Word: algebras
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Professor Whitehead was perhaps best known for two early works, written before his arrival in Cambridge--"A Treatise on Universal Algebra," (1898), and "Principia Mathematics," (1910), in which he collaborated with is friend and former pupil Bertrand Russell. In the latter, a monumental three-volume opus, the authors cut one of the major tasks of philosophy in half by demonstrating that there is a definite connection between pure mathematics and logic...
...waste of time for most high-school students to read Il Penseroso, Ivanhoe, Silas Marner and other compulsory classics. It would be enough for many to secure "sufficient competence in reading to comprehend newspapers and magazines reasonably well." Only a gifted few can achieve any real understanding of algebra or geometry. It should, therefore, be a matter of choice whether a student takes algebra, literature, Latin, foreign languages...
...Algebra at Five. Today, in a faded yellow-brick-and-plaster house in Adyar, Maria Montessori is hard at work. She lectures in Italian two or three times a week; Mario translates into English for her. She is surer than ever of one thing: "The child is capable of achieving culture at an age hitherto unsuspected." She now teaches arithmetic at 3½, algebra at five, and finds that eight-year-olds learn algebra quicker than 14-year-olds, for they consider it a game, instead of something to dread. An 18-month-old child, she says, is "perhaps happiest...
...conferred on a man who hardly cares, and may be denied to another who strives most desperately for it. Guilt may overthrow a man who (by human standards) is unconscious that he has incurred any guilt. Chance, the irrational number by which man confesses the failure of his intellectual algebra, may throw a man off course for a whole lifetime, and even beyond the grave. "When you have once been misled by bells tolling in the night," wrote Kafka, "you can never find the right path again...
Professor MacLane, who will concentrate on the study of "the borderline between algebra and algebraic topography," did research work during the war with the Applied Mathematics Group at Columbia. An active member of several mathematical societies, he was on the Board ematical societies, he is on the oBard of Governors of the Mathematical Association of America...