De partitiefunctie van Rademacher

Bachelor thesis (2018)

Authors

R.M. Ros Electrical Engineering, Mathematics and Computer Science

Contributors

J.G. Bosman (mentor)
Dion Gijswijt (coach)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2018 Robin Ros
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Published Date

09-07-2018

Language

Dutch

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

There are several ways to write the number 5 as a sum of positive integers, disregarding order. A quick calculation shows that this can be done in 7 ways: 5 = 5, 5 = 4 + 1, 5 = 3 + 2, 5 = 3 + 1 + 1, 5 = 2 + 2 + 1, 5 = 2 + 1 + 1 + 1 and 5 = 1 + 1 + 1 + 1 + 1. In the same way, we can count the number of ways for each integer n. Although this calculation is trivial, a closed form for this function is not as easily obtained as one for combinations, for example. This work formulates and proves Rademacher's formula for these partition numbers. It also tries to uncover some key ideas behind the proof, the supporting theory and other inspirations.