An Introduction to Mathematical Proofs

1st Edition

Nicholas A. Loehr

CRC Press
October 28, 2019 Forthcoming
Textbook - 416 Pages - 67 B/W Illustrations
ISBN 9780367338237 - CAT# 318961
Series: Textbooks in Mathematics

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Summary

This book contains an introduction to mathematical proofs. The topics appearing in Parts I through VII constitute the standard core material in proofs course. Part VIII develops properties of the real numbers from the ordered field axioms. The book maintains a targeted focus on helping students master key skills needed for later work, as opposed to giving a dry treatment of logic and set theory. A friendly conversational style couples with the necessary level of precision and rigor. The lecture format facilitates a continual cycle of examples, summaries, and review of previous material. Every lecture ends with an immediate review of the main points just covered. Three review lectures give detailed summaries. The essential core material is supplemented by more advanced topics in optional sections. Heavy emphasis is placed on proof templates, creating proof outlines for complex statements based on the logical structure. Many sample proofs are accompanied by annotations. Our coverage of induction is more extensive than some other texts. A careful distinction between the graph of a function and the function itself is made.

Key Features:

  • Arranged by fifty one-hour lectures. The lecture format facilitates a continual cycle of examples, summaries, and
    review of previous material.
  • Parts I and VII cover all the essential topics for a Transition to Advanced Mathematics course.
  • Part VIII offers advanced topics typcially found in an Advanced Calculus course.
  • Heavy emphasis is placed on proof templates, which create proof outlines for complex statements.
  • Induction is covered more than in other texts.

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