Read the notes for lecture 2, and try the deformation problem. I also wrote some more about Sprouts -- you could try to see if there is a good strategy if you play on a torus. This is your assignment on the Topology unit. Write a page or two about one of the problems discussed in class. So far I have mentioned Sprouts (played on different surfaces) and also given you a deformation problem (what I can expand on next cxlass0. I will also give you a problem about the Mobius strip.

Student’s Name Professor’s Name Course Date Math Problems Problem 1.2. A pretzel has two holes that "hold" a doughnut (see Figure 1.2 (a)). Show that the pretzel can be deformed in such a way that one of its "handles" will unlink itself from the doughnut (Figure 1.2 (b)). The link between the doughnut and the handles can be broken in a continuous transformation of the pretzel can be attained by twisting it in a manner that unlinks them without deforming any shape (Prasolov 2). The first step in unlinking the two is to the initial configuration that involves beginning with the linked doughnut and pretzel. Secondly, continuous deformation is applied to keep the doughnut fixed together and deform the pretzel gradually (McDuff). The pretzel can be envisioned having a structure that is continuously and smoothly stretched bent when being deformed. The third phase is link breaking, which involves pulling the handle away while adjusting the construction of the pretzel ensuring it pulls out of the doughnut during the process of deformation (Prasolov 2). The pulling away of the pretzel from the doughnut will also involve manipulating the pretzel, twisting, and bending to the point the connection between the two is delinked. The final configuration of the system will involve one handle of the pretzel pulling out of the doughnut and being in a new configuration where the two are no longer...