Algebraic number theory is a foundational branch of mathematics that investigates the properties of algebraic numbers and their relationships through the lens of field extensions and rings of integers ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

THE general outlines and the methods employed by the author will be familiar to readers who have seen the first volume. He has made a study of standard works and papers by Bachmann, Hensel, Hubert, ...

Diophantus of Alexandria revolutionized algebra with Arithmetica, pioneering symbolic notation and abstract number theory.

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. §14.2 Algebraic Topology. Topology is generally introduced as I described it in §AG.6, ...

You scrambled up a Rubik’s cube, and now you want to put it back in order. What sequence of moves should you make? Surprise: You can answer this question with modern algebra. You might remember ...

Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve. The equations are fundamental to maths as well as science, where they have broad applications ...