The Should I Become a Mathematician? Thread

Mariogs379

@mathwonk, do you know of a good real analysis book for R^n? I hear Baby Rudin's treatment of it is awful...(not that I liked the first half of Rudin...)

Snow-Leopard

What do you mean by good, Level Low to Rudin or High. I have used 3 books in this order to Real Analysis, Lang to Rudin to Royden.

Mariogs379

I guess same level as Rudin would be good but more expository, clearer, etc...

A. Bahat

Try Spivak's Calculus on Manifolds, or maybe Edwards's Advanced Calculus of Several Variables.

mathwonk

I have often recommended books by sterling berberian and by george f. simmons. look at the first few pages of this thread as well as at the thread on mathematics books.

http://www.physicsforums.com/forumdisplay.php?f=225

dkotschessaa

I'm not sure if I've asked this before - but if I want to go for a PhD after I get my bachelor's, wouldn't it behoove me to go straight for it rather than a masters? And to do it in the same place I get my Bachelors?

A couple of considerations:

Being older and married, it's not easy to think about just picking up and going somewhere else for graduate school. And as a PhD student I'd be at least semi-employed. Right now my wife is supporting me. She doesn't mind - sort of - but does occasionally inquire (understandably) just how long this is going to take.

I'm starting to think I would like teaching, even though I hadn't considered it much before. I've been having very good experiences in peer leading and tutoring. Not to mention I've had some really bad professors who make me go "hmm... I could do that better... if I knew the subject anyway."

Worried that if we have kids in the next year or so I'd be somewhat of an absentee parent though.

mathwonk

Is is usual to enroll directly in the PhD program and not stop for a separate masters. I got a masters by default part way through my PhD program, which was a good thing since I did not finish the PhD that first time through. At my school the masters requirements were a subset of the PhD requirements so all I had to do was apply for the MA after satisfying them.

It is usual to change schools from BA to PhD, just to gain more mathematical exposure, i.e. to meet more people and more perspectives, and to choose a place that has a specialty in your area of interest. But in special cases it is not unheard of to stay where you are, and having a family and a local job is such a special case.

There have certainly been successful PhD candidates at UGA who were undergrads there, indeed some of the best and brightest undergrads just went straight on without moving away.

Regardless of choices, getting a PhD in math is very demanding on you and your family. So choose a good advisor and supportive department. if you already have one, I would not take it for granted that it can be reproduced elsewhere.

dkotschessaa

Thanks as always for your encouragement (tempered with a kind dash of reality).

One of the things I really like about my university is the environment. I've gotten to know many of them quite well and they've been extremely supportive.

I'm sure it wouldn't be easy. Right now I find it hard to take more than 2 math classes during a semester without falling behind. This makes me nervous about *any* grad program, given the pace. But getting paid, even just a little, to advance my knowledge? Beats working in I.T. again.

It's a bit to early to decide exactly what I'll be doing, but I am trying to map out all the possible avenues right now.

-Dave K

tinylights

Just to follow up on my math crisis upon getting into Calc II... just got back results for the first test! I got a 95%! Guess I won't have to become an English major after all lol :)

QuantumP7

My math obsession has totally screwed up my sleep schedule.

dkotschessaa

It's worse than video games sometimes.... No electronics required!

didu205

I quit my lovely girlfriend just to have more time doing math and physics.
I also stop playing video games and also playing guitar often.

Im on my last year pursuing an bsc degree majoring in pure math and applied maths, im also doing extra physics modules as i want to go for a msc in theoretical physics or even up to a phd if im lucky.

many dumbass told me why doing maths, physics while i already had a nice degree and job in computer engineering, they told me mathematician and physicist is a waste of time and lot of ashole things.., i told em Hey u know what i'm doing math and physics as i love the subject, not for getting extra money, if there wasnt math and physics u would still be in stone age dumbass.

mathwonk

"I quit my lovely girlfriend just to have more time doing math and physics.
I also stop playing video games and also playing guitar often."

