Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
An outrageous graphic novel that investigates key concepts in mathematics Integers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body. Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Travel with Detective von Neumann as he leaves no clue unturned, from shepherds’ huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the frustration—and the excitement—of our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all. Beautifully drawn and exquisitely detailed, Prime Suspects is unique, astonishing, and witty—a once-in-a-lifetime opportunity to experience mathematics like never before.
Number Theory Revealed: An Introduction acquaints undergraduates with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.
The purpose of Granville Sharpe's Cases on Slavery is twofold: first, to publish previously unpublished legal materials principally in three important cases in the 18th century on the issue of slavery in England, and specifically the status of black people who were slaves in the American colonies or the West Indies and who were taken to England by their masters. The unpublished materials are mostly verbatim transcripts made by shorthand writers commissioned by Granville Sharp, one of the first Englishmen to take up the cause of the abolition of the slave trade and slavery itself. Other related unpublished material is also made available for the first time, including an opinion of an attorney general and some minor cases from the library of York Minster. On the slave ship Zong, there are transcripts of the original declaration, the deposition by the chief mate, James Kelsall and an extract from a manuscript that Professor Martin Dockray was working on before his untimely death. The second purpose, outlined in the Introduction, is to give a social and legal background to the cases and an analysis of the position in England of black servants/slaves brought to England and the legal effects of the cases, taking into account the new information provided by the transcripts. There was a conflict in legal authorities as to whether black servants remained slaves, or became free on arrival in England. Lord Mansfield, the chief justice of the court of King's Bench, was a central figure in all the cases and clearly struggled to come to terms with slavery. The material provides a basis for tracing the evolution of his thought on the subject. On the one hand, the huge profits from slave production in the West Indies flooded into England, slave owners had penetrated the leading institutions in England and the pro-slavery lobby was influential. On the other hand, English law had over time established rights and liberties which in the 18th century were seen by many as national characteristics. That tradition was bolstered by the ideas of the Enlightenment. By about the 1760s it had become clear that there was no property in the person, and by the 1770s that such servants could not be sent abroad without their consent, but whether they owed an obligation of perpetual service remained unresolved.
This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.
The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functions such as the partition function. More specific topics include the Erdos-Kac Theorem, cyclotomic polynomials, combinatorial methods, quadratic forms, zeta functions, Dirichlet series and $L$-functions. All these create an intimate understanding of the properties of integers and lead to fascinating and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gerald Tenenbaum.
One of the most active areas in mathematics today is the rapidly emerging new topic of ``additive combinatorics''. Building on Gowers' use of the Freiman-Ruzsa theorem in harmonic analysis (in particular, his proof of Szemeredi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain and his co-authors have given non-trivial estimates for hitherto untouchably short exponential sums. There are further important consequences in group theory and in complexity theory and compelling questions in ergodic theory, discrete geometry and many other disciplines. The basis of the subject is not too difficult: it can be best described as the theory of adding together sets of numbers; in particular, understanding the structure of the two original sets if their sum is small. This book brings together key researchers from all of these different areas, sharing their insights in articles meant to inspire mathematicians coming from all sorts of different backgrounds.
Andrew Carnegie era un inmigrante, un chico pobre que trabajaba en una fábrica de algodón, un hombre que amasó una gran fortuna como barón del acero y luego se convirtió en uno de los filántropos más generosos e influyentes que el mundo ha conocido. Su célebre sentencia, según la cual quien muere rico muere en desgracia, ha inspirado a filántropos y empresas filantrópicas durante generaciones. Durante su vida, puso en práctica sus ideas creando una familia de organizaciones que siguen trabajando para mejorar la condición humana, promover la paz internacional, fortalecer la democracia y crear un progreso social que beneficie a hombres, mujeres y niños en los Estados Unidos y en todo el mundo.Aquí, en sus propias palabras, el Sr. Carnegie cuenta la dramática historia de su vida y su carrera, esbozando los principios por los que vivió y que hoy sirven como pilares de la filantropía moderna.
A critically acclaimed autobiography that exemplifies the American Dream by one of nineteenth-century America’s most philanthropic businessmen. Scottish immigrant Andrew Carnegie worked his way up from bobbin boy to telegraph operator to railroad man, learning key lessons along the way that would eventually lead to his unparalleled success in the steel business. Documenting a world of tariffs, insider deals, and Wall Street sharks, The Autobiography of Andrew Carnegie opens a window into the great industrialist’s decision-making process. His insights on education, business, and the necessity of giving back for the common good set an inspirational example for aspiring executives and provide a fitting testament to the power of the American dream. This ebook has been professionally proofread to ensure accuracy and readability on all devices.
A dramatic intellectual biography of Victorian jurist Travers Twiss, who provided the legal justification for the creation of the brutal Congo Free State Eminent jurist, Oxford professor, advocate to the Archbishop of Canterbury, Travers Twiss (1809–1897) was a model establishment figure in Victorian Britain, and a close collaborator of Prince Metternich, the architect of the Concert of Europe. Yet Twiss’s life was defined by two events that threatened to undermine the order that he had so stoutly defended: a notorious social scandal and the creation of the Congo Free State. In King Leopold’s Ghostwriter, Andrew Fitzmaurice tells the incredible story of a man who, driven by personal events that transformed him from a reactionary to a reformer, rewrote and liberalised international law—yet did so in service of the most brutal regime of the colonial era. In an elaborate deception, Twiss and Pharaïlde van Lynseele, a Belgian prostitute, sought to reinvent her as a woman of suitably noble birth to be his wife. Their subterfuge collapsed when another former client publicly denounced van Lynseele. Disgraced, Twiss resigned his offices and the couple fled to Switzerland. But this failure set the stage for a second, successful act of re-creation. Twiss found new employment as the intellectual driving force of King Leopold of Belgium’s efforts to have the Congo recognised as a new state under his personal authority. Drawing on extensive new archival research, King Leopold’s Ghostwriter recounts Twiss’s story as never before, including how his creation of a new legal personhood for the Congo was intimately related to the earlier invention of a new legal personhood for his wife. Combining gripping biography and penetrating intellectual history, King Leopold’s Ghostwriter uncovers a dramatic, ambiguous life that has had lasting influence on international law.
Experience inner-city paddling with a guide that tells the story of Vancouver and Victoria from water level. Explore history with the tales behind the people, bridges, lighthouses, museums and watercraft you will see as you explore these waterways. Paddling Through History explains place names, geology and other highlights, and is illustrated with maps and photos.
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The correspondence in this volume is related to Johnson's presidency during the Reconstruction Era, including the president's impeachment and the subsequent trial, which resulted in the Senate narrowly voting not to remove him from office.
Canada resident and avid outdoorsman Andrew Hempstead gives you his unique perspective on British Columbia, from dining at the best of Vancouver's 3,000 restaurants and cafés to skiing and snowboarding on the world-class slopes of Whistler/Blackcomb. Hempstead offers unique trip ideas that utilize the region's amazing outdoor options, such as Winter Fun and B.C. Road Trip. Packed with information on dining, transportation, and accommodations, Moon British Columbia has lots of options for a range of travel budgets. Complete with guidance on whale-watching near Telegraph Cove, hiking the Stanley Glacier Trail, and camping near Mount Robson, Moon British Columbia gives travelers the tools they need to create a more personal and memorable experience.
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