Proof, Sets, and Logic (M. Randall Holmes)

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Proof, Sets, and Logic (M. Randall Holmes)

This book teaches basic ideas from logic and sets theory as well as the fundamental definitions of algebra to prepare readers for future study in the field of mathematics. It also addresses the significance of creating and comprehending mathematical proofs.

The author offers a smooth, practical explanation of number systems while incorporating important concepts from set theory and logic. He also exhorts readers to follow the fundamental guideline that you are not allowed to use any results that you have not yet proven.

The book starts out by concentrating on the logical constructs found in common mathematical terminology, introducing readers to conventional proof techniques and Russell's Paradox. Following the establishment of this base, subsequent chapters explore more rigorous mathematical exposition that outlines the necessary components of Zermelo-Fraenkel set theory and constructs the natural numbers and integers in addition to the rational, real, and complex numbers in a rigorous yet understandable way.

Abstraction is introduced as a tool, and a special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas.

In the book's conclusion, the Axiom of Choice, ordinal numbers, and cardinal numbers are introduced together with a self-contained proof of Abel's Theorem and an investigation of deeper set theory.

This book is a great complement for transition courses that get students ready for the rigorous mathematical reasoning of advanced calculus, real analysis, and contemporary algebra, as well as upper-undergraduate mathematics courses on proofs, logic and set theory. Professionals in all facets of mathematics education who are curious about mathematical proofs and the basis of all mathematics will find this book to be a useful reference.

Ebook Details

About the Authors
M. Randall Holmes is a professor of mathematics at Boise State University.
Published Date / Year
eBook Format
PDF (473 pages)

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