What the heck does a mathmatician do?

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Mathematicians with a PhD often pursue careers in academia, research institutions, or applied fields, where they can engage in theoretical work or practical applications. While applied mathematicians typically focus on real-world problems, pure mathematicians contribute by developing new theories and principles that can later be utilized in various scientific and engineering contexts. Some pure mathematicians also find opportunities in industries that require specialized problem-solving skills, such as cryptography or statistical consulting. The discussion highlights the intrinsic value of pure mathematics, even if its immediate practical applications are not always apparent. Ultimately, mathematicians play a crucial role in advancing knowledge and understanding, which benefits society as a whole.
  • #31
matt grime said:
Abstract linear algebra ought to be about linear maps, not matrices, and arbitrary fields, not just over R, or possibly C. Things like the Jordan Canonical form (every linear maps is conjugate to the composition of matrices of two certain types, approximately a diaginal matrix and one with 1s on the places immediately above the diagonal and zeroes elsewhere). It should not be about solving n equations in m unknowns which depressingly a lot of places teach as linear algebra. properly linear algebra is the representation theory of k, field, not linear equations.

You basically summed it up right on.

The problem is that they are still doing it over R and C, which is sad. He tells the students to replace F (field) with R.

I really don't get this school at all.
 
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  • #32
Hmm, that seems a little more than what we are doing. We are not doing Jordan forms (although they are listed in the description of the class), and we will just be starting linear maps this coming up week. The book we are using is Lang: Introduction To Linear Algebra and we will be covering the entire book.
 
  • #33
mattmns said:
Hmm, that seems a little more than what we are doing. We are not doing Jordan forms (although they are listed in the description of the class), and we will just be starting linear maps this coming up week. The book we are using is Lang: Introduction To Linear Algebra and we will be covering the entire book.

Is this your first Linear Algebra course?

This is what I'm using right now...

https://www.amazon.com/gp/product/0130084514/?tag=pfamazon01-20

We will cover just about everything minus a section here and there.

Note: This is my 3rd Linear Algebra course! We have students who didn't know what a basis of a vector space was. Now, the whole class is slowing down and we may not cover much of the text... sad.

The entire responbility of preparing for graduate school rests on my shoulders. You can't really trust my school to prepare you.
 
  • #34
Jason, that's the same text used to teach the enriched linear algebra sequence (MATH 146 and MATH 245) at Waterloo. Just thought you'd like to know.
 
  • #35
devious_ said:
Jason, that's the same text used to teach the enriched linear algebra sequence (MATH 146 and MATH 245) at Waterloo. Just thought you'd like to know.

That's nice, but we aren't learning much from the textbook right now.

The professor basically came to a complete stop and started teaching linear combinations and what not.
 
  • #36
Yeah it is my first linear algebra course. At my school we have only 2 (undergrad) linear algebra classes. One is for engineers (with applications) the other is for math/physics majors (with proofs).
 
  • #37
JasonRox said:
That's nice, but we aren't learning much from the textbook right now.

The professor basically came to a complete stop and started teaching linear combinations and what not.

Don't get me wrong though. He's a great professor, but I think he just slowed down too too much. Far too much actually.

If I were him, I would continue teaching as it is, and only slow down for tutorials. Now, the students who want to learn more are learning things they learned earlier, which isn't good because it was a pre-requisite to begin with.
 
  • #38
mattmns said:
Yeah it is my first linear algebra course. At my school we have only 2 (undergrad) linear algebra classes. One is for engineers (with applications) the other is for math/physics majors (with proofs).

What program are you in?
 
  • #39
Secondary math education right now, but I might switch to pure.
 
  • #40
mattmns said:
Secondary math education right now, but I might switch to pure.

If you love math, go for it.
 
  • #41
JasonRox said:
If you love math, go for it.
I almost definitely will. The problem with Math Education is that I don't get to take that many actual math classes, I would basically be done with Math at the end of this semester. And at the end of this semester I will have taken only: abstract algebra, discrete structures, vector analysis, linear algebra, and general statistics/probability (1 semester of each). And there is so much more math out there that I want to learn.
 
  • #42
Nothing000 said:
What does someone do once they get their PhD in Mathematics? Besides teaching, how many people that get math degrees actually work in the field of math, and get paid for it? Do they just prove theorums and things like that? I can understand that applied mathmeticians can use their kowledge for many practical things, but how do pure mathmaticians contribute to society, besides for knowleges sake by doing math proofs that haven't been done before?


Have you seen the movie "Beautiful mind"?
 
  • #43
heman said:
Have you seen the movie "Beautiful mind"?

I haven't seen it, but is it about mathematics?
 
  • #44
It is a movie based on the life of John Nash.
 
  • #45
JasonRox said:
I haven't seen it, but is it about mathematics?

you should try to see it,,atleast once and you will really like it.
 
  • #46
heman said:
you should try to see it,,atleast once and you will really like it.

Is that the guy who cracked the Nazi code during the WWII?
 
  • #47
They did not tell about the name of the code in the movie but yeah he broke some very big code during WorldWarII..was projected as the biggest codebreaker in the movie and i didn't look for the litereature in reality.
 
  • #49
I don't think he broke a big code in WW2. The movie is set post WW2, even when he is in school. If you recall, the opening seen has the deen of the school saying that it was the mathmaticians that stopped the war, implying they played a large role in the development of the atomic bomb. So I guess that code that he breaks was just something dealing with the cold war.
 
  • #50
Nothing000 said:
I don't think he broke a big code in WW2. The movie is set post WW2, even when he is in school. If you recall, the opening seen has the deen of the school saying that it was the mathmaticians that stopped the war, implying they played a large role in the development of the atomic bomb. So I guess that code that he breaks was just something dealing with the cold war.


just wait i am downloading the movie to see ..if that is true:approve:
 
  • #51
It is true. He was still in school AFTER WW2. Just look up John Nash and read about when he was born and when he went to school, there is no need to download the movie.
 
  • #52
it takes 1 min. to download movie..

the year was 1953,,
"and the code related to radio transmission from moscow"
so you are absolutely right.
 
  • #53
I thought he got a nobel in economics ?!?
 
  • #54
Alan Turing was one of the people who cracked enigma at Bletchley Park (do none of you know your history?!), father of modern computing, Turing test and all that. Nash got the Nobel Prize. He founded (non-competitive) game theory, look up Nash equilibrium.

There is a film about Bletchley called 'Enigma' (starring Rachel Weisz, or Kate Beckinsale or someone like that). Also the Enigma machine was captured by members of the Royal Navy, not American submariners contrary to U-571 another rubbish film saved only by Jon Bon Jovi's comical demise.

Turing killed himself, and Nash was institutionalized for psychiatric disorders that are sadly twisted in the film version of his life. The (pretty much completely fictional in many ways) film A Beautiful Mind apparently has a 'dream' or delusion that he thought he was helping crack some code, when he wasn't.
 
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  • #55
matt grime said:
U-571 another rubbish film saved only by Jon Bon Jovi's comical demise.

LOL! I am glad I saved my $8!

Jim Simons is a mathematician, and a billionaire?:smile:

...maybe I shouldn't be too surprised.
 
  • #56
back to linear algebra. if you are not challenged by your line alg class, please download my 15 page linear algebra book, from my webpage, and see if you can follow it, filling in the details. it goex beyond jordan normal form in only 15 pages. see how good you are.

http://www.math.uga.edu/~roy/
 

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