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Science
By 1514, the reclusive cleric Nicolaus Copernicus had written and hand-copied an initial outline of his heliocentric theory-in which he defied common sense and received wisdom to place the sun, not the earth, at the center of our universe, and set the earth spinning among the other planets. Over the next two decades, Copernicus expanded his theory through hundreds of observations, while compiling in secret a book-length manuscript that tantalized mathematicians and scientists throughout Europe. For fear of ridicule, he refused to publish.
In 1539, a young German mathematician, Georg Joachim Rheticus, drawn by rumors of a revolution to rival the religious upheaval of Martin Luther's Reformation, traveled to Poland to seek out Copernicus. Two years later, the Protestant youth took leave of his aging Catholic mentor and arranged to have Copernicus's manuscript published, in 1543, as De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres)-the book that forever changed humankind's place in the universe.
In her elegant, compelling style, Dava Sobel chronicles, as nobody has, the conflicting personalities and extraordinary discoveries that shaped the Copernican Revolution. At the heart of the book is her play And the Sun Stood Still, imagining Rheticus's struggle to convince Copernicus to let his manuscript see the light of day. As she achieved with her bestsellers Longitude and Galileo's Daughter, Sobel expands the bounds of narration, giving us an unforgettable portrait of scientific achievement, and of the ever-present tensions between science and faith.
Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.
The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning:
The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.
The three-part survey begins with an introduction that defines the trace map, considers the augmentation ideal in considerable detail, and provides all the necessary group ring results for later characterizations of dimension subgroups. A second section on linear identities characterizes prime and semiprime group rings, brings semisimplicity considerations into play, and offers construction techniques for obtaining primitive group rings. The final part, an exploration of finiteness properties, consists chiefly of a study of Noetherian group rings. Hundreds of exercises of varying difficulty appear throughout the text.