A Transition to Advanced Mathematics – D. Smith, M. Eggen, R. Andre – 5th Edition

Description

A TRANSITION TO ADVANCED helps make the transition from to more proofs-oriented mathematical study. The most successful of its kind, the 5th edition continues to provide a firm foundation in major concepts needed for continued study and guides users to think and express themselves mathematicallyato analyze a situation, extract pertinent facts, and draw appropriate conclusions.

The authors place continuous emphasis throughout on improving users’ ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough on both routine and more challenging .

Students will come away with a solid intuition for the types of mathematical reasoning they’ll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

Table of Contents

1. Logic and Proofs.
2. Set Theory.
3. Relations.
4. Functions.
5. Cardinality.
6. Concepts of Algebra: Groups.
7. Concepts of Analysis: Completeness of the Real Numbers.
Answers to Exercises.
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