Lewis Carroll's books have delighted children and adults for generations, but behind their exuberant fantasy and delightful nonsense was the mind of a brilliant mathematician. Now his forgotten achievements in the world of numbers are brought to light by acclaimed author and mathematician Robin Wilson. Here he explores the curious imagination of a man whose pioneering work at Oxford University included investigations into voting patterns and tennis seeding, who dreamt up numerical conundrums in bed at night and who filled his writings with problems, paradoxes, puzzles and teasing games of logic. Taking us into a world of mock turtles and maps, gryphons and gravity, Lewis Carroll in Numberland reveals the singular mind of a genius.
Charles Lutwidge Dodgson is best known for his 'Alice' books, Alice's Adventures in Wonderland and Through the Looking-Glass, written under his pen name of Lewis Carroll. Yet, whilst lauded for his work in children's fiction and his pioneering work in the world of Victorian photography, his everyday job was a lecturer in Mathematics at Christ Church, Oxford University. The Mathematical World of Charles L. Dodgson (Lewis Carroll) explores the academic background behind this complex individual, outlining his mathematical life, describing his writings in geometry, algebra, logic, the theory of voting, and recreational mathematics, before going on to discuss his mathematical legacy. This is the first academic work that collects the research on Dodgson's wide-ranging mathematical achievements into a single practical volume. Much material appears here for the first time, such as Dodgson's personal letters and drawings, as well as the results of recent investigations into the life and work of Dodgson. Complementing this are many illustrations, both historical and explanatory, as well as a full mathematical bibliography of Dodgson's mathematical publications.
“A fine mathematical biography.”—John Allen Paulos, New York Times Book Review Just when we thought we knew everything about Lewis Carroll, here comes this “insightful . . . scholarly . . . serious” (John Butcher, American Scientist) biography that will appeal to Alice fans everywhere. Fascinated by the inner life of Charles Lutwidge Dodgson, Robin Wilson, a Carroll scholar and a noted mathematics professor, has produced this revelatory book—filled with more than one hundred striking and often playful illustrations—that examines the many inspirations and sources for Carroll’s fantastical writings, mathematical and otherwise. As Wilson demonstrates, Carroll made significant contributions to subjects as varied as voting patterns and the design of tennis tournaments, in the process creating large numbers of imaginative recreational puzzles based on mathematical ideas. Some images in this ebook have been redacted.
This gorgeous 150th anniversary edition of Alice's Adventures in Wonderland is also a revelatory work of scholarship. Alice's Adventures in Wonderland--published 150 years ago in 1865--is a book many of us love and feel we know well. But it turns out we have only scratched the surface. Scholar David Day has spent many years down the rabbit hole of this children's classic and has emerged with a revelatory new view of its contents. What we have here, he brilliantly and persuasively argues, is a complete classical education in coded form--Carroll's gift to his "wonder child" Alice Liddell. In two continuous commentaries, woven around the complete text of the novel for ease of cross-reference on every page, David Day reveals the many layers of teaching, concealed by manipulation of language, that are carried so lightly in the beguiling form of a fairy tale. These layers relate directly to Carroll's interest in philosophy, history, mathematics, classics, poetry, spiritualism and even to his love of music--both sacred and profane. His novel is a memory palace, given to Alice as the great gift of an education. It was delivered in coded form because in that age, it was a gift no girl would be permitted to receive in any other way. Day also shows how a large number of the characters in the book are based on real Victorians. Wonderland, he shows, is a veritable "Who's Who" of Oxford at the height of its power and influence in the Victorian Age. There is so much to be found behind the imaginary characters and creatures that inhabit the pages of Alice's Adventures in Wonderland. David Day's warm, witty and brilliantly insightful guide--beautifully designed and stunningly illustrated throughout in full colour--will make you marvel at the book as never before.
Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.
This entertaining and serious book covers some key subjects, of number theory, algebra and analysis in the general theory of sixth-form and early-undergraduate mathematics. The reader-friendly style creates motivation to tackle more formal texts, ability to understand and enjoy mathematics, willingness to appreciate the proofs. Alice, Tweedledum, Twedledee and other L. Carroll?s characters make the book ingenious and pleasant. The main points in the exposition deal with logic, theorem proving, prime factorization, numbers and operations on them, equivalence relation, Euclid?s algorithm, induction, permutations, and transpositions, axioms for R, cardinality, sequences and series, convergence, graphs and continuity, selected exercises with hints and solutions, references with useful recommendations.--Reviewer: K.Peeva (Sofia).
With almost 5 million copies sold 60 years after its original publication, generations of readers have now journeyed with Milo to the Lands Beyond in this beloved classic. Enriched by Jules Feiffer’s splendid illustrations, the wit, wisdom, and wordplay of Norton Juster’s offbeat fantasy are as beguiling as ever. “Comes up bright and new every time I read it . . . it will continue to charm and delight for a very long time yet. And teach us some wisdom, too.” --Phillip Pullman For Milo, everything’s a bore. When a tollbooth mysteriously appears in his room, he drives through only because he’s got nothing better to do. But on the other side, things seem different. Milo visits the Island of Conclusions (you get there by jumping), learns about time from a ticking watchdog named Tock, and even embarks on a quest to rescue Rhyme and Reason. Somewhere along the way, Milo realizes something astonishing. Life is far from dull. In fact, it’s exciting beyond his wildest dreams!
The first modern English edition of diverse Enlightenment-era writings by Prussian monarch Frederick the Great Frederick II of Prussia (1712–1786), best known as Frederick the Great, was a prolific writer of philosophical discourses, poems, epics, satires, and more, while maintaining extensive correspondence with prominent intellectuals, Voltaire among them. This edition of selected writings, the first to make a wide range of Frederick’s most important ideas available to a modern English readership, moves beyond traditional attempts to see his work only in light of his political aims. In these pages, we can finally appreciate Frederick’s influential contributions to the European Enlightenment—and his unusual role as a monarch who was also a published author. In addition to Frederick’s major opus, the Anti-Machiavel, the works presented here include essays, prefaces, reviews, and dialogues. The subjects discussed run the gamut from ethics to religion to political theory. Accompanied by critical annotations, the texts show that we can understand Frederick’s views of kingship and the state only if we engage with a broad spectrum of his thought, including his attitudes toward morality and self-love. By contextualizing his arguments and impact on Enlightenment beliefs, this volume considers how we can reconcile Frederick’s innovative public musings with his absolutist rule. Avi Lifschitz provides a robust and detailed introduction that discusses Frederick’s life and work against the backdrop of eighteenth-century history and politics. With its unparalleled scope and cross-disciplinary appeal, Frederick the Great’s Philosophical Writings firmly establishes one monarch’s multifaceted relevance for generations of readers and scholars to come.
In today's world, we are increasingly exposed to the words 'machine learning' (ML), a term which sounds like a panacea designed to cure all problems ranging from image recognition to machine language translation. Over the past few years, ML has gradually permeated the financial sector, reshaping the landscape of quantitative finance as we know it.An Introduction to Machine Learning in Quantitative Finance aims to demystify ML by uncovering its underlying mathematics and showing how to apply ML methods to real-world financial data. In this book the authorsFeatured with the balance of mathematical theorems and practical code examples of ML, this book will help you acquire an in-depth understanding of ML algorithms as well as hands-on experience. After reading An Introduction to Machine Learning in Quantitative Finance, ML tools will not be a black box to you anymore, and you will feel confident in successfully applying what you have learnt to empirical financial data!
Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.
