Knot Theroy

The podcast discussed much of the following:
Knot theory is so abstract resulting in obnoxious formulas & numbers stumping calculators, making knot theory interesting, challenging, and valuable. Conclusions are "funny" from research & proofs . The more mathematicians look into knot theory, the "better" the conclusions/formulas become. I thought it was interesting that she connected the theorem to Champagne, but the reasoning made sense. Champagne is an unpractical drink that could cause a headache, much like knot theory. 

Mathematics is constantly being analyzed. Mathematicians expand upon each other's work and manipulate theories in different ways. There are many ways to explain and visualize various things. I think this idea is extremely important for both students and teachers. Just because one person or resource says to do something one way, doesn't mean that's the only way to do it. Same goes for learning styles. Not all kids learn the same way, so utilizing various strategies and methods helps students learn more efficiently. 

Going into this course, I knew absolutely nothing about knot theory and how it connected to the algebra world. This course has been truly fascinating, and I am so happy I took the leap and tried it! Everything we have covered so far has been new and enlightening; from tangles, to knots, to tri-coloration & tangle numbers. 

This course definitely has been challenging in many ways. It took a good couple weeks to finally nail down how to draw the tangles and knots we were working with, but I am finally getting the hang of it! Also, being able to take the concepts we covered in class and directly try to manipulate them at home on my own has been challenging. There have been some weeks where I go home lost and I think to myself, "What the heck did we just do?", but there have also been weeks where I go home feeling confident. I think my biggest challenge is being able to apply the theorems we uncover to specific exercises. I usually work very well with seeing examples first, so that when practicing, I have something to mirror off of. 

I have loved how hands on this class has been. I definitely am a learner that needs hands on instruction when developing abstract concepts. It helps me visualize what is happening, so that I can get the full picture.