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Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

The edition offers a new critical text of De rerum natura. It has been established after fresh collation of the manuscripts and a critical evaluation of previous editorial scholarship. It is equipped with a critical apparatus, an apparatus of source

In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.

Hardcover. Item is sealed in shrink wrap. HCW

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

No dust jacket. Ex-library book with typical stickers and stampings. Priority Mail is available on this item. No international shipping.

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gödel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

Hardcover; light fading, light shelf wear to exterior; otherwise contents in very good condition with clean text, firm binding.

Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions.

Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of e and π, cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.

Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background.

To flourish, humans need to develop virtues of independent thought and acknowledged social dependence. In this book, a leading moral philosopher presents a comparison of humans to other animals and explores the impact of these virtues.

In these three lectures, Cavell situates Emerson at an intersection of three crossroads: a place where both philosophy and literature pass; where the two traditions of English and German philosophy shun one another; where the cultures of America and Europe unsettle one another. "Cavell's 'readings' of Wittgenstein and Heidegger and Emerson and other thinkers surely deepen our understanding of them, but they do much more: they offer a vision of what life can be and what culture can mean. . . . These profound lectures are a wonderful place to make [Cavell's] acquaintance."—Hilary Putnam

Book by Doyle, Peter G., Snell, Laurie

Often questions about tiling space or a polygon lead to questions concerning algebra. For instance, tiling by cubes raises questions about finite abelian groups. Tiling by triangles of equal areas soon involves Sperner's lemma from topology and valuations from algebra. The first six chapters of Algebra and Tiling form a self-contained treatment of these topics, beginning with Minkowski's conjecture about lattice tiling of Euclidean space by unit cubes, and concluding with Laczkowicz's recent work on tiling by similar triangles. The concluding chapter presents a simplified version of Rédei's theorem on finite abelian groups. Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper level algebra courses, but teachers, researchers and professional mathematicians will find the book equally appealing.

Unread book in perfect condition.

"The Venus of Milo: An Archaeological Study of the Goddess of Womanhood" by Paul Carus is a profound exploration of one of the most iconic sculptures of the ancient world. Carus delves into the history, art, and cultural significance of the Venus de Milo, a statue that embodies beauty, femininity, and mystery. Through meticulous research, he examines the artistry and craftsmanship that define this Hellenistic masterpiece, while also contemplating the goddess' representation in various historical contexts. Carus highlights the statue’s enduring influence on art and literature, reflecting on its impact on the perception of femininity. The author's insightful analysis is augmented by his philosophical musings on the nature of beauty and its interplay with human experience. This classic text remains a vital resource for art historians, scholars, and anyone intrigued by the confluence of archaeology and the timeless ideals of womanhood that the Venus of Milo represents.

Carus's complete recording with Frieder Bernius and the Kammerchor Stuttgart of Felix Mendelssohn's sacred choral works represents a magnificent act of interpretation and editing. A better recording can hardly be imagined. This edition, which has won numerous prizes and has now been released as a box at a reasonable price, should form part of every CD collection.

Lucretius (Titus Lucretius Carus) lived ca. 99–ca. 55 BCE, but the details of his career are unknown. He is the author of the great didactic poem in hexameters, De Rerum Natura (On the Nature of Things). In six books compounded of solid reasoning, brilliant imagination, and noble poetry, he expounds the scientific theories of the Greek philosopher Epicurus, with the aim of dispelling fear of the gods and fear of death and so enabling man to attain peace of mind and happiness.In Book 1 he establishes the general principles of the atomic system, refutes the views of rival physicists, and proves the infinity of the universe and of its two ultimate constituents, matter and void. In Book 2 he explains atomic movement, the variety of atomic shapes, and argues that the atoms lack colour, sensation, and other secondary qualities. In Book 3 he expounds the nature and composition of mind and spirit, proves their mortality, and argues that there is nothing to fear in death. Book 4 explains the nature of sensation and thought, and ends with an impressive account of sexual love. Book 5 describes the nature and formation of our world, astronomical phenomena, the beginnings of life on earth, and the development of civilization. In Book 6 the poet explains various atmospheric and terrestrial phenomena, including thunder, lightning, earthquakes, volcanoes, the magnet, and plagues.The work is distinguished by the fervour and poetry of the author.

Titus Lucretius Carus (ca. 99–55 b.c.) is known primarily as the Roman author of the long didactic poem De Rerum Natura (On the Nature of Things). In it, he set out to explicate the universe, embracing and refuting ideas of the great Greek philosophers.             Now available in paperback, this annotated scholarly edition of the Latin text of De Rerum Natura has long been hailed as one of the finest editions of this monumental work. It features an introduction to Lucretius’s life and work by William Ellery Leonard, an introduction to and commentary on the poem by Stanley Barney Smith, the complete Latin text with detailed annotations, and an index of ancient sources.