Mathematics

For one-semester courses in Transition to Advanced Mathematics that emphasize the construction and writing of mathematical proofs. 

Focusing on the formal development of mathematics, this text teaches students how to read and understand mathematical proofs and to construct and write mathematical proofs.  Developed as a text for a writing course requirement, issues dealing with writing are addressed directly and practices of good writing are emphasized throughout the text.  Active learning is emphasized with preview activities for each section and activities in each section that enable both teachers and students to test understanding and explore ideas in a traditional or non-lecture setting.  Elementary number theory and congruence arithmetic are used throughout.

• Strong focus on reading and writing proofs in mathematics — Incorporates guidelines for writing mathematical proofs. Issues dealing with writing are addressed directly and practices of good writing are emphasized throughout the text.

• Instruction in the process of constructing proofs — Uses a "know-Show table" that teaches students to work backward from what it is they are trying to prove while at the same time working forward from the assumptions of the problem.

• Thorough discussion of several important proof techniques including direct proof, proof of the contrapositive, proof by contradiction, proof using cases, and mathematical induction.

• Emphasis on active learning — helps students become actively involved in their own learning process by

        * Including two or three preview activities at beginning of each section that review prior mathematical work and introduce new concepts and definitions that will be studied in the section.

        * Incorporating severel "progress checks" in each section, which are short exercises or activities designed to help students determine if they are understanding the material as it is

            presented.

        * Including activities at the end of each section. These activities can be done individually or in a collaborative learning setting.

• Emphasis on mathematical content that will be important in many upper level mathematics courses including elementary number theory, congruence arithmetic, set theory, recursion, functions, relations, and equivalence relations.

• Several Progress Checks now appear throughout each section of this edition.  They are exercises or activities designed to check student understanding of important concepts.
• Additional exercises have been added to provide greater variety for students.
• Select sections include Evaluation of Proofs, which are exercises designed to show students how to prove and successfully write proofs. 
• A chapter summary now follows each chapter to help students prepare for exams.
• More answers to exercises are now provided in an appendix of this edition.

1. Introduction to Writing in Mathematics.

2. Logical Reasoning.

3. Constructing & Writing Proofs in Mathematics.

4. Set Theory.

5. Mathematical Induction.

6. Functions.

7. Equivalence Relations.

8. Topics in Number Theory.

9. Finite and Infinite Sets

Appendix: Guidelines for Writing Mathematical Proofs.

instructors Solutions for IRC download only, 2/E
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©2007 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0131877194 | ISBN-13: 9780131877191
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