Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

    A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    Role of the unconscious in invention; the medium of ideas — do they come to mind in words? in pictures? in mathematical terms? Much more. "It is essential for the mathematician, and the layman will find it good reading." — Library Journal.

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

    Such a device would operate under a different set of physical laws: The laws of quantum mechanics. Johnson gently leads the curious outsider through the surprisingly simple ideas needed to understand this dream, discussing the current state of the revolution, and ultimately assessing the awesome power these machines could have to change our world.

    This book is a fascinating and accessible summary of Roger Penrose's current thinking on those areas of physics in which he feels there are major unresolved problems. It is also a stimulating introduction to the radically new concepts that he believes will be fruitful in understanding the workings of the brain and the nature of the human mind.

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

    Gamow, physicist and gifted writer, has sketched an intriguing portrait of the scientists and clashing ideas that made the quantum revolution…”—Christian Science MonitorIn 1900, German physicist Max Planck postulated that light, or radiant energy can exist only in the form of discrete packages or quanta. This profound insight, along with Einstein's equally momentous theories of relativity, completely revolutionized man's view of matter, energy, and the nature of physics itself.In this lucid layman's introduction to quantum theory, an eminent physicist and noted popularizer of science traces the development of quantum theory from the turn of the century to about 1930—from Planck's seminal concept (still developing) to anti-particles, mesons and Enrico Fermi's nuclear research. Gamow was not just a spectator at the theoretical breakthroughs which fundamentally altered our view of the universe, he was an active participant who made important contributions of his own. This “insider's” vantage point lends special validity to his careful, accessible explanation of Heisenberg's Uncertainty Principle, Neils Bohr's model of the atom, the pilot waves of Louis de Broglie and other path-breaking ideas.In addition, Gamow recounts a wealth of revealing personal anecdotes which give a warm human dimension to many giants of 20th-century physics. He end the book with the Blegdamsvej Faust, a delightful play written in 1932 by Niels Bohr's students and colleagues to satirize the epochal developments that were revolutionizing physics. This celebrated play is available only in this volume.Written in a clear, lively style, and enhanced by 12 photographs (including candid shots of Rutherford, Bohr, Pauli, Heisenberg, Fermi and other notables), Thirty Years that Shook Physics offers both scientists and laymen a highly readable introduction to the brilliant conception that helped unlock many secrets of energy and matter and laid the groundwork for future discoveries.(Back Cover)