"This picture book traces the impressive career of Sophie Kowalevski, the first woman to receive a doctorate in mathematics requiring original research. As a girl, Sophie is fascinated by the equations her father uses to wallpaper her room. She proves herself a prodigy, and tutors are impressed enough to give her private lessons. Despite universities that refuse to allow women on campus or to pay them to teach, Sophie is able to distinguish herself with her research into partial differential equations. Sophie receives a doctorate and becomes the first female professional mathematician in Northern Europe. The book mentions several of Kowalevski's mathematical contributions and closes with an encouraging message about women in mathematics"--

This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.

A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe? In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe. Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.

Managing Data in Motion describes techniques that have been developed for significantly reducing the complexity of managing system interfaces and enabling scalable architectures. Author April Reeve brings over two decades of experience to present a vendor-neutral approach to moving data between computing environments and systems. Readers will learn the techniques, technologies, and best practices for managing the passage of data between computer systems and integrating disparate data together in an enterprise environment. The average enterprise's computing environment is comprised of hundreds to thousands computer systems that have been built, purchased, and acquired over time. The data from these various systems needs to be integrated for reporting and analysis, shared for business transaction processing, and converted from one format to another when old systems are replaced and new systems are acquired. The management of the "data in motion" in organizations is rapidly becoming one of the biggest concerns for business and IT management. Data warehousing and conversion, real-time data integration, and cloud and "big data" applications are just a few of the challenges facing organizations and businesses today. Managing Data in Motion tackles these and other topics in a style easily understood by business and IT managers as well as programmers and architects. Presents a vendor-neutral overview of the different technologies and techniques for moving data between computer systems including the emerging solutions for unstructured as well as structured data types Explains, in non-technical terms, the architecture and components required to perform data integration Describes how to reduce the complexity of managing system interfaces and enable a scalable data architecture that can handle the dimensions of "Big Data"

A survey of Descartes' scientific career from his student days at the Jesuit College of La Flèche to his departure for Sweden in 1649.