Mathographics

Stimulating, unique book explores the possibilities of mathematical drawing through compass constructions and computer graphics. Over 100 full-page drawings demonstrate possibilities: five-point egg, golden ratio, 17-gon, plughole vortex, blancmange curve, pentasnow, turtle geometry, many more. Exercises (with answers). "A wealth of intriguing and lovely ideas." — Information Technology & Learning.

This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.

A collection of essays explores the aesthetic, graphic, literary, scientific, mathematical, and computer-related aspects of the spiral in nature and in the man-made world.

Compass drawings - String drawings - Perspective drawings - Trigonometry - Computer drawings_

More than fifty years ago, Thomas Szasz showed that the concept of mental illness—a disease of the mind—is an oxymoron, a metaphor, a myth. Disease, in the medical sense, affects only the body. He also demonstrated that civil commitment and the insanity defense, the paradigmatic practices of psychiatry, are incompatible with the political values of personal responsibility and individual liberty. The psychiatric establishment’s rejection of Szasz’s critique posed no danger to his work: its defense of coercions and excuses as "therapy" supported his argument regarding the metaphorical nature of mental illness and the transparent immorality of brutal psychiatric control masquerading as humane medical care. In the late 1960s, the launching of the so-called antipsychiatry movement vitiated Szasz’s effort to present a precisely formulated conceptual and political critique of the medical identity of psychiatry. Led by the Scottish psychiatrist R. D. Laing, the antipsychiatrists used the term to attract attention to themselves and to deflect attention from what they did, which included coercions and excuses based on psychiatric principles and power. For this reason, Szasz rejected, and continues to reject, psychiatry and antipsychiatry with equal vigor. Subsuming his work under the rubric of antipsychiatry betrays and negates it just as surely and effectively as subsuming it under the rubric of psychiatry. In Antipsychiatry: Quackery Squared, Szasz powerfully argues that his writings belong to neither psychiatry nor antipsychiatry. They stem from conceptual analysis, social-political criticism, and common sense.

Ranging from ancient Greek and Roman problems to the most modern applications of special mathematical techniques for amusement, this popular volume contains material to delight both beginners and advanced mathematicians. Its 250 lively puzzles, problems, situations, and demonstrations of recreational mathematics feature full solutions and analyses. Fifty-seven highly unusual historic problems are derived from ancient Greek, medieval European, Arabic, and Hindu sources. Other problems are based on "mathematics without numbers," geometry, topology, the calendar, arithmetic, and the mathematics of chess moves. Fifty pages comprise numerical pastimes built out of figurate numbers, Mersenne numbers, Fermat numbers, cyclic numbers, automorphic numbers, and prime numbers; probability problems are also fully analyzed. More than forty pages are devoted to magic squares, and the concluding portion of the book presents more than twenty-five new positional and permutational games of permanent value. A discussion of fairy chess is followed by rules and procedural information on latruncles, go, reversi, jinx, ruma, lasca, tricolor, four-story towers, tetrachrome, and other games. More than a collection of wonderful puzzles, this volume offers a thorough, rigorous, and entertaining sampler of recreational mathematics, highlighted by numerous insights into specialized fields.

This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.