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