This repository holds the tex files and the pdf of presentations and papers that I had to write and give during my studies of Mathematics at Jacobs University Bremen.
This presentation, along with its paper, was an introductory lecture to exapnder graphs and their properties. Neither the presentation nor the paper go into the topic of Random Walks on finite expanders as my focus was to introduce my fellow classmates, who did not have any background in graph theory at the time, to the world of graphs. The paper is a written version of what was said during my lecture. It also provides additional examples and non-mathematical analogies for ease of understanding in addition to the main concepts.
This presentation aimed to introduce the function π(n) which gives the number of prime numbers until n. The main topic of the presentaiton was showing that π(n) is bounded, and those bounds were proven by Chebyshev. The presentation proves Chebyshev's Theorem for weaker bounds.
This presentation aims at giving the basics of analyzing the behavior of fixed points of continous dynamical systems in one dimension. As well as providing defintions of certain concepts such as flows, fixed points, and stability.