An accessible and engaging introduction to mathematical proof integrating ideas from a real study
A mathematical proof is an inferential argument for a mathematical statement. Since the time of the earliest Greek mathematicians, the proof has been a keystone of the science of mathematics. The purpose of this ebook is to help college students learn to understand and follow the structure and function of mathematical proof and to deliver proofs of their own.
An Introduction to Proof through Real Analysis, (PDF) is based on course material developed and improved over thirty years by Professor Daniel J. Madden and was designed to serve as a complete text for both first analysis and first proofs courses. Authored in an accessible and engaging narrative style, this ebook systematically includes the basic techniques of proof writing, beginning with real numbers and transitioning to logic, topology, set theory and continuity. The ebook proceeds from natural numbers to rational numbers in an acquainted way and justifies the need for an exact definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which validates the notion that the real numbers are adequate for solving all geometric problems.
- Uses a particular mathematical idea as the stress of each type of proof presented
- Written in an appealing narrative style to tell the story of proof and its meaning, function, and construction
- Proceeds from traditional guides to proofs by including elements of both real analysis and algebraic representation
- Developed from information that has been class-tested and fine-tuned over thirty years in university introductory courses
- Focuses solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects
This ebook is the perfect introductory textbook to proofs for second and third-year undergraduate mathematics students, particularly students learning real analysis for the first time, those who have completed a calculus sequence, and those learning proofs for the first time.
NOTE: The product only includes the ebook An Introduction to Proof through Real Analysis, in PDF. No access codes are included.