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.

    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.

    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.

    The story chronicles with unblinking objectivity the harrowing experiences of Jenny, reared in a satanic cult, in a life so untenable as to fracture the self. In the healing process, these experiences, made of nightmare stuff, are assimilated, with the help of therapists with little to guide their committed and necessarily innovative treatment. The horrifying revelations of Jennys healing journey will shock, inspire, and give caution to us all.

    According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

    Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

    In 1985 Andrew Collins and a psychic colleague uncovered an inscribed spearhead, buried as part of an occult ritual. Claiming to have forged a telepathic link with its maker - a lone figure practising a dangerous form of black magic - the pair were directed to other desecrated holy places, unaware that their adversary was now hunting them, resulting in a confrontation leading to what have been described as disturbing displays of psychic powers. Then, in the early hours of 16th October 1987, as southern England was being hit by its first hurricane for more than two-and-a-half centuries, individuals across the country are said to have reported the same nightmare, revealing the hidden secrets of the hurricane and the power of "the black alchemist".

    This completely updated edition brings you all the latest information about LaTeX and the vast range of add-on packages now available--over 200 are covered! Full of new tips and tricks for using LaTeX in both traditional and modern typesetting, this book will also show you how to customize layout features to your own needs--from phrases and paragraphs to headings, lists, and pages. Inside, you will find: Expert advice on using LaTeX's basic formatting tools to create all types of publications--from memos to encyclopedias In-depth coverage of important extension packages for tabular and technical typesetting, floats and captions, multicolumn layouts--including reference guides and discussions of the underlying typographic and TeXnical concepts Detailed techniques for generating and typesetting contents lists, bibliographies, indexes, etc. Tips and tricks for LaTeX programmers and systems support New to this edition: Nearly 1,000 fully tested examples that illustrate the text and solve typographical and technical problems--all ready to run! An additional chapter on citations and bibliographies Expanded material on the setup and use of fonts to access a huge collection of glyphs, and to typeset text from a wide range of languages and cultures Major new packages for graphics, "verbatim" listings, floats, and page layout Full coverage of the latest packages for all types ofdocuments--mathematical, multilingual, and many more Detailed help on all error messages, including those troublesome low-level TeX errors Like its predecessor, The LaTeX Companion, Second Edition, is an indispensable reference for anyone wishing to use LaTeX productively. The accompanying CD-ROM contains a complete plug-and-play LaTeX installation, including all the packages and examples featured in the book.

    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.

    It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

    It has been out of print for many years and until the release of this brand new edition was as rare as hen's teeth, with some old copies fetching prices of up to USD $600.00. This new edition features a beautiful new cover and has been revised and updated by the author. Know this: I, Mercurius, have set down a full, true and infallible account of the Great Work. But I give you fair warning that unless you seek the true philosophical gold and not the gold of the vulgar; unless your heart is fixed with unbending intent on the true Stone of the Philosophers, unless you are steadfast in your quest, abiding by God s laws in all faith and humility and eschewing all vanity, conceit, falsehood, intemperance, pride, lust and faintheartedness, read no further lest I prove fatal to you. In 1952 a country clergyman called Smith begins his tortuous quest for the Holy Grail of alchemy - the Philosophers' Stone which transmutes base metal to gold and confers immortality. As he pits himself against the bizarre perils of the GreatWork, it becomes clear that his arcane transformations are as much spiritual as chemical. Gradually the shadow of alchemy falls over those around him; a young girl whose sudden pregnancy is a local scandal; Janet, trapped in a barren marriage; and Robert who pursues his own quest for the legendary blue glass of Chartres. Thirty years later, Eileen comes to live in Smith's vicarage. In the medieval cellar she unearths a hidden manuscript and begins to read of secret fire and mysterious prime matter, a green lion and a raven's head, a fatal conjunction of king and queen, a descent into Blackness and putrefaction. As she penetrates farther into the alchemical labyrinth, she is haunted both by her own history and by that of her neighbours, the menacing Mrs Zetterberg and the disfigured Pluto - and, finally, by the enigma of Smith himself. In separate but interwoven accounts, Smith and Eileen strive towards the one thing necessary for the Work's success -the great Secret guarded by the paradoxical Mercurius, who leads them to the zero point where Heaven is wedded to Earth and the miraculous Stone appears at the intersection of time and eternity. By reconstructing a highly sophisticated but almost forgotten world-view, Mercurius restores to us our own spiritual heritage which, rooted in the alchemists' dark retorts, will perhaps flower in the light of the future.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    Publilius Syrus, Moral Sayings We've been very fortunate to receive fantastic feedback from our readers during the last four years, since the first edition of How to Solve It: Modern Heuristics was published in 1999. It's heartening to know that so many people appreciated the book and, even more importantly, were using the book to help them solve their problems. One professor, who published a review of the book, said that his students had given the best course reviews he'd seen in 15 years when using our text. There can be hardly any better praise, except to add that one of the book reviews published in a SIAM journal received the best review award as well. We greatly appreciate your kind words and personal comments that you sent, including the few cases where you found some typographical or other errors. Thank you all for this wonderful support.