This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    At the same time adjacent portions of philosophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part."This volume of essays has a unity and bears throughout the imprint of Quine's powerful and original mind. It is written with the felicity in the choice of words which makes everything that Quine writes a pleasure to read, and which ranks him among the best contemporary writers on abstract subjects." (Cambridge Review)"Professor Quine's challenging and original views are here for the first time presented as a unity. The chief merit of the book is the heart-searching from which it arose and to which it will give rise. In vigour, conciseness, and clarity, it is characteristic of its author." (Oxford Magazine)

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    The lifetime work of Professor Alexander Schmidt of Königsberg, this book has long been the indispensable companion for every person seriously interested in Shakespeare, Renaissance poetry and prose of any sort, or English literature. It is really two important books in one.Schmidt’s set contains every single word that Shakespeare used, not simply words that have changed their meaning since the seventeenth century, but every word in all the accepted plays and the poems. Covering both quartos and folios, it carefully distinguishes between shades of meaning for each word and provides exact definitions, plus governing phrases and locations, down to the numbered line of the Cambridge edition of Shakespeare. There is no other word dictionary comparable to this work.Even more useful to the general reader, however, is the incredible wealth of exact quotations. Arranged under the words of the quotation itself (hence no need to consult confusing subject classifications) are more than 50,000 exact quotations. Each is precisely located, so that you can easily refer back to the plays or poems themselves, if you wish context.Other features helpful to the scholar are appendixes on basic grammatical observations, a glossary of provincialisms, a list of words and sentences taken from foreign languages, a list of words that form the latter part of word-combinations. This third edition features a supplement with new findings.

    Every religion has angels, Sylvia tells us. Different from spirit guides, angels are spiritual messengers who are available to help us if we will simply ask for their assistance. Sylvia goes on to discuss the properties of angels; the true nature of God, good, evil, and the Other Side; and explains how we can overcome guilt, accept ourselves, and thereby understand our own particular “contract.” In the second half of the program, Sylvia leads a meditation that invokes the presence of our angels and individual spirit guides, and invites them to communicate with us. We feel their protection, receive their healing, and with Sylvia’s encouragement, learn how to ask them for the help we desire.

    Longtime users will recognize these distinctive characteristics of the casebook: - multi-disciplinary approach that utilizes a variety of critical and social perspectives to explore constitutional law - extensive textual summaries of the state of the law and its development - comprehensive book ideal for a two-semester course - clear and concise coverage of First Amendment law The Fifth Edition reflects recent developments and class experience: - issues of constitutional obligation and constitutionalism in times of crisis incorporated into the opening chapter - reorganization of materials on the powers of Congress, with the materials on other powers of congress separated into a new Chapter 3 - completely updated chapter on the Distribution of National Powers, with new material growing out of the war on terrorism and its implications for free speech, immigration, naturalization, privacy, and due process, as well as enemy combatant controversies - notes are shortened, simplified, and thoroughly updated

    

    Liliana is a beautiful and educated young Jewish woman. She marries Henry and becomes a mother to Rebecca. She has a full life ahead of her in Poland, or so it seems. The time period is the beginning of World War II, when the Germans invade Poland. To protect her, Liliana and Henry entrust Rebecca to their Christian friends. Shortly thereafter, Henry is among those taken to the concentration camp. Time passes, and Liliana knows little about the fate of her husband or daughter. To survive, Liliana (now known as Helena) assumes the identity of a Polish aristocrat and ends up working for a German officer named Robert. In a twist of fate, Robert and Helena fall in love with each other and get married. Unknown to Liliana, Henry survives and reunites with their daughter Rebecca. He finds a way to communicate with Liliana, only to find out that she started a new life. Liliana has yet to reveal her true identity to her German husband. Filled with guilt and longing for Rebecca, she thinks of putting an end to all of the lies. Will Liliana finally overcome her fears and reunite with her daughter? Parallel Lives is based on a true story. It brings the reader on a captivating journey of the "parallel lives" of a family who was separated by war. The journey takes the reader though a myriad of human emotions, including: love, jealousy, fear, despair, and freedom.

    In this lively book of essays, Stephen Wolfram takes the reader along on some of his most surprising and engaging intellectual adventures in science, technology, artificial intelligence and language design.

    Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

    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.

    This is such a book. Max Born is a Nobel Laureate (1955) and one of the world's great physicists: in this book he analyzes and interprets the theory of Einsteinian relativity. The result is undoubtedly the most lucid and insightful of all the books that have been written to explain the revolutionary theory that marked the end of the classical and the beginning of the modern era of physics.The author follows a quasi-historical method of presentation. The book begins with a review of the classical physics, covering such topics as origins of space and time measurements, geometric axioms, Ptolemaic and Copernican astronomy, concepts of equilibrium and force, laws of motion, inertia, mass, momentum and energy, Newtonian world system (absolute space and absolute time, gravitation, celestial mechanics, centrifugal forces, and absolute space), laws of optics (the corpuscular and undulatory theories, speed of light, wave theory, Doppler effect, convection of light by matter), electrodynamics (including magnetic induction, electromagnetic theory of light, electromagnetic ether, electromagnetic laws of moving bodies, electromagnetic mass, and the contraction hypothesis). Born then takes up his exposition of Einstein's special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein's mechanics and dynamics, relativity of arbitrary motions, the principle of equivalence, the geometry of curved surfaces, and the space-time continuum, among other topics. Born then points out some predictions of the theory of relativity and its implications for cosmology, and indicates what is being sought in the unified field theory.This account steers a middle course between vague popularizations and complex scientific presentations. This is a careful discussion of principles stated in thoroughly acceptable scientific form, yet in a manner that makes it possible for the reader who has no scientific training to understand it. Only high school algebra has been used in explaining the nature of classical physics and relativity, and simple experiments and diagrams are used to illustrate each step. The layman and the beginning student in physics will find this an immensely valuable and usable introduction to relativity. This Dover 1962 edition was greatly revised and enlarged by Dr. Born.

    Reorganized chapters on bonding, coordination chemistry and organometallic chemistry are also included.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Derived from the authors' Archaeology: Discovering Our Past, this book follows the same organizing principle but in less detail.