Wooster Woodruff Beman
Most acclaimed
Solid geometry
1899
In world history, post-classical history refers to the period from about 500 CE to about 1450 or 1500 CE, roughly corresponding to the European Middle Ages following the decline of the western Roman Empire. The post-classical period is characterized by the expansion of certain civilizations geographically, by ongoing wars fought over land, resources and religion, and by the development of trade networks between often-distant civilizations. This period is also called—with various implications and emphases—the medieval era, the post-antiquity era, the post-ancient era, or the pre-modern era. In Asia and the Middle East during this time, the spread of Islam helped produce a series of caliphates which fostered the Islamic Golden Age, leading to advances in science and greater trade between those in the Asian, African, and European continents. East Asia experienced the entrenchment of the power of a unitary and Imperial China, the dynastic governance and culture of which influenced Japan, Korea and Vietnam.
Elements of Algebra
This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems. Algebra has a pedigree stretching back at least as far as Euclid, but today its connections with other parts of mathematics are often neglected or forgotten. By developing algebra out of classical number theory and geometry and reviving these connections, the author has made this book useful to beginners and experts alike. The lively style and clear exposition make it a pleasure to read and to learn from.