Math-S 415 Honors Complex Analysis
Complex analysis is, according to a physicist I met, “The only subject clearly created by God.”
We will get to see why. For example:
1. Take the number e, and raise it to the power pi times i, and add 1…you get 0.
So the five most fundamental numbers in the universe are related by a single beautiful equation.
2. The Fundamental Theorem of Algebra: every nonconstant polynomial has a root in the complex plane.
3. The usual definition of being differentiable, applied to functions from the complex plane to itself, turns out to be equivalent to the condition that the function preserves angles (at places where the derivative doesn’t vanish.)
4. A complex-differentiable function is determined by its boundary values.
5. Complex analysis is the birthplace of topology, algebraic geometry, and analytic number theory.
Come join us!!!
Questions? Need permission? Contact instructor Kevin M. Pilgrim pilgrim@indiana.edu .
Filed under: Academic Help
iubmath 