Should I Become a Mathematician?

[dkotschessaa]

I would think any research would show favorably for math, especially something as math intensive as physics, unless I'm mistaken.

 

[Dougggggg]

The conversation about other languages has me wondering if when you go to different countries how much does the mathematical language change, in both english and non english speaking countries?

 

[dkotschessaa]

The conversation about other languages has me wondering if when you go to different countries how much does the mathematical language change, in both english and non english speaking countries?

Maybe another thread should be started? This is a topic I find interesting.

What I've found with languages is that technical terminology is less likely to have evolved far from it's latin roots, so many of the words are cognates. Look up "quadratic" in Google translate and you'll find that the term is similar. (cuadrático in spanish and portuguese, quadratisch in German).

I think the non Indo-European languages have adopted the latin or english terms, so they might still have cognates, but I have no evidence of this since google translate renders the translations in whatever script the language uses.

Though I did find that Icelandic translates "quadratic" as "stigs."

I'm not sure what you're asking in reference to English speaking languages though. You mean perhaps British English as opposed to American English or something? I've found that when languages start to diverge, it's usually the more "common" dialog that changes - and that technical terms, again, don't change much, probably because they are more precise. Though in England you might say "formuler." :)

-DaveKA

 

[Dougggggg]

Maybe another thread should be started? This is a topic I find interesting.

What I've found with languages is that technical terminology is less likely to have evolved far from it's latin roots, so many of the words are cognates. Look up "quadratic" in Google translate and you'll find that the term is similar. (cuadrático in spanish and portuguese, quadratisch in German).

I think the non Indo-European languages have adopted the latin or english terms, so they might still have cognates, but I have no evidence of this since google translate renders the translations in whatever script the language uses.

Though I did find that Icelandic translates "quadratic" as "stigs."

I'm not sure what you're asking in reference to English speaking languages though. You mean perhaps British English as opposed to American English or something? I've found that when languages start to diverge, it's usually the more "common" dialog that changes - and that technical terms, again, don't change much, probably because they are more precise. Though in England you might say "formuler." :)

-DaveKA

I am thinking about going to the University of Edinburgh for graduate school and I may even look at other schools possibly too, whatever school is best for me even if it is a different culture. I also like the idea of possibly doing some study abroad type things as well.

 

[uman]

One annoying example is that in France, open intervals are written with square brackets going the other direction, as opposed to parentheses. For example, what Americans write (0, 4] would be written ]0,4] in France.

 

[Dougggggg]

One annoying example is that in France, open intervals are written with square brackets going the other direction, as opposed to parentheses. For example, what Americans write (0, 4] would be written ]0,4] in France.

That would take some getting used to. There is probably somewhere on the internet that has important changes in translation in mathematical things. Maybe not all the way down to every word that you would learn in learning the language itself.

 

[qspeechc]

One annoying example is that in France, open intervals are written with square brackets going the other direction, as opposed to parentheses. For example, what Americans write (0, 4] would be written ]0,4] in France.

Sometimes confusion can occur when we write (0,4): is it an open interval of the real line or an ordered pair? The French system makes more sense to me.

 

[matqkks]

Isn't the French notation more intuitive?

 

[hunt_mat]

It's the french for you. Going against all other conventions just to be unique.

 

[dkotschessaa]

Back to the topic of reading great mathematicians, I could use some help in ":https://www.physicsforums.com/showthread.php?t=459668"[/URL]. I didn't want to divert the current thread for this topic.

-DaveKA

 

[mathwonk]

dk, the link did not open for me. where is it? basic advice though, just read them, as much or as little as you can, you will definitely benefit. I thought I was a smart guy, but I made no progress at all (reading textbooks and listening to course lectures) until I spent time around actual mathematicians, listening to them talk and watching them work. However I did benefit later from reading great mathematicians. textbooks don't do much. they do something, but not all you want. it is a little like my friend the sword master asking me why his teacher was teaching him a certain move, and I conjectured that at a crucial moment he would understand. My belief was that he was being taught something that would help him in danger, instinctively. There are exceptions - some very dedicated and gifted people can improve slowly by practice and routine instruction, but some of us need and blossom under personal and inspired tutelage. Everyone, even the most modest among us, benefits from reading the masters. These are referred to as people who may not be saints, but who have "been with saints".

 

[sponsoredwalk]

https://www.physicsforums.com/showthread.php?t=459668

 

[Periotic]

Yeah, but I would rather be Theoretical Physicist. :shy:​

 

[Mariomaruf]

I'm a freshman in high school who has spent tedious years dealing with the school system and what you might call it's ignorance when evaluating the student body for candidates who want a future career or passion which they are dedicated towards, but this year my high school allowed me to change everything that was holding me back for so many years. Right now, I'm in AP Calc, but you could say I pretty much learn nothing new there because I'm so far down the road of math that calculus is just an elementary tool I use for some higher things. I teach 6 kids: an 8th grader, a high school freshman, two high school juniors, and two high school seniors; and doing so is helping me to understand what the students' individual needs are, and how they choose to interpret math. We're all blazing through the curriculum at just a little faster than university speeds, and it always makes me proud when we can do that and they understand it well even with sprinkles of upper level theory, so well in fact that they go to teach others.

