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Prime ministers --- Great Britain. --- Prime Minister of Britain --- Great Britain --- Politics and government

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The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

Riemann hypothesis. --- Numbers, Prime. --- Number theory. --- Riemann, Bernhard,

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"A collection of short, accessible chapters on the key aspects of Winston Churchill's military and political career and his impact on 20th-century history."--

Prime ministers --- Churchill, Winston, --- Influence. --- Great Britain --- Politics and government

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The prime ministership remains the main prize in Australian politics, but it is a precarious one. Leadership turnover in recent years has seen more prime ministers rise and fall than at any time since the decade after federation. What explains this volatility? The Pivot of Power is the second volume in a unique blend of collective biography and institutional history that shows the skills, limitations and passions of incumbents are only part of the story. The ways in which prime ministers thrive and fail are influenced by the resources at their command, the evolving nature of the parties they lead, the daunting public expectations they face under a relentless media gaze, and the challenges that history throws at them. Recent changes in these areas have had a destabilising effect and made the role of prime minister more onerous than ever. After decades of strong national leadership, the office has rarely seemed quite so confounding as it does for its contemporary holders. The Pivot of Power explains how this has come about. And its rich account of prime-ministerial fortune since the mid-twentieth century yields historical lessons for overcoming the current malaise.

Prime ministers --- Politicians --- History. --- Australia --- Politics and government.

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With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions. Chapters include new mathematical ideas and open problems, some of which are proved in the text. Vector valued MGPF sequences, extensions of Conway’s Subprime Fibonacci sequences, and linear complexity of bit streams derived from GPF sequences are among the topics covered in this book. This book is perfect for the pure-mathematics-minded educator in a small undergraduate college as well as graduate students and advanced undergraduate students looking for a significant high-impact learning experience in mathematics.

Mathematics. --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Numbers, Prime. --- Sequences (Mathematics) --- Mathematical sequences --- Numerical sequences --- Mathematics --- Prime numbers --- Numbers, Natural --- Math --- Science