The connection between addition and multiplication

Описание: You can use the logarithm and the exponential function to go back and forth between the addition world, and the world of multiplication. But the deepest connection, in my opinion, comes from the relationship between lie algebra's and their associated lie groups.

A very important property of the exponential function (if not the most important) is that it has a power series expansion. This power series allows us to define exponential or logarithm of matrices.

Furthermore, when you use addition and multiplication to create polynomials, you need to know about polynomial rings, their algebraic varieties, and corresponding ideals. But a very important role is also played by rotational symmetry groups.

This video series is an attempt to develop intuition about the true nature of the relationship between lie algebra's and lie groups from a geometric point of view, while also covering a number of various concepts which constitute the foundations of algebraic geometry.