Should I Become a Mathematician?

[QuantumP7]

"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.

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 got to take a breather, and let your bf/gf take a breather, too, you 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 mathematics 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 don't 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 want to do with the math, and if applied, would you want it to intersect with physics in what areas?


anyhoo, that's my two cents

 

[mathwonk]

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!

 

[Mariogs379]

@mathwonk,

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

 

[Trogdor02]

Hi mathwonk, what's your impression of UMass Amherst? I'm interested in number theory

 

[RJinkies]

136 University of Massachusetts Amherst

University of Massachusetts-Amherst Worcester, MA
[Queens University is similar in style]
[#85 Best Library]
[#48 Top End Physics]
[#64 Top End Mathematics]
[#50 Chemistry Top End]
[#10 Artificial Intelligence]
[#27 World Ranking Physics]
[Tied #75-100 World Ranking Mathematics]
[#50 World Ranking Engineering Technology]

 

[andrewkg]

For checking rankings of schools there's a site, "USNews school rankings" I think that's what it is called. Anyways, it has just about everything on any college you can think of.

 

[Trogdor02]

Rankings of schools don't really give you any useful information.

 

[RJinkies]

My rule of thumb a University is only as good as its syllabus and textbooks.

Some of the best undergraduate experiences come from dinky little places, Griffith who did the EM/Quantum/Particle Physics books, chooses to teach at a smaller college.

And many rankings can be related to the research, $$$, prestige factor, stuff which might not really be fundamentally important to getting an undergrad degree.

If you don't like their textbooks, run...

 

[mathwonk]

UM Amherst looks very strong to me. I went to their website and looked for people working in number theory, algebraic geometry and algebraic groups and representations. I do not know most of them, but then I looked them up on math genealogy and I know their advisors, all very strong.

At first the only reservation I had was there were so many from the same PhD school. But that school was outstanding, namely MIT. And moreover on closer look, they had different advisors and those advisors are outstanding and in varying specialties.

Last, most of the young guys at Amherst are turning out students. So I think it looks excellent. Also, it is maybe a little isolated geographically, but a very nice little town, and not even the only good college in that town.

 

[Trogdor02]

Thanks!

 

[dexterdev]

Advice for an engineer,want books with physical significance concepts

What is advice to an engineer seeking concepts like ODE, PDE, Vector calculus so as to apply in Electromagnetics etc? I am looking for books that also explain the physical significance of equations, help visualize things (other than raw derivations and equations) on ODE, PDE, Vector calculus etc. Any suggestions for me...

-Devanand T

 

[RJinkies]

i'll wait for others to suggest some books there first

but i will chime in with

a. Schaum's Outline - Vector Analysis
b. Springer SUMS series - Vector Calculus - Matthews
[80% of the books in the series seem recommended]
c. Stroud and Booth Programmed Instruction Series - Vector Calculus
d. Phillips [1933] 236 pages
e. Taylor [1939] 180 pages
f. Hay [1953] 193 pages [Dover]

Diff Eqs
possibly
a. Braun
b. Hubbard
c. Rainville [not sure what year that one came out]
d. Brauer [from the 60s]
e. Ross
f. Nelson 1952 [299 pages]
g. Phillips 3ed 1951 [149 pages]
h. Leighton 1952 [174 pages]
i. Stroud and Booth Programmed Instruction Series - Differential Equations
j. Jordan and Smith - Nonlinear Ordinary Differential Equations - Oxford

PDE
a. Haberman
b. Zachmanoglou
c. Pinchover
d. Gwynne Evans - Springer SUMS series

-----

That's my list for
a. easy vector
b. easy diff eqns
c. easy pde

anyone with an opinion or browsed the titles with good or bad thoughts, chime in...
but it's my list for books that hold your hand, are extremely short, or got some visualizations.

I wasnt too confident i could yank out some titles, since I'm still searching for more feedback...and obscure books... but it's my stab at it

 

[dexterdev]

thanks for the suggestion...

 

[mathwonk]

I am not an authority on this. But if I were to suggest, I would propose going to a library and looking at books on ODE and PDE by V. Arnol'd. There is also a cheap Dover paperback called differential equations of physics by L. Hopf that might be helpful in a general almost informal way.

