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Invitation To Q-series, An: From Jacobi's Triple Product Identity To Ramanujan's "Most Beautiful Identity"
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
Jacobi's Maze
Time Travel. Adventure. Conspiracy. Murder. Join the Wicks, a Nomadic family that settles down in small mountain town Maple Falls, Washington. Their lives will never be the same, and no one knows if that's a good thing or a bad thing. (This is BOOK TWO in a trilogy called THE AMBER GRAVE. BOOK ONE is called INTO THE BLOOD. It is also sold here on Lulu.com)
Dr. Jacobi's Works
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Theory and Application of Quantum Molecular Dynamics
This book gives an updated and detailed presentation of modern quantum-mechanical treatments and practical computational methods for dynamical processes of small molecular systems. The main emphasis is on the recent development of successful theories and computational methods for the reactive scattering process. Specific applications are given in detail for a number of benchmark chemical reaction systems in the gas phase and gas surface. Differing from traditional physics books focusing on abstract collision theory for elastic collisions, the book has been written in a fashion in which the development of general reactive or rearrangement scattering theory is accompanied by practical applications for realistic reaction systems.
Schelling Versus Hegel
In tracing Friedrich von Schelling's long philosophical development, John Laughland examines in particular his disentanglement from German idealism and his reaction, later in life, against Hegel. He argues that this story has relevance beyond the facts themselves and that it explains much about the direction philosophy took in the first century of the modern period.
A 20-D Table of Jacobi's Nome and Its Inverse
Jacobi's Nome q is given to twenty decimals as a function of the modulus-squared, k squared, the modular angle arc sin k, and the complementary modulus k' for k squared : 0(.001) 999; arc sin k : 0(.10) 89 degrees (.01) 89.99 degrees (.0002) 90 degrees; k' : 0001(.0001).02. The latter table also gives values of an approximation valid in this range to the order of (k') squared, as well as the ratio of the true and approximate values and second central differences of the latter ratio. The fourth table gives k and k' as functions of q for q = 0(.001).5. (Author).
Friedrich Jacobi and the End of the Enlightenment
Places Friedrich Jacobi as figure at the crux of modernity, showing how he shaped German idealism, Romanticism and existentialism.
Mary Putnam Jacobi and the Politics of Medicine in Nineteenth-century America
In the late nineteenth century, as Americans debated the "woman question," a battle over the meaning of biology arose in the medical profession. Some medical men claimed that women were naturally weak, that education would make them physically ill, and th
