Mathematics

For one-semester courses in Transition to Advanced Mathematics and Proofs. For undergraduates beginning mathematics courses after calculus.

Focusing on the formal development of mathematics, this text teaches students how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. This text assumes students have taken one semester of calculus.

• Strong focus on writing in mathematics—Incorporates guidelines for writing mathematical proofs.

  • Provides students with examples of well-written proofs, and ensures that each proof presented is written according to the guidelines introduced in Ch. 1.

• 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.

  • Helps students organize their thoughts so that they can write a proof in a coherent manner that conveys an understanding of the proof to the reader.

• Section-beginning Preview Activities —Reviews prior mathematical work; and introduces new concepts and definitions that will be used when that section is discussed in class.

  • Prepares students to participate in the classroom discussion of material. Enables instructors to assign explorations prior to class so that students are ready for new material.

• Activities throughout—Relates to the material contained in each section.

  • Enables both students and instructors to test understanding and explore ideas in a non-lecture setting in the classroom. May also be used as exercises.

• Focus on Congruence Notation and Elementary Number Theory— Introduces modular arithmetic early and uses it consistently throughout as a way to demonstrate ideas in direct proof, proof by contrapositive, proof by contradiction, proof by cases, and even mathematical induction.

  • Gives students a strong knowledge base of an important mathematical idea, while providing instructors with a consistent reference point and examples of how mathematical notation can greatly simplify a concept.

• Accessible writing on many topics—Requires only prior experience in Calculus I.

  • Teaches students a great deal about mathematical reasoning, while adding important mathematical content.

1. Introduction to Writing in Mathematics.


2. Logical Reasoning.


3. Constructing and Writing Proofs in Mathematics.


4. Set Theory.


5. Mathematical Induction.


6. Functions.


7. Equivalence Relations.


8. Topics in Number Theory.


9. Topics in Set Theory.


A: Guidelines for Writing Mathematical Proofs.


B: Answers and Hints for Selected Exercises.


C: List of Symbols.

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  Mathematical Reasoning Writing and Proof, 2/E
  Sundstrom
  ©2007 | Prentice Hall | Cloth; 544 pp | Instock
  ISBN-10: 0131877186 | ISBN-13: 9780131877184
  Brief Description | Buy from myPearsonStore

  

  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.

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ISBN-10: 013238485X | ISBN-13: 9780132384858
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