Real Analysis: A First Course
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Author Description
Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical methods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.
Menrva's Summary
THE THESIS
This text investigates the foundational principles of real analysis by providing a structured, student-centered introduction to the subject. Russell A. Gordon, an experienced mathematics educator, utilizes a pedagogical approach that emphasizes clarity and logical progression. The book builds upon standard calculus concepts to introduce more rigorous mathematical proofs and abstract structures, ensuring that students can transition effectively from elementary to advanced analysis.
THE SCOPE MAP
What You Will Find
- Comprehensive coverage of real number properties, sequences, and series.
- Detailed exploration of functions of bounded variation and convex functions.
- Introduction to metric spaces and numerical methods of integration.
- Over 1600 exercises designed to reinforce theoretical understanding and problem-solving skills.
THE AUTHORITY PERSPECTIVE
Mathematics instructors frequently cite this text for its accessible prose and logical organization of complex topics. It is widely regarded as a foundational resource for undergraduate students beginning their study of formal mathematical analysis.
Page Count:
400
Publication Date:
2001-06-01
Publisher:
Pearson
ISBN-10:
0201437279
ISBN-13:
9780201437270
Analysis
Mathematics
textbook
Mathematical Analysis
Calculus
