Friday November 1 section 14.3.

1. I don't quite get when they introduced the variable x in the proof of 14.15. what is x?

2. where does the proof in 14.15 fails if p is composite?

Wednesday October 30, section 14.2.

1.  need some explanation on the proof of Theorem 14.6, why G is abelian and why every element of G generates a cyclic subgroup implies G is cyclic
2. its interesting how we can indirectly proof corollary 14.8 about solubility of Sn.

Monday October 28, section 14.1.

1. I saw the examples in 14.2 but I think more explanation on that would be helpful.
so I am free to pick any subgroups that would satisfy the required condition?

2. Know the G is soluble tells us a lot about the subgroups of G

review Oct 25

review

Careers in Math: Katherine Socha 24 Oct

Katherine demonstrated how we can apply the math knowledge and theorems we have into the real world by making some very general assumptions. 

She showed the example of understanding how wave speed and wave length correlates.

Then she also showed how we can understand the pendulum motion through simple differential equations.

Turns out that we a little bit of differential equations knowledge, you can analysis what region of fluid would move inside the jellyfish's belly and what region of fluid would get pushed away. 

I think what I got from this talk is that there are really a lot of interesting problems we can solve with the math that I am learning right now, applying the math into real life takes some creativity, but once you found the relation and were able to model it you get beautiful result and your understanding of that certain phenomenon is enhanced so much.

Wednesday October 23 section 13.1.

1. Galois Theory has made so much more sense with the example shown in this chapter. Most application of it makes sense. In number 8 of the example, I suppose the goal is to first look at the operation, then find out what's fixed inorder to get the right coefficient, finally grouping the terms to get a single term that can represent the fixed fields? How do I know what form I am expecting ( (1+i)E in the example)  , or do I just have to try until I found the element?

2. When the Galois group is not isomorphic to a dihedral group, can I still draw a picture like the one in the book?

Monday October 21 section 12.1

1. The notation in the definition of Fundamental Theorem of Galois Theory is really confusing. I would like to see some examples on how that work, especially how * and + works.

2. Its interesting to see the close correspondent between the intermediate fields and subgroups of the Galois group.

Internship information session

Five students who have done internship during their undergraduate years where invited to talk about their internship experience

They mentioned about being proactive in presenting yourself if you want to do well in an interview.

Programming skills is useful to have in getting a variety of internship.

A lot of them involved in internships that asked them to program instead of just doing math, they think what the companies look for more is your problem solving skills instead of specific math knowledge.

However to be honest, since I am looking to go to graduate school right after, I would rather spend the extra time I have in doing undergraduate research than to go for an internship.

Friday October 18 section 11.2.

1. the second equivalent statement in Theorem 11.9 is a bit hard to understand


2. We can obtain information about whether L:K is normal by looking at its Galois group according to Theorem 11.14

Wednesday October 16 section 11.1.

1. Isn't Proposition 11.4 something we've proved before?

2. the figure 11.1 is interesting. Does drawing the picture with one continuous hand (like we can draw a three valve or five valve star with one hand but not a four valve star) relate to the way we can construct this K-monomorphisms?

Wednesday October 9 section 9.1.

1. The isomorphism part in Lemma 9.5 and Theorem 9.6 is a bit difficult to understand.

2. so determining whether a polynomial split over a field is essentially unfolding all those linear factors containing the root and see if it match?

Savage teach award - Dr. Jarvis

This talk is inspiring. It is surprising to me how much role hard work plays in doing well in Mathematics. The study those psychologist have done really reflect that out brain can be developed according to how we train it, by doing more problems, allowing out brain to think, just like how we exercise our body and get better on it.


It is also interesting that Dr. Jarvis pointed out that Asians do well in Math greatly due to their determination in working out the problem. That they spent more time in the problem then American thus causing them a better performance.

I like the quote he posted: "learning is a struggle." that we must struggle if we want to learn. That we must go for the challenging problems if we to improve.