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# Introduction to Mathematical Structures and Proofs

Solutions manual for even numbered exercises is available on springer.com for instructors adopting the text for a course

Discusses the multifaceted process of mathematical proof by thoughtful oscillation between what is known and what is to be demonstrated

Presents more than one proof for many results, for instance for the fact that there are infinitely many prime numbers

Shows how the processes of counting and comparing the sizes of finite sets are based in function theory, and how the ideas can be extended to infinite sets via Cantor's theorems

Contains a wide assortment of exercises, ranging from routine checks of a student's grasp of definitions through problems requiring more sophisticated mastery of fundamental ideas

Demonstrates the dual importance of intuition and rigor in the development of mathematical ideas

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Part of the Undergraduate Texts in Mathematics book series (UTM)