QUES: In addition to numerous articles on mathematics, Whitehead wrote three major books on the subject: A Treatise on Universal Algebra (1898), Principia Mathematica (co-written with Bertrand Russell and published in three volumes between 1910 and 1913), and An Introduction to Mathematics (1911). The former two books were aimed exclusively at professional mathematicians, while the latter book was intended for a larger audience, covering the history of mathematics and its philosophical foundations. Principia Mathematica in particular is regarded as one of the most important works in mathematical logic of the 20th century.
Who was the intended audience of Whitehead's first two mathematics books?

ANS: professional mathematicians

QUES: Starting at the transition between the Middle to Upper Paleolithic period, some 80,000 to 70,000 years ago, some hunter-gatherers bands began to specialize, concentrating on hunting a smaller selection of (often larger) game and gathering a smaller selection of food. This specialization of work also involved creating specialized tools, like fishing nets and hooks and bone harpoons. The transition into the subsequent Neolithic period is chiefly defined by the unprecedented development of nascent agricultural practices. Agriculture originated and spread in several different areas including the Middle East, Asia, Mesoamerica, and the Andes beginning as early as 12,000 years ago.
In what period did all hunter-gatherers begin to specialize?

ANS: unanswerable

QUES: Steven Waldman notes that; "The evangelicals provided the political muscle for the efforts of Madison and Jefferson, not merely because they wanted to block official churches but because they wanted to keep the spiritual and secular worlds apart." "Religious freedom resulted from an alliance of unlikely partners," writes the historian Frank Lambert in his book The Founding Fathers and the Place of Religion in America. "New Light evangelicals such as Isaac Bachus and John Leland joined forces with Deists and skeptics such as James Madison and Thomas Jefferson to fight for a complete separation of church and state."
What did religious freedom result from?

ANS: an alliance of unlikely partners

QUES: Symmetry groups are groups consisting of symmetries of given mathematical objects—be they of geometric nature, such as the introductory symmetry group of the square, or of algebraic nature, such as polynomial equations and their solutions. Conceptually, group theory can be thought of as the study of symmetry.t[›] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element performs some operation on X compatibly to the group law. In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too). By a group action, the group pattern is connected to the structure of the object being acted on.
What term describes the introductory symmetry group of the square?

ANS:
geometric nature