# An Introduction To Proof Through Real Analysis

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An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement

An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J

Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.

Daniel J

Dr

He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990

Jason A

Madden and was designed to function as a complete text for both first proofs and first analysis courses

Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award

Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA

Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics

The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers

The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own

The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems

Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity

Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction Uses a particular mathematical idea as the focus of each type of proof presented Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis