Elementary Real Analysis

Written by Thomas Bieske, Elementary Real Analysis: A Practical Introduction, 1st Edition is a 2025 academic textbook designed to guide students through key analytical concepts. Published by Academic Press, this volume establishes the rigorous foundations required for advanced mathematical reasoning and upper-level coursework.

The material opens with essential background topics, examining sets alongside the algebraic and order properties of real numbers and properties of integers. Moving forward, the text develops core elementary topics, delivering structured coverage of mathematical functions, relations, sequences, and functional continuity across consecutive chapters.

To assist independent practice, each chapter includes a variety of exercises designed to reinforce core concepts and support self-directed study. Beyond core undergraduate requirements, the text provides structured preparation for early graduate-level mathematics students who require deeper foundational insights into real analysis.