Chapter 39 Canonical Form of van der Waerden's Theorem
Project by: Alison Liang and Peter Tran.
\(\textbf{Summary:}\)Our project is to become experts on the Canonical form of van der Waerden's theorem and its proof. In our final presentation, we had demonstrated our understanding of the theorem and provided a more approachable way for the class to deepen their understanding of van der Waerden's theorem.
For the presentation, we have adopted the elementary proof for the theorem since it only requires basic calculus and some knowledge from the class. The core of the proof is to use Gallai-Witt's theorem, which is a consequence of the Hales-Jewett theorem.
From this project, we got an opportunity to walk through what does a project looks like in research. From looking for references and understanding the ma- terial, to constructing the proof, these are all valuable experiences that help us to become more successful as mathematicians. Also, working in a team helped us become more responsible and kept us motivated throughout the project.
\(\textbf{Canonical form of van der Waerden's theorem:}\)
