A Course in Real Analysis

Approx.668 pages

Autorentext
Neil A. Weiss (deceased) received his Ph.D. from UCLA and subsequently accepted an assistant-professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor. Weiss has taught mathematics, probability, statistics, and operations research from the freshman level to the advanced graduate level. In recognition of his excellence in teaching, he received the Dean's Quality Teaching Award from the ASU College of Liberal Arts and Sciences. He has also been runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences. Weiss's comprehensive knowledge and experience ensures that his texts are mathematically accurate, as well as pedagogically sound.Weiss has published research papers in both theoretical and applied mathematics, including probability, engineering, operations research, numerical analysis, and psychology. He has also published several teaching-related papers.In addition to his numerous research publications, Weiss has authored or coauthored books in real analysis, probability, statistics, and finite mathematics. His texts-well known for their precision, readability, and pedagogical excellence-are used worldwide.

Klappentext
"The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference"--

Zusammenfassung
Provides a foundation of real analysis concepts and principles. Balancing theory and applications with a wealth of examples and exercises, this book takes a progressive approach of skill building to help students learn to absorb the abstract. It includes real world applications, probability theory, harmonic analysis, and dynamical systems theory.

Inhalt

1. Set Theory2. The Real Number System and Calculus3. Lebesgue Measure on the Real Line4. The Lebesgue Integral on the Real Line5. Elements of Measure Theory6. Extensions to Measures and Product Measure7. Elements of Probability8. Differentiation and Absolute Continuity9. Signed and Complex Measures10. Topologies, Metrics, and Norms11. Separability and Compactness12. Complete and Compact Spaces13. Hilbert Spaces and Banach Spaces14. Normed Spaces and Locally Convex Spaces15. Elements of Harmonic Analysis16. Measurable Dynamical Systems17. Hausdorff Measure and Fractals