UWEC CERCA 2025

Liouville’s theorem is a fundamental result in complex analysis which has profound implications across various fields. The theorem states that if a function is both bounded and entire, then it must be constant. These seemingly simple constraints on a function lead to powerful conclusions, as Liouville’s theorem demonstrates its importance in proofs such as that of the Fundamental Theorem of Algebra. This presentation will explore the proof of Liouville’s theorem, highlighting its reliance on Cauchy's integral formula.