Hmmm...Isn't that sort of like having a diet where you only eat one type of food, like maybe liver pate'?

As founding math advisor, I cannot in good conscience fully support your judgment here.

QuantumP7

I don't have anywhere near the experience that mathwonk does, but I have to agree with him here. I was trying to power my way through Spivak's ch. 5 problems (there are 41 or 42 of them, and this my first time doing epsilon-delta proofs, so it took me a while), but I found myself getting frustrated and a little bored. I actually took a few days off from doing math to play some computer games, and when I went back to doing math, I was happily doing the rest of the problems.

Math is a great girlfriend/boyfriend. But sometimes you've gotta take a breather, and let your bf/gf take a breather, too, ya know? Absence makes the heart grow fonder. <3

P.S. I made it through Ch. 5 unscathed. And could probably do epsilon-delta proofs in my sleep now.

dkotschessaa

I think with certain endeavors it is natural to have a period of time where you might hyperfocus/obsess a little bit about it. I know when I first got into music I did that. Hopefully you come back out of the cave after awhile.

My approach to things these days is more balanced, but if I were a 20something college student I would probably do the same for math.

Mariogs379

@mathwonk, just accepted to the Brandeis program!

pretty sure I'm going this fall!

RJinkies

Hercuflea> Is it possible to receive an applied math Ph.D, but do your dissertation in some other area of science or engineering? I am asking because I want to get a solid foundation on some mathematics courses (functional analysis, advanced and numerical linear algebra, ODE's, PDE's, hilbert spaces, several complex variables) at the graduate level, but I would not really have a chance to take all of these courses if I did an engineering Ph.D. However It seems like it would be the best of both worlds if I could go for an applied math Ph.D. and do my dissertation in nuclear fusion which is ultimately my intended research interest, whilst being able to get the solid mathematical background. Do you know if this is a common thing to do in applied math programs?


Well it sounds like you want a Physics PhD in fusion and do research there, and you'd like a math PhD as well. Now i'm not qualified in any way or form, but i would think that I'd tailor yourself to go the Mathematical Physics route, do all the plasma stuff in grad school, but balancing yourself evenly on the mathmatics side and the physics side, from what i seen with undergrad mathematical physics options, it's a physics degree with lots of useful and unusual math, and depending on your interesting you can go the math route or the physics route.

And there is the option of doing a physics degree and then a math degree if you really wanted to spend the time money and energy... or you could just choose a balanced physics degree, and hopefully both interests are coherent enough so you don't feel like you're in two worlds of really hard learning...

I'd like to know what courses you took, and what your feelings were on the different math and physics courses, and what higher classes you're curious about in the physics and math both...

and what you'd like to do with all that applied math... etc

---

I mean i think you could get 70% of what you want with a MA in Plasma Physics


after you take [usually] a 4th year undergrad course in introduction to Plasma Physics

this might open up:

----
a. Phys 507 - Plasma Physics
b. Phys 532 - Plasma Dynamics
c. Phys 533 - Laser Physics [less weighty]
d. Phys 531 - Advanced Plasma Physics - seminar course [less weighty]

e. Math - PDE's
f. Math - Functional Analysis
----

and you could do some of the courses in quantum or nuclear physics/particle physics later with more math courses with the next hoop..


As for the math, i would feel that the best path would be the 'typical' mathematical physics route, and the grad math stuff, you just buy the books on your own time, or just balance things semester by semester with your physics as the main route, packing on a deadly math course a little at a time.


i would think that as an undergrad you'd aim for 70% of this outline... and if you take an extra year for your degree, maybe you dont need to take as much in grad school...

