His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    With problems and solutions. Includes 99 illustrations.

    Mingling acute observation with often wild speculation, it offers a fascinating view of the world as it was understood in the first century AD, whether describing the danger of diving for sponges, the first water-clock, or the use of asses’ milk to remove wrinkles. Pliny himself died while investigating the volcanic eruption that destroyed Pompeii in AD 79, and the natural curiosity that brought about his death is also very much evident in the Natural History — a book that proved highly influential right up until the Renaissance and that his nephew, Pliny the younger, described ‘as full of variety as nature itself’. John F. Healy has made a fascinating and varied selection from the Natural History for this clear, modern translation. In his introduction, he discusses the book and its sources topic by topic. This edition also includes a full index and notes.

    The eloquent and dramatic epic poem captures the terrible anger of Achilles, "the best of the Achaeans," over a grave insult to his personal honor and relates its tragic result--a chain of consequences that proves devastating for the Greek forces besieging Troy, for noble Trojans, and for Achilles himself. The poet gives us compelling characterizations of his protagonists as well as a remarkable study of the heroic code in antiquity. The works attributed to Homer include the two oldest and greatest European epic poems, the Odyssey and the Iliad. These have been published in the Loeb Classical Library for three quarters of a century, the Greek text facing a faithful and literate prose translation by A. T. Murray. William F. Wyatt now brings the Loeb's Iliad up to date, with a rendering that retains Murray's admirable style but is written for today's readers.

    Homer's poems occupy, as Adam Nicolson writes "a third space" in the way we relate to the past: not as memory, which lasts no more than three generations, nor as the objective accounts of history, but as epic, invented after memory but before history, poetry which aims "to bind the wounds that time inflicts."The Homeric poems are among the oldest stories we have, drawing on deep roots in the Eurasian steppes beyond the Black Sea, but emerging at a time around 2000 B.C. when the people who would become the Greeks came south and both clashed and fused with the more sophisticated inhabitants of the Eastern Mediterranean.The poems, which ask the eternal questions about the individual and the community, honor and service, love and war, tell us how we became who we are.

    

    

    Each chapter includes many illustrative examples to assist the reader. The book emphasizes methods for finding solutions to differential equations. It provides many abundant exercises, applications, and solved examples with careful attention given to readability. Elementary Differential Equations includes a thorough treatment of power series techniques. In addition, the book presents a classical treatment of several physical problems to show how Fourier series become involved in the solution of those problems. The eighth edition of Elementary Differential Equations has been revised to include a new supplement in many chapters that provides suggestions and exercises for using a computer to assist in the understanding of the material in the chapter. It also now provides an introduction to the phase plane and to different types of phase portraits. A valuable reference book for readers interested in exploring the technological and other applications of differential equations.

    It includes some discussion of word usage, citing examples and characteristic phrases. Generally speaking, only words used by late writers and scientific terms have been omitted fromthe full lexicon. From Homer downwards, to the close of Attic Greek, care has been taken to include all words, as well as those used by Aristotle, Plutarch in his Lives, Polybius, Strabo, Lucian, and the writers of the New Testament.

    Provides a review of introductory noncalculus-based physics for those who do not have a strong background in mathematics.

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.

    430 to ca. 354 BCE) was a wealthy Athenian and friend of Socrates. He left Athens in 401 and joined an expedition including ten thousand Greeks led by the Persian governor Cyrus against the Persian king. After the defeat of Cyrus, it fell to Xenophon to lead the Greeks from the gates of Babylon back to the coast through inhospitable lands. Later he wrote the famous vivid account of this 'March Up-Country' ("Anabasis"); but meanwhile he entered service under the Spartans against the Persian king, married happily, and joined the staff of the Spartan king, Agesilaus. But Athens was at war with Sparta in 394 and so exiled Xenophon. The Spartans gave him an estate near Elis where he lived for years writing and hunting and educating his sons. Reconciled to Sparta, Athens restored Xenophon to honour but he preferred to retire to Corinth.Xenophon's "Anabasis" is a true story of remarkable adventures. "Hellenica, " a history of Greek affairs from 411 to 362, begins as a continuation of Thucydides' account. There are four works on Socrates (collected in Volume IV of the Loeb Xenophon edition). In "Memorabilia" Xenophon adds to Plato's picture of Socrates from a different viewpoint. The "Apology" is an interesting complement to Plato's account of Socrates' defense at his trial. Xenophon's "Symposium" portrays a dinner party at which Socrates speaks of love; and "Oeconomicus" has him giving advice on household management and married life. "Cyropaedia, " a historical romance on the education of Cyrus (the Elder), reflects Xenophon's ideas about rulers and government; the Loeb edition is in two volumes.We also have his "Hiero, " a dialogue on government; "Agesilaus, " in praise of that king; "Constitution of Lacedaemon" (on the Spartan system); "Ways and Means" (on the finances of Athens); "Manual for a Cavalry Commander;" a good manual of "Horsemanship;" and a lively "Hunting with Hounds. The Constitution of the Athenians, " though clearly not by Xenophon, is an interesting document on politics at Athens. These eight books are collected in the last of the seven volumes of the Loeb Classical Library edition of Xenophon.

    Writing with a pitch and heat that gets to the heart of the unforgiving classical world, Carson, a poet and classicist, translates four of the eighteen surviving plays by Euripides.Includes Heracles, Hecuba, Hippolytus, Alcestis.

    Instead of ambush, skirmish, maneuver, or combat between individual heroes, the Greeks of the fifth century b.c. devised a ferocious, brief, and destructive head-on clash between armed men of all ages. In this bold, original study, Victor Davis Hanson shows how this brutal enterprise was dedicated to the same outcome as consensual government--an unequivocal, instant resolution to dispute.The Western Way of War draws from an extraordinary range of sources--Greek poetry, drama, and vase painting, as well as historical records--to describe what actually took place on the battlefield. It is the first study to explore the actual mechanics of classical Greek battle from the vantage point of the infantryman--the brutal spear-thrusting, the difficulty of fighting in heavy bronze armor which made it hard to see, hear and move, and the fear. Hanson also discusses the physical condition and age of the men, weaponry, wounds, and morale.This compelling account of what happened on the killing fields of the ancient Greeks ultimately shows that their style of armament and battle was contrived to minimize time and life lost by making the battle experience as decisive and appalling as possible. Linking this new style of fighting to the rise of constitutional government, Hanson raises new issues and questions old assumptions about the history of war.