12 Dec 2013 How Math is Changing Movies by Dr. Dorff

the top 20 grossing movies in the world all involved computer animation

he also talked about how the creation of moving characters involves matrix transformation.

the math involved also help us do amazing animation like modeling the water flow when some exterior object changes the water flow

Wednesday December 11 sections 24.1-24.3

1. How did they combine the sum in 24.3?

2. its interesting to see the method they used in proof irrationality and transcendental indirectly

Careers in Math: Goldman Sachs Thursday, Dec 5th, 4pm

Panna Pavangadkar of Goldman Sachs talked about the way technology is important and how it is applied in the company, together with the jobs that a mathematician can get in Goldman Sachs.

She talked a lot about data management.

Friday December 6 sections 22.1-22.2.

1.  I understand why the choice of phi and phai would work, but is it the only choice?

2. I noticed that the determinant equals to (phi-phai)^2, does that tell us an information?

Wednesday December 4 sections 21.5-21.7.

1. how does theorem21.7 fills in the gap for the proof of Vandermonde-Gauss

2. its interesting to see how we can find out the expression of the phi function with equation 21.11

Monday December 2, sections 21.3-21.4.

1. dont quite understand how they got alpha expressed as a function of theta in 21.7/ what has that to do with alpha1^10 lies in fixed field of Q(theta)?

2. interesting to see that we have a general way to solve the nth root of unity

Monday November 25, sections 20.1-20.2.

1. where's the proof for theorem 20.3?

2. interesting to see the multiplicative group again

Friday November 22 sections 18.4-18.5.

1. How is theorem 18.19 different from theorem 15.9?

2. its interesting to see how all the taus cancel out in the proof of Hilbet's theorem

Careers in Math: Careers in Federal Service Thursday, Nov 21th

Careers in Math: Careers in Federal Service

Thursday, Nov 21th, 4pm, 1170 TMCB

Ann Cox, the Program Manager for the Cyber Security Division of HSARPA

Ann talked about the importance of Cyber space security and the consequences of it if our cyber space is being attacked. that could cause traffic system shut down, electricity shut down or even stop the supply of clean water.

the math that she presented has a lot to do with graph theory and is quite difficult to follow...

below are 7 important qualities she think would be helpful to work in the company:

1. technical proficiency is necessary but not sufficient

2. People skills

3. Public speaking

4. Situational awareness: office, enterprise, national

5. know the rules and follow them

6. pay attention to the authorities you work under

7. Leadership

Wednesday November 20, sections 18.1-18.3.

1. some explanation on the proof of Lemma 18.4 would be helpful

2. Why do they use the definition on 18.7 for symmetric?

Careers in Math: Applied Math

Geophysicist and Pension Actuary John Grange will present “Making a Living with a Math Degree.”

John Grange has worked as a Geophysicist for Shell and as an Actuary for twenty some years

His physics minor has helped him getting the job as a Geophysicist.
He has taken two actuary exam, which has really gave him a head start for him to start his actuary career.

skills that are important to employer 
1. computer programming skills, excel especially 
2. communication skills, be able to make complex idea simple and present it to others in an understanding way.
3. some experience

Friday November 15 sections 17.5-17.6.

1. (Defn 17.17) when they say that the elements 2,...,n belong to K, not Z, what do they mean?

2. the way they find the roots of the polynomial over Z2 is interesting

Wednesday November 13 sections 17.1-17.4.

1. what's the difference between the splitting field we learned before and the splitting field in 17.5?

2. Generalization is interesting

Friday November 8 sections 16.1-16.2.

1. old stuff from 371. most materials are familiar. explaining more in detail about quotient ring on irreducible polynomial would be good though.

2. some of the examples in 16.4 is interesting

Careers in Math - Jean Steiner November 8

Quantitative analysis at Google

Jean talked about what she mainly does in Google as a quantitative analysts. in deciding which webpage shows up first when someone search for a certain key word, the engine would calculate how probable it is for people to want that certain website when they typed that keyword.
to calculate the importance of a certain website, a function that has the importance of other webpage that links to the chosen webpage as input, and the importance of the chosen webpage as output.
these importance of the webpages are interrelated, and turns out you can form a matrix with those data, and finding the eigen value will allow you to calculate the importance of each individual webpage.

Wednesday November 6 sections 15.2-15.3.

1. I am missing the point there. why does having three real root implies the polynomial is not soluble by radicals?

2. Is it often still for mathematicians to research on Quintic equations?

Monday November 4 section 15.1.

1. This section has a lot of proofs. Lemma 15.7 is kind of hard to follow

2. interesting to see the connect between radical expressions and soluble.

Careers in Math: Healthcare Thursday, Oct. 31th

Today is about the company Epic, a software developer for the health care system all over US and in multiple nations around the world. 

The company is growing really fast in the past few year, beginning from 2002 the employee size is growing about 20% every year, and it raised from about 800 employees in 2002 to about 6500 employees in 2013.

there's 3 major role that mathematicians would have in the company. 

1. Problem-solver, Technical services

2. Business Intelligence Developer

2. Software Development

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.

Wednesday October 2 Section 7.2.

1. dont understand the part in the proof of theorem 7.5 how by theorem 7.4 would be a power of 2.

2. seems like a very useful way of determining the impossibility of proofs. any shape that requires numbers other than square root of 2 cant be draw with the ruler and compass construction. 

