Integration is treated before differentiation -- this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

    It requires, in short, an understanding of probability. In this Very Short Introduction, John Haigh introduces the ideas of probability--and the different philosophical approaches to probability--and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions and discusses a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes.

    ForewordThe Discovery of Tutankhamun's TombTutankhamun & His WorldColor PlatesCatalogueBibliography

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995.In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities.Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.

    The manuscript was a palimpsest-a book made from an earlier codex whose script had been scraped off and the pages used again. Behind the script of the thirteenth-century monk's prayer book, the palimpsest revealed the faint writing of a much older, tenth-century manuscript. Part archaeological detective story, part science, and part history, The Archimedes Codex tells the extraordinary story of this lost manuscript, from its tenth-century creation in Constantinople to the auction block at Christie's, and how a team of scholars used the latest imaging technology to reveal and decipher the original text. What they found was the earliest surviving manuscript by Archimedes (287 b.c.-212 b.c.), the greatest mathematician of antiquity-a manuscript that revealed, for the first time, the full range of his mathematical genius, which was two thousand years ahead of modern science.

    This volume begins with a discussion of the cells that make up living beings, as well as the basics of protein synthesis, metabolism, energy production, and photosynthesis. It goes on to cover ecosystems and material cycles; the mechanisms of respiration; lipids, cholesterol, and blood types; and the roles and structures of enzymes and proteins. Readers explore genes and DNA; the differences between biochemistry and molecular biology; and the mystery surrounding the origin of the cell—all with the aid of original Manga cartoons. This EduManga title is co-published with Ohmsha, Ltd. of Tokyo, Japan, and is one in a series of translations from Ohmsha's bestselling Japanese originals.

    From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material. 'A lively and stimulating book' Philosophy

    Linear algebra is tightly integrated into the text.

    This second edition of The 12 Step Prayer Book features 183 passages gleaned from Twelve Step meetings and adapted from common prayers and devotions. It includes: --44 new prayers and readings --a guide for daily reading --traditional and best-loved recovery prayers, and --Step and meeting prayers. This book is an excellent accompaniment to Easy Does It: A Book of Daily Twelve Step Meditations.

    The Creation of Patriarchy, the first book in her two-volume magnum opus Women and History (1986) received wide review attention and much acclaim, winning the prestigious Joan Kelly Prize of the American Historical Association for the best work on Women's History that year. Ms hailed the book for providing a grand historical framework that was impossible even to imagine before the enlightenment about women's place in the world provided by her earlier work and that of other feminist scholars. New Directions for Women said it may well be the most important work in feminist theory to appear in our generation. Patriarchy traced the development of the ideas, symbols, and metaphors by which men institutionalized their domination of women. Now, in The Creation of Feminist Consciousness, the eagerly awaited concluding volume of Women and History, Lerner documents the twelve-hundred-year struggle of women to free their minds from patriarchal thought, to create Women's History, and to achieve a feminist consciousness. In a richly documented narrative filled with inspiring portraits of women, Lerner ranges from the Middle Ages to the late 19th century, tracing several important ways by which women strove for autonomy and equality. One of the most remarkable sections examines over twelve hundred years of feminist Bible criticism. Since objections to women's thinking, teaching, and speaking in public were based on biblical authority--most notably, passages from Genesis and the writings of St. Paul--women returned again and again to these texts, in an attempt to subvert patriarchal dominance and establish their equality with men. This survey of biblical criticism allows Lerner to illustrate her most important insight--the discontinuity of women's history. She describes how women's history was not passed on from generation to generation, forcing women in effect to reinvent the wheel over and over again. In a series of fascinating portraits of individual women who resisted patriarchal indoctrination, Lerner discusses women mystics such as Hildegard of Bingen, Julian of Norwich and later Protestant mystics, and brings to life the many women of great literary talent, from Christine de Pisan to Louise Labe to Emily Dickinson, who simply bypassed patriarchal thought and created alternate worlds for themselves. Documenting the 1,200 year struggle of women to free their minds from patriarchal thought, create a women's history, and achieve a feminist consciousness, this brilliant work charts new ground for feminist theory, the history of ideas, and the development of women's place in our intellectual tradition.

    Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

    Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest. Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or atoms of symmetry. Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed the Monster--a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe. This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science--and especially readers of such books as Fermat's Last Theorem.

    When the headmaster forces Minagi's entire class to study Einstein's theory of relativity over summer school, Minagi volunteers to go in their place. There's just one problem: He's never even heard of relativity before! Luckily, Minagi has the plucky Miss Uraga to teach him. Follow along with The Manga Guide to Relativity as Minagi learns about the non-intuitive laws that shape our universe. Before you know it, you'll master difficult concepts like inertial frames of reference, unified spacetime, and the equivalence principle. You'll see how relativity affects modern astronomy and discover why GPS systems and other everyday technologies depend on Einstein's extraordinary discovery. The Manga Guide to Relativity also teaches you how to: Understand and use E = mc2, the world's most famous equation Calculate the effects of time dilation using the Pythagorean theorem Understand classic thought experiments like the Twin Paradox, and see why length contracts and mass increases at relativistic speeds Grasp the underpinnings of Einstein's special and general theories of relativity If the idea of bending space and time really warps your brain, let The Manga Guide to Relativity straighten things out.