A Gateway to Higher Mathematics
This textbook prepares students for the mathematical concepts they will encounter at the higher levels of the undergraduate math curriculum. Students will learn how to interpret and construct the proofs necessary to advance to courses such as abstract algebra, number theory, real analysis, and complex analysis.
Key Features:
- Applies methods of proof carefully to theorems.
- Numerous exercises are provided at the end of each section.
- Significant coverage of the role of the real number system in effective proof writing.
- Instructiors can select the topics to fit their course requirements.
Chapter 1 Logic and Techniques for Proofs
Chapter 2 Elementary Set Theory
Chapter 3 The Development of the Integers
Chapter 4 Properties and Application of Integers
Chapter 5 Fields and the Rational Numbers
Chapter 6 The Development of the Real Numbers
Chapter 7 Some Additional Properties of Real Numbers