 

[dexterdev]

thanks... will try to get those books

 

[RJinkies]

Arnold's Diff Eqn book is probably meant for a second class or honours people, but i bought it just for it being the first Russian translation math book that didnt scare the pants off me being dry and terse, and it had wonderful freaky diagrams of 'Phase Spaces', and it might be changed now [was there a newer edition and translation]

but the 70s 80s 90s had the classic MIT paperback which was Green and Purple

but it's definitely a book i liked, when i was just browsing and i think my three books on Diff Eq's was Lipgarbagez [who did a few Schaum's Outlines in the 60s/70s] it was a 70s 80s Red McGraw Hill with the creepiest Red lizard skin cloth and a black and gold spine...

and i would always look at the last problem in the book of some intimidating PDE of a critical mass of uranium being the final thing you study in the book. The other was some late 60s-early 70s blue hardcover that was an elementary intro to DE [friendliest used copy i could find anywhere], and what seemed like the best rewrite of the rather terse and wildly changing examples in DiPrima-Boyce [i think it was the 5th Edition about 1990-1991 which was green-black-blue] that seemed like they made it friendlier in the beginning, added a lot more explanations and examples, and tackled chaotic and dynamical systems which started to perk up in the mid-late 80s... [like Devaney's book being one of the more popular and pretty good ones]

My guess is get the smallest easiest shortest books on diff equations that toss you the essence of things without getting lost in the forest, and then see what speaks to you as a deeper book...

Mathwonk, Didnt you once say something once years ago about how there were lots and lots of good differential equation books out there? [where with other topics you can hit a lot of rotten textbooks]...wait i think you said that about complex variable books [oops]

Any minor suggestions, or obscure books on Diff Equations you like at all?one thing i thought most neat about looking at the older books was how slim they were... like they only started getting huge in the late 60s...or latersample:

McGraw-Hill
1933 - 263 pp
1942 - 341 pp
1950 - 356 pp
1952 - 174 pp
1952 - 215 pp

Wiley
1933 - 299 pp
1949 - 288 pp
1951 - 149 pp

Prentice-Hall
1933 - 409 pp

Ginn
1950 - 205 ppExceptions

Boole - Macmillian 1859 - 485 pp
Ince - Longmans 1927/Dover 1945 - 558 pp
Forsyth - MacMillian 1914/Dover - 584 ppBasically the huge books were the early ones and then when people wanted to get useful after Ince, the trend was thin little practical books from the 30s and still into the 60s..

Some physicists seem to say that some of the little books get right to the essence with no fat, and i wonder that's what we saw a lot more of in the about 1960-1975 were a lot of Elementary Differential Equation books for beginners, for a lite-course...

[but then again, back then in the late 60s early 70s you could still get 240 page books on Organic Chem, Diff Equations, Biochem, Linear Programming] and some thin calculus books too!]

 

[mathwonk]

well i answered this but the browser erased my post and i don't have time now to rewrite it. (Hopf, Braun, Hurewicz, time dependent vector fields, Feynman, Devaney's pictures and interactive DVD, chaos...)

 

[RJinkies]

some comments in my notes on Braun inside a Boyce-DiPrima review...[The best introductory books on differential equations are from the Springer Verlag yellow book series...check out the ones by Braun or Hubbard; they have more discussion and are more of learning texts than this one [Boyce-DiPrima]. When examples are provided to illustrate a concept, they are either extremely terse and misty, or wordy and annoyingly obscure the point. In addition, the authors don't even attempt to provide a general method for arriving at equations to represent real world phenomenon. For people wanting to learn something more positive from a differential equations text (something about differential equations!) try engineering and advanced engineering mathematics by Kenneth Stroud (esp the advanced one). For more rigorous explanations and comprehensiveness try Morris Tenenbaum.]

[one credit for Braun, Stroud, Tenenbaum and Hubbard - one demerit for Boyce-DiPrima]and i found this in my notes...

