
#3385
Feb113, 02:04 PM

P: 53





#3386
Feb113, 02:25 PM

P: 27

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




#3387
Feb113, 08:57 PM

P: 150

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




#3388
Feb213, 11:41 AM

Sci Advisor
HW Helper
P: 9,421

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 



#3389
Feb1213, 12:56 PM

P: 519

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 semiemployed. 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. 



#3390
Feb1213, 01:06 PM

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P: 9,421

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. 



#3391
Feb1213, 01:26 PM

P: 519

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 



#3392
Feb1213, 05:25 PM

P: 18

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 :)




#3393
Feb1313, 12:22 AM

P: 56

My math obsession has totally screwed up my sleep schedule.




#3395
Feb1513, 12:04 AM

P: 3

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. 



#3396
Feb2013, 07:28 PM

Sci Advisor
HW Helper
P: 9,421

"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. 



#3397
Feb2113, 05:43 AM

P: 56

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 epsilondelta proofs in my sleep now. 



#3398
Feb2113, 06:40 AM

P: 519

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. 



#3399
Feb2113, 10:47 AM

P: 27

@mathwonk, just accepted to the Brandeis program!
pretty sure I'm going this fall! 



#3400
Feb2113, 08:04 PM

P: 83

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 



#3401
Feb2113, 09:07 PM

Sci Advisor
HW Helper
P: 9,421

dear Mariogs, congratulations!!! They have changed greatly since my day. they are now more into number theory, than classical algebraic geometry. Do say hello to my advisor Allan Mayer. He is very helpful and also brilliant. And it seems Igusa is graduate advisor, so check in with him too. Do not be shy about asking people for advice and help!




#3402
Feb2513, 08:24 AM

P: 27

@mathwonk,
will do. i just shot you a pm, talk soon! 


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