Monday September 30 Section 7.1

1. is the p1 and p2 in figure 7.2 suppose to be the center of the circle?
the Ki notation in this chapter is really hard to understand.

2. its really interesting how the construction of graph can be linked to algebra

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?

just over an hour on average. Lecture helps the most in doing the assignments, but the reading beforehand do help me make sense of the lecture. 

• What has contributed most to your learning in this class thus far?

lecture and homework. office hour is helpful too. If possible, I would like to have extra office hours during this next week so that I can get extra help while I prepare for the midterm

• What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)

I would appreciate more office hours. Also, having a review sheet for the midterm and some past midterm sample to practice on would be really helpful.

Careers in Math 26 Sep Thur

the Career in Math talk didn't really talk about any difficult problems, so I would just write down a few things I found interesting about it.


The talk is about Raytheon, a company that develops innovative technology for National defense.

the speaker emphasize that the problems that they are solving is often very difficult and involve high level math skills. Going to graduate school is encouraged since that gives you much more skills in those problem solving.

they just developed a technology for crowd control. It sends out microwave of certain frequency that will not go pass our skin so wound't cause any damage to body, but makes people under the wave feels uncomfortable, thus able to evacuate a crowd.

Friday September 27 Section 6.2.

1. this chapter's idea is rather easy to understand. the proof of short tower law is a bit hard to follow with all those subscript, but its easy to see how the short tower law works in real example.

2. interesting to see that algebraic extensions need not be finite while every finite extension is algebraic.

Wednesday September 25 Sections 5.4 and 6.1.

1. How is the Lemma 5.14 a restatement of Lemma 5.9? I don't see how the basis in Lemma 5.14 relates to Lemma 5.9

2. interesting to see that the complex number are two-dimensional over the real numbers.
It is obvious to see that the degree of real numbers over the rationals is infinite; what about the degree of the real numbers over the irrationals? would it be one?

Monday September 23 Sections 5.2-5.3.

1. in theorem 5.7, we require the alpha to be algebraic over K just to ensure there exist a polynomial giving a root of alpha? or for some other purpose?

2. modulo rules applying to polynomials looks very useful, since we have developed so many theorems on modulo arithmetic already

Friday September 20 Sections 4.2-4.3 and 5.1.

1. the notation in Definition 4.12 is hard to understand.

2. So Example 4.11 has demonstrated that i + sqrt(5) is enough to generate Q(i,-i,sqrt(5), -sqrt(5)). but with other situations, like if I have a (i)^(1/3), how do I tell if something is enough to generate all the needed elements?

the extension example shows that pi has a different type of irrationality than just square root of like 2 or 3?

Wednesday September 18 Section 4.1.

1. why is a monomorphism being an one to one mapping would maps from a small field to a large field? (K to L) (p.50)

2. so far it seems like in finding Q(X), we only need to try out the possibilities in multiplying some elements to X to get all the possible forms that it generate. Are there examples where we need to look at the inverse also to include all the possible forms the X could generate?

Sections 3.5-3.6 (due Mon Sep 16)

1. the example in 3.23 is a bit confusing. I understand why t^4+2 is irreducible over Z5; but when they go to Z3 suddenly they found a factorization of the polynomial and concluded it reducible. So how do they come up with the factorization in Z3?

2. How is finding the multiplicity of the zeros useful?
in p.45 it points to figure 1.1 when explaining the multiplicity, but I can't find the right figure 1.1

3.2-3.4, Due Sep 13

1. Example 3.13 about proving irreducibility with Theorem 3.12 is a bit hard to understand.

2. The eisenstein's criterion is an interesting way to show an polynomial irreducible.

Sections 2.3 and 3.1 For Sep 11

1. why is the factorization unique in the Division Algorithm proposition 3.1?
its easy to see in real numbers, but how do we know if we cannot expressed the polynomial in another form with complex number?

2. Its interesting to see the extension of prime in integers to polynomials in theorem 3.9                           would the same method be used in finding how to express the hcf into f and g?

1.0-1.4, due on September 6

1. I am still not very familiar and comfortable with using omega (the primitive cube root as defined in the book) to express the multiplicative inverse (like in homework 1.5, I still couldn't think of ways to express 1/(p+qa+ra^2) in the x+ya+za^2 form)

The Cardano's Formula part is a bit difficult to follow.

2. A side question that comes to me while reading page 5: do theoretical Mathematicians (as opposed to Applied Mathematicians that study Math problems with rather immediate practical usage) makes significantly less than Applied Mathematicians?

Also, the existence of Complex number has made much more sense to me when the book explain it from the prospective of the need of solving more and more difficult polynomial equations, how we expanded from N to Z to Q, R and eventually C so that we can expressed the roots of the polynomials. I am interested to know if there's a set bigger than C that is required to solve some equations.

Introduction, due September 6

1. I am a Junior Math major.

2. I took Math 314, 334, 341, 371

3. I am quite interested in number theory, in fact I am hoping to join a number theory research group soon. 

4. Dr. Lawlor is the best. He thinks about how to present the lesson so that we can easily remember the important theorems; He has lots of office hours so I never felt hindered to go asking him questions and most of the things that I am confused during class were answered during that time. Most of all, I see a real sincerity from him in teaching and helping students.

5. I am from Hong Kong, served mission in England. I play Chinese Chess and Go a lot. 

6. The current office is not a problem for me but I would appreciate if there can be office hours on Tuesday and Thursday too (like Tuesday and Thursday around 2 or 3pm)