But the ideal undergrad degree, would be this:

Mathematical Physics
------------------------------


Calculus
------------
Math 151 Calculus I
Math 152 Calculus II
Math 251 Calculus III
Math 252 Vector Calculus I
Math 313 Vector Calculus II / Differential Geometry
Math 466 Tensor Analysis [needs Differential Geometry]
Math 471 Special Relativity [needs Differential Geometry and Butkov] [Butkov needs Diff Eqs and Griffith EM]

Analysis and Topology
--------------------------
Math 242 Intro to Analysis
Math 320 Theory of Convergence [aka Advanced Calculus of One Variable]
Math 425 Introduction to Metric Spaces
Math 426 Introduction to Lebesque Theory
Math 444 Topology

Differential Equations
------------------------------
Math 310 Introduction to Ordinary Differential Equations
Math 314 Boundary Value Problems
Math 415 Ordinary Differential Equations [needs Complex Analysis]
Math 418 Partial Differential Equations [needs Differential Geometry]
Math 419 Linear Analysis [needs Theory of Convergence]
Math 467 Vibrations [needs Symon]
Math 470 Variational Calculus [needs Symon and Differential Geometry]

Complex Analysis
-------------------------
Math 322 Complex Analysis
Math 424 Applications of Complex Analysis

Linear Algebra
--------------------
Math 232 Elementary Linear Algebra
Math 438 Linear Algebra
Math 439 Introduction to Algebraic Systems [aka Abstract Algebra]


minor things

Fluid Mechanics [fluid motion/air motion/turbulence] - engineering like - turbulent gases and liquids
------------------
Math 362 Fluid Mechanics I [needs Vector Calculus and Symon]
Math 462 Fluid Mechanics II [needs Boundary Value Problems]

Continuum Mechanics [aka deformation/stress/elasticity] - engineering like - elastic solids
--------------------------
Math 361 Mechanics of Deformable Media [needs Vector Calculus and Engineering Dynamics]
Math 468 Continuum Mechanics [needs Differential Geometry and Boundary Value Problems]

Probability and Statistics
-----------------------------
Math 272 Introduction to Probability and Statistics
Math 387 Introduction to Stochastic Processes

Numerical Analysis
-----------------------
Math 316 Numerical Analysis I [needs Fortran or PL/I]
Math 416 Numerical Analysis II [needs Differential Equations]


Mechanics - 1
------------
Phys 120 Physics I
Phys 211 Intermediate Mechanics [Symon]
Phys 413 Advanced Mechanics [Goldstein]

Electricity and Magnetism - 2
------------------------------
Phys 121 Physics II
Phys 221 Intermediate Electricity and Magnetism
Phys 325 Relativity and Electromagnetism
Phys 326 Electronics and Instrumentation
Phys 425 Electromagnetic Theory

Waves and Optics - 3
---------------------
Phys 355 Optics

Quantum Mechanics - 4
------------------------
Phys 385 Quantum Physics
Phys 415 Quantum Mechanics
Phys 465 Solid State Physics - [should be separate but basic QM is needed for these branches]
Nusc 485 Particle Physics - [should be separate but basic QM is needed for these branches]

Thermodynamics and Statistical Mechanics - 5
--------------------------------------------------
Phys 344 Thermal Physics
Phys 345 Statistical Mechanics

Mathematical Physics
-------------------------
Phys 384 Methods of Theoretical Physics I
Phys 484 Methods of Theoretical Physics II

Plasma Physics [if offered]
-----------------
Phys 477 Applied Plasma Physics


[the Fourth Year EM and QM courses will blur with Grad school sometimes depending on the textbook/school/syllabus]

[but you could see yourself as saying the goal is to get that 400 level EM and 400 level QM course as the cupcake icing to all those courses]



Grad School
--------------
a. Phys 507 - Plasma Physics
b. Phys 532 - Plasma Dynamics
c. Phys 533 - Laser Physics [less weighty]
d. Phys 531 - Advanced Plasma Physics - seminar course [less weighty]

not sure what courses would be suitable or appeal to others
but there are always Mechanical/Aeronautical Engineering courses with Fluid Dynamics and Magnetohydrodynamics [and textbooks that overlap] as well as Nuclear Engineering/Particle Physics/Atomic physics being things to add to things...

You can always buy the textbooks on math if you got your dream niche in physics...

but what would you wanna do with the math, and if applied, would you want it to intersect with physics in what areas?


anyhoo, that's my two cents