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> In the 19th century, impelled by strange coincidences in the theory of infinite sums and integrals, mathematicians began to develop a theory of calculus for functions of a complex variable. What they discovered was a surprising and beautiful geometric structure, which was quickly linked to the burgeoning physical theories of electromagnetism and fluid flow, revolutionized the study of differential equations and number theory, and ultimately inspired the modern field of topology. The goal of our class is to explain and understand those developments. We will begin with a visual exploration of the complex numbers, and proceed to develop complex calculus and the geometric constructions associated with it. Along the way, we will investigate connections with fourier analysis, physics, topology, music, and cartography. The class is also a case study in why mathematics is awesome: how seemingly simple questions lead to beautiful structures, surprising connections, and, of course, more questions.
Helpful Links:
- [Google Group (mailing list)](http://groups.google.com/group/after-klein)
Class-by-Class Notes:
- [Lecture 1](ClassJune26)
- [ClassJune28](Fourier Series)
- [Lecture 2](ClassJune28)
- [Lecture 3](ClassJuly5)
Problems:
- [Problem Set 1]()
- [Problem Set 2]()
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## Using LaTeX Math
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