I'm also taking AP Chem and AP Bio if it matters, and my counselor is seeing what he can do to get me into undergrad/grad work at Princeton next year, so it's nice to finally have all of my education set straight for me. I won't say how I got them to recognize me, but I will say that I'm about up past analysis and intermediate topology.

I'm really not sure what to do right now, but I'm really worried that the pure math that I really love to do won't be able to get me a good job or anything, so what I really want to know is

A) Where do I go from topology?
B) What do I do after my Ph.D in math?

 

[Boogeyman]

Does anyone take part in the International Mathematics Olympiad?

 

[tcbh]

I'm a 2nd year math major at a quarter school. I've already taken the first upper division course in Linear Algebra (goes up through IP spaces, Normal and Self-adjoint operators and Diagonalizability) and the second quarter isn't a graduation requirement. But I was wondering, do most grad schools expect that applicants will have covered subjects like Dual Spaces or Jordan Canonical Form?

To be honest, I've found analysis much more interesting, and I'd like to take a few classes on logic. The 2nd quarter of Linear Algebra is only offered once a year, so by the time I take it many quarters will have passed and I'm afraid I'll be a bit rusty. I'm not even sure what would be the most important material to review.

 

[mathwonk]

@ Periotic: Is there a difference?

 

[mathwonk]

@Mariomaruf: Have you read some of the early pages of this thread? There is a lot of general advice there.

Would you say you have mastered calculus at the level of the book by Spivak? And is your topology at the level of Munkres? If so, you are indeed sailing along.

There are always jobs for pure mathematicians at a certain level, as professors in university, and the pay is not terrible, especially at places like Princeton.

As to what to do next, if you only know calculus at the high school AP level, then read Spivak. If you are already really past that and know only some beginning analysis, you might try Rudin, or a complex analysis book like the one of Cartan, or Lang, or easier, the one of Frederick Greenleaf.

Since your studies seem specialized in topology and analysis, you might start learning some algebra, such as from Theodore Shifrin, or even Michael Artin. Or maybe you should begin with linear algebra, such as from Friedberg Insel and Spence, or Shilov, or Hoffman and Kunze.

There are a number of free sets of course notes on my website as well, whatever they are worth.

 

[mathwonk]

tcbh: yes jordan form is always tested on the algebra prelim exam at UGA. and dual spaces are fundamental in many areas of math including analysis.

You might get some use out of the free course notes for math 4050 or 845, on my web page:

http://www.math.uga.edu/~roy/

 

[mathwonk]

I'm sorry Boogeyman, I wasn't in the Olympiad. You might email Malcolm Adams, or Valery Alexeev at university of georgia math dept for information, or Valery's son Boris, who is a grad student at Princeton:

http://www.math.princeton.edu/~balexeev/

I think Boris at least took the Putnam exam, and Valery may have been in the Olympiad.

 

[sponsoredwalk]

Hi Mathwonk, just reading some of the notes on your website & I think I've found a small
error, apologies If I'm wrong or if it's been pointed out countless times before

7. Math 4050. Advanced undergraduate linear algebra:

http://www.math.uga.edu/~roy/4050sum08.pdf

On page 2 in the axioms for k x V → V (scalar multiplication axioms)

5) “associativity”: for all a,b, in k, and all x in V, (a+b)x = ax + bx;

7) distributive over addition in k: for all a,b in k, all x in V, (a+b)x = ax + bx;

Shouldn't 5) be:

5) “associativity”: for all a,b, in k, and all x in V, (ab)x = a(bx) ?

I checked the book "Linear Algebra Thoroughly Explained" (page 8)" to make sure,
Either everyone skipped over it as your notes tell them to or I'm just confused, it's late

I'm a 2nd year math major at a quarter school. I've already taken the first upper division course in Linear Algebra (goes up through IP spaces, Normal and Self-adjoint operators and Diagonalizability) and the second quarter isn't a graduation requirement. But I was wondering, do most grad schools expect that applicants will have covered subjects like Dual Spaces or Jordan Canonical Form?

To be honest, I've found analysis much more interesting, and I'd like to take a few classes on logic. The 2nd quarter of Linear Algebra is only offered once a year, so by the time I take it many quarters will have passed and I'm afraid I'll be a bit rusty. I'm not even sure what would be the most important material to review.

https://www.amazon.com/dp/1402054947/?tag=pfamazon01-20

 

[sponsoredwalk]

What you wrote is commutativity. (ab)x = a(bx)

Check page 8 of the linear algebra book I linked to, they say:

The associative property of the multiplication of numbers with respect to scalar multiplication:

(ab)x = a(bx)

They give only 4 porperties for scalar multiplication vector spaces &
commutativity is included seperately, unless there is something
deficient in this book I don't think it's wrong.

edit: lol @ deleted post, thought I just got another response that wasn't
showing up on the thread, common enough to scare me

 

[Shackleford]

Check page 8 of the linear algebra book I linked to, they say:

The associative property of the multiplication of numbers with respect to scalar multiplication:

(ab)x = a(bx)

I immediately deleted my post. It was a knee-jerk post. Matrices do not generally commute.

