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Introduction to Mathematical Analysis I [Lafferriere] - mklabgr - 09-03-2026
Introduction to Mathematical Analysis I — Second Edition
Authors: Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen
Publication year: 2016
Publisher: Portland State University Library
ISBN: 978-1-365-60552-9
Subject: Real Analysis / Mathematical Analysis
Introduction to Mathematical Analysis I is an introductory but rigorous textbook in real analysis, designed primarily for students who have already completed the standard calculus sequence and are ready to move from computational calculus to proof-based mathematics. Its central aim is to establish the logical foundations underlying calculus and prepare students for more advanced work in analysis. The book begins with fundamental tools of analysis and the completeness of the real numbers before developing sequences and convergence, limits, continuity, and differentiation. These topics correspond roughly to a one-quarter, ten-week undergraduate course.
A major emphasis is placed on mathematical rigor and proofs. Familiar calculus ideas are reconsidered from a more abstract viewpoint: rather than simply calculating a limit or derivative, students are expected to understand why the relevant theorems are true and how they follow from the properties of the real numbers. The authors nevertheless try to keep the presentation adaptable; instructors can avoid some of the more abstract topological terminology and work instead with familiar notions such as open and closed intervals. The text also contains more advanced optional topics, including semicontinuity, convex functions, and generalized differentiation of nondifferentiable convex functions, which can serve as student projects.
The second edition significantly expanded the pedagogical material: the authors streamlined several sections, supplied additional proofs and detailed worked examples, and added more than 50 examples and about 100 new exercises or exercise parts. A final chapter provides solutions and hints for selected exercises. This makes the book particularly suitable as a bridge between elementary calculus and a traditional university real-analysis text, especially for mathematics students who need to develop proof-writing skills before studying more advanced analysis.
Key takeaways
- Builds a rigorous foundation for real analysis.
- Best suited to students who already know undergraduate calculus.
- Main topics: completeness, sequences, convergence, limits, continuity, and differentiation.
- Strong emphasis on proofs and mathematical reasoning, rather than computation alone.
- Contains many worked examples and exercises, plus optional material in convex analysis and generalized differentiation.
BOOK