 29. Projects -- Appendix -- References -- Inde IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Websit 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 ava Mathematics Study and teaching (Higher) Technical writing Study and teaching (Higher) Gorkin, Pamela editor. Available for UP System via Springer Link. https://link.springer.com/book/10.1007/978-1-4419-9479-0 FO UPD DMLR QA 13 D34 2011eb Electronic Resource