 

[Ryker]

Check page 8 of the linear algebra book I linked to, they say:

The associative property of the multiplication of numbers with respect to scalar multiplication:

(ab)x = a(bx)

Yeah, you're right about associativity, that is (5), although I'm sure this is just a typo on mathwonk's side.

 

[mathwonk]

thank you sponsored walk! i suspect this means you are the first person to read these notes!

 

[mathwonk]

notice how i cleverly avoided such errors in the defn in my shorter notes "rev lin alg", p.1, line 7,

http://www.math.uga.edu/%7Eroy/rev.lin.alg.pdf

 

[Dougggggg]

First day of DE and I think I have feel in love. It takes everything I learned in Calculus, puts a spin on it, and makes it more useful.

 

[mathwonk]

Douggggg, you might enjoy reading pages 17-20 of those same notes from my web page for math 4050. I.e. "Jordan form", the hardest topic in beginning linear algebra, is nothing but the matrix of a constant coefficient differential operator in a standard basis given there. oops, pardon me I pronounced your name wrong, Dougggggg.

 

[Dougggggg]

Ha, I will check it out, I haven't gotten to Linear Algebra yet, but I will check it out for sure. Can I find it through one of the links above?

 

[mathwonk]

here is the linear algebra book link:https://www.math.uga.edu/sites/default/files/inline-files/4050sum08.pdf

 

[Dougggggg]

Wait, did you write this? It seems like everything is pretty well stated. I do think I may need a bit more studies before I can truly understand all that to a level I would like but it seems really clear and laid out.

 

[raff]

Is the quick way really the quick way...

I have a MBA in Finance and want to eventually get a Master's in Math. I see two learning options:

1- Use standard University Fare: Stewart for Calculus, Boyce for DE, Lay for Linear Algebra, etc.

This way "looks" quickest and easiest. For example, I did all of the problems in a section of Stewart and they were painless. Boyce also seems very clear and well explained.

2- The other way is to choose more demanding texts. For example, Apostol or Spivak for Calculus, Hubbard or Robinson for DE, Halmos and/or Axler for Linear Algebra, etc.

This way will be challenging but much more interesting. I read a section of Apostol, it took me days to fiqure out one of the harder problems.

My purpose in getting the Masters in Math is not to become a Mathematician rather to work in Quantitative Finance.

My question is whether I will really be "saving" time by choosing the 1st path.

Another question, I read Lang's "Basic Mathematics" as a refresher prior to beginning my MBA. It is a great book; he assumes intelligence. His introductory books on Calculus (the initial versions) and Introduction to Linear Algebra seem much shorter than standard books. How does Lang on Calculus compare to Spivak or Apostol?

 

[tcbh]

tcbh: yes jordan form is always tested on the algebra prelim exam at UGA. and dual spaces are fundamental in many areas of math including analysis.

You might get some use out of the free course notes for math 4050 or 845, on my web page:

http://www.math.uga.edu/~roy/

Thanks. I just noticed that it's on the basic exam here too. I guess I have another year to decide

 

[Mariomaruf]

@mathwonk

I already did Shilov's Linear Algebra , tenenbaum and pollard's Diff Eq's, and Rudin's Real/Complex Analysis. Stockton is letting me go there on Tuesdays and Thursdays to learn what they call advanced calculus starting next week, where I spend the first half of the high school day here and the second half at stockton, and I'll also be dropping AP Calc and picking up Physics C. I'll try those books on Abstract Algebra because I've only rarely seen what it is, but I think my understanding of Calculus is fairly full fledged, and this class will sharpen it a little for me.

 

[mathwonk]

those 4050 notes are the lecture notes i wrote for my summer course. If they help I am truly delighted. on my web page are more detailed notes for math 845, in the 843-4-5 sequence that are much more thorough. also the notes for math 8000 are also there, but more sophisticated than the 4050 notes.
mariomaruf, you sound very advanced. as such, you will get lots of help, but if i can help i will be glad to do so.

take a look at artin's algebra, spivak's calculus on manifolds, or loomis and sternberg advanced calculus (free download from sternberg's web page), arnol'd's ODE, and some of my free notes on my web page, like math 843-4-5. check out also milnor's topology from the differentiable viewpoint.

edit years later: you know, unless my notes really call out to you, I have to admit they totally violate my advice to read the masters. However one very good student did tell me they helped him prepare for prelims in algebra.