07-25-2026, 08:55 PM
Real Infinite Series
BY Daniel D. Bonar
Summary
Real Infinite Series is an accessible yet thorough introduction to the theory of infinite series of real numbers, designed for undergraduate students, teachers, and anyone wishing to deepen their understanding of mathematical analysis. The book begins with the fundamental definitions of infinite series and gradually develops the major convergence and divergence tests before moving to more sophisticated techniques developed by mathematicians such as Cauchy, Kummer, Raabe, Gauss, and Abel.
Special attention is given to the harmonic and alternating harmonic series, highlighting their remarkable properties and unexpected appearances throughout mathematics. Beyond the standard curriculum, the authors present over one hundred elegant and surprising results that reveal the richness of infinite series, followed by a collection of challenging Putnam Competition problems with complete solutions. The final chapter explores the lighter side of the subject through mathematical puzzles, visual demonstrations, and common fallacies, encouraging readers to think critically about seemingly convincing arguments.
Three appendices provide true-or-false questions, historical notes on the harmonic series, and an extensive bibliography for further study. Written in a clear and engaging style, the book combines rigorous mathematics with problem solving, historical context, and recreational mathematics, making it an excellent companion for both classroom learning and independent exploration.
BOOK
BY Daniel D. Bonar
Summary
Real Infinite Series is an accessible yet thorough introduction to the theory of infinite series of real numbers, designed for undergraduate students, teachers, and anyone wishing to deepen their understanding of mathematical analysis. The book begins with the fundamental definitions of infinite series and gradually develops the major convergence and divergence tests before moving to more sophisticated techniques developed by mathematicians such as Cauchy, Kummer, Raabe, Gauss, and Abel.
Special attention is given to the harmonic and alternating harmonic series, highlighting their remarkable properties and unexpected appearances throughout mathematics. Beyond the standard curriculum, the authors present over one hundred elegant and surprising results that reveal the richness of infinite series, followed by a collection of challenging Putnam Competition problems with complete solutions. The final chapter explores the lighter side of the subject through mathematical puzzles, visual demonstrations, and common fallacies, encouraging readers to think critically about seemingly convincing arguments.
Three appendices provide true-or-false questions, historical notes on the harmonic series, and an extensive bibliography for further study. Written in a clear and engaging style, the book combines rigorous mathematics with problem solving, historical context, and recreational mathematics, making it an excellent companion for both classroom learning and independent exploration.
BOOK
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