Reading Writing and Proving : A Closer Look at Mathematics 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. 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 Index.