Reality Checks in Graduate mathematics

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Be harsh to me , convince an enthusiastic little kid why one shouldn't go to graduate school in mathematics.
Be as close to reality as possible.

How when why where..
If you haven't got a sense by now what is real maths like then maybe you should reconcider.
If you had undergrads degree in maths then maybe you wouldn't need to ask this question.
I remember you started a thead on why is math so hard to learn; well it's not, everything in BSc is a child's play, so to speak.
It depends on school.

What do you mean by this question anyway?
I have Masters in maths heading to grad the next year if circumstances allow.

Ed: Well I think it's a long way but it's a journey worth taking.
Reality is that's a tremendous amount of work. I understand how bright ambitious people skim through wikipedia and think they are made for this or that there is not much else to it.
Enthusiasm is the first step and if you stick to the plan then you surely can do anything.
The second step is getting to a decent college. Grad school is miles away unless you're a prodigy, then you probably know more than I do anyway. It's all a matter of process NOT a final destination. You have no clue where life's going to take you but if you feel that maths is for you and you understand what it has to offer then I think you should go for it. Again - it doesn't matter about the grad school, with a good maths degree you can do anything you want. Dive further into its depths or go and be a rich scumbag.

If you do go, make a decision: applied mathematics or theoretical mathematics. If you are not brilliant or genius class, applied mathematics would be better for you.

ruveyn

Everything involved in getting a Master's in math is child's play as well.


I think you mean engineering or some related discipline would be better. Working as an applied mathematician requires brilliance on the same level as being a pure mathematician. An applied mathematician still needs to know topology, real variable theory, abstract algebra, etc, and if you want to get published as an applied mathematician you still need to provide rigorous proofs.

For an applied mathematician the problems are of a more limited scope than creating a brand new field of mathematics or solving a Major Unsolved Problem like the Riemann Conjecture. The very best applied mathematicians are creative, original and skillful but they are trying to do something quite different than the theoretical mathematicians.

Besides applied mathematicians are allowed to "cheat" by using approximations. I think applied mathematicians get to use more weapons to attack their limited discrete problems than do theoretical mathematicians who have to invent their weapons de novo. And usually other people make the weapons for the applied mathematician. Example: Einstein got a free gift from Riemann to attack the problem of covariant laws and gravitation. If Einstein had to invent tensors and curvature from the git go he probably would not have had enough left to solve gravitation.

ruveyn

ruveyn, I think you may be unaware of just what mathematicians, both pure and applied, actually do in their day to day lives.

The pure mathematicians, as a general rule, are not creating new branches of mathematics either. If they were we would have a lot more branches than we do now. And applied mathematicians have come up with new branches. Chaos theory, nonlinear dynamics, bifurcation analysis, etc, all come from applied mathematicians. And applied mathematics has a lot of major unsolved problems, just as pure mathematics does, and applied mathematicians have to try to prove a theorem to settle these questions, just as a pure mathematician would.


Now you are definitely referring to engineers and scientists, not mathematicians of any kind. An applied mathematician must still prove his theorem and is held to exactly the same standards of rigor as any pure mathematician.

just go for it Go for your dream. It's totally doable. If you have the dedication, go for it! You don't need to be a genius to study math.

The top flight theoretical types are busy solving problems (which means proving theorems) that other top flight theoretical types could not. For example the resolution of Fermat's Last Theorem by Andrew Wiles in 1993. The current Holy Grail is the Riemann Hypothesis. I am not sure if the Poincare Conjecture has been cleared up or not.

Occasionally first line theoretical mathematicians find better ways of proving Old Theorems.

And some times they find ways of justifying bad reasoning of the past. For example Abraham Robinson figuring out how to make infinitesimals kosher. He invented non-standard analysis.

In a general way, the first rate theoretical types give us a new way of looking at things. For example Riemann's invention of general tensors nailed down the notion of curvature which was first addressed by Gauss, his mentor. Riemann inadvertently created a cottage industry for the Italian Tensor Mafia.
Which turned out to be very good news for Einstein.

So what do you think is the difference (if any) between first rate theoretical math and first rate applied math?

ruveyn

Why one should not go into graduate mathematics: less money than many other graduate majors and limited job choices in the field.

Why one should go into graduate mathematics: success and happiness will follow if you do what you love and focus on what you are good at.


I was a math major. I took some graduate courses focusing on pure mathematics before dropping out to focus on making a living.

It depends on school!

A grad degree in mathematics, to the job market, only tells prospective employers that you're really smart, because no lay person I know actually knows what pure mathematics is about. A grad degree in statistics, physics, comp science, engineering etc. tells the employer which area you're really smart in, so it increases your chances of getting a job if you look like the exact square peg for his square hole.

But yes, pure math people have more bragging rights than the applied math people - but only in academe.

At the same time you can easily go from a bachelor in pure math to a master in applied math or statistics. But yeah, a simple pure math bachelor degree is not that much helpful.

The best things is to take a minor degree in something else. With a minor physics or computer science you could go into other branches of research like mathematical physics and quantum theory.
Btw, many computer scientist are pretty much pure mathematician. This is the same for theoretical physicists.

Basically just what branch of mathematics they study. An "applied" mathematician might specialize in analysis, PDEs or nonlinear dynamics, while a "pure" mathematician might study topology/geometry or algebra. The applied mathematician still has to prove theorems in order to be taken seriously as a "real" applied mathematician.

The first-rate theoretical mathematicians have as their holy grail the proof of the Riemann Hypothesis, as you said. For first-rate applied mathematicians, the interesting problem is the solution to the Navier-Stokes equations- another Millennium Prize problem, and not something for which a computer approximation is considered acceptable as a true resolution.

There are many people who get degrees in applied mathematics and then work on scientific problems, eg constructing models for various physical or biological systems. These people are generally considered to be scientists in their field of application first, and applied mathematicians second if at all.


Not really. What constitutes a Master's in math is pretty standard and consistent across schools, and none of it is so terribly deep. Some places will water down the curriculum to be a joke, but I was referring to the typical MS math program you might find at a top-flight school.

[quote="Orwell"][/quote]
Everything in life might just as well be a child's play.

Well, the standard for getting a PhD in math is much more daunting. You actually have to come up with some piece of novel mathematics, which is extremely challenging. A course in real variables or algebraic topology may be difficult, but you can basically just sit down with some books and work at it until you get it. Trying to prove a theorem that no one else has proved before... that's another question entirely.

if (!education) ? income = false : income = true ;

I'm kidding. I have a GED and I'm doing fine. You don't need college. It's just a waste of time and money...