An Invitation to Real Analysis

Adopting a student-centered approach, this book anticipates and addresses the common challenges that students face when learning abstract concepts like limits, continuity, and inequalities. The text introduces these concepts gradually, giving students a clear pathway to understanding the mathematical tools that underpin much of modern science and technology. In addition to its focus on accessibility, the book maintains a strong emphasis on mathematical rigor. It provides precise, careful definitions and explanations while avoiding common teaching pitfalls, ensuring that students gain a deep understanding of core concepts, and blending algebraic and geometric perspectives to help students see the full picture. The theoretical results presented in the book are consistently applied to practical problems. By providing a clear and supportive introduction to real analysis, the book equips students with the tools they need to confidently engage with both theoretical mathematics and its wide array of practical applications.

Features

• Student-Friendly Approach making abstract concepts relatable and engaging
• Balanced Focus combining algebraic and geometric perspectives
• Comprehensive Coverage: Covers a full range of topics, from real numbers and sequences to metric spaces and approximation theorems, while carefully building upon foundational concepts in a logical progression
• Emphasis on Clarity: Provides precise explanations of key mathematical definitions and theorems, avoiding common pitfalls in traditional teaching
• Perfect for a One-Semester Course: Tailored for a first course in real analysis
• Problems, exercises and solutions

Andrew D. Hwang earned his PhD in mathematics at the University of California, Berkeley. After a 30-year career as a mathematician in academia, he now pursues mathematical art, design, education, and outreach through his company, Differential Geometry (diffgeom.com).