In this diploma thesis, we will introduce discrete harmonic and analytic functions. Definitions will be based on definitions and theorems, known for harmonic and holomorphic functions. That is why we will start the diploma thesis by defining harmonic functions. We will show that the average value of a harmonic function over a ball is equal to the value of this function at the center of the ball. We will then define holomorphic functions and prove Morera's theorem. We will define some basic terms in graph theory, and in the last part of the thesis, we will define discrete harmonic and analytic functions. We will give examples for both.
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