[Mathwonk taught ODE with four texts:
a. An Introduction to Ordinary Differential Equations - Coddington - Dover 1989
b. A Second Course in Elementary Differential Equations - Waltman - Dover 1987
c. Differential Equations and Their Applications - Third Edition - Braun - Springer 1975/1983
d. Ordinary Differential Equations - Arnold - MIT Press 1978]
[Mathwonk thinks that Braun is the one text with the most to offer a beginner]and Braun's 1975 book

[This book is extraordinarily clear as well as being concise (but never too much so) in the mathematical parts. Discussion of applications is verbose, but is kept in separate sections; this material can be omitted entirely or read later without any detrimental effect to the flow of the book. However, the discussion of the applications is interesting and deep, and would be useful (and fun) for motivated students to read.]

[The book begins with a no-nonsense discussion of how to solve differential equations analytically. Unlike many books, it gives clear instructions to the reader as to how to know which techniques are applicable. Also, it does not introduce qualitative or numerical methods until it has already developed a number of analytic techniques, and in my opinion, this results in greater clarity than the path most books take of integrating (or should I say jumbling?) the material together. The book gradually and logically covers the ground between analytic and numerical, moving towards actually writing algorithms, which are included in the text. The emphasis is always on understanding. Exercises are straightforward and useful.]

[This book is simply wonderful for anyone studying differential equations for the first time. I do not understand why undergraduate institutions use the more commercialized texts instead of ones like this. This is a great book; it would be excellent for a textbook or for self-study.]----

- Schaum's Outlines on Diff Equations

[recommended by Baez/physics]

- Tenenbaum - Dover

[A very lengthy, but good introduction to ordinary differential equations. Also, it's relatively cheap - Jason Williams/physics]
[liked by Alexander Shaumyan/math]
[This book is rigorous but understandable]
[many MIT people use it for self study]
[THE book on ordinary differential equations. All you need is right here. This is probably the best mathematics book you will EVER find. - Patrick M Thompson Australia]
[unique - Mathwonk]

- Hans Stephani - Differential Equations: Their Solution Using Symmetry - Cambridge 1999 -
[Baez]

- Elementary Differential Equations - Earl D. Rainville
[my favourite ODEs text/anonymous]

- Differential Equations With Applications and Historical Notes*- George F Simmons
[some felt simmons was the best math book for physicists]

- Elementary Differential Equations - Fred Brauer - WA Benjamin 1968

[i think this was the little blue book i bought years ago]

- Differential Equations: A First Course - Third Edition - Martin M. Guterman and Nitecki - Harcourt Brace 1992

[liked by mathwonk]
[appears to be a fine book - well written, clear, and rigorous]
[the examples are displayed beautifully]
[would be a first choice for mathwonk to teach Differential Equations]

I think that Guterman-Nitecki book has the best looking differential equations textbook cover I've seen, next to the old Second Edition MIT Arnold [the third edition by Springer is lousy typesetting and just a trickle of new stuff]

It's silvery and blue and red and mirrored looking - congrats to Harcourt Brace for a good book and a good cover!

------Anyone got any comments on Zill, it's liked by people who dislike Boyce-DiPrima and well the MAA likes both books.

3 star for Boyce-DiP as an Introductory Text 1969
2 stars - Simmons/Robertson 1972
2 stars - Zill 1980
2 stars - Edwards/Penney 1985
2 star for one of the older Hubbard books by Springer-Verlag 1991
2 stars - Redheffer/Port 1991and if anyone knows what was popular as an elementary textbooks before Braun and Boyce in the late 50s early 60s late 60s early 70s, chime in...

 

[RJinkies]

Here's something interesting, if you are interested in the Russian Hardcore mathematicians who like Arnold's books...

-

Having forewarned you, here are my favorite introductory books on differential equations, all eminently suitable for self-study. - Victor Protsak

Piskunov, Differential and integral calculus
Filippov, Problems in differential equations
Arnold, Ordinary differential equations
Poincare, On curves defined by differential equations
Arnold, Geometric theory of differential equations
Arnold, Mathematical methods of classical mechanics

 

[Mathematicize]

Combinatorics Books and Future Study

Hi all,

I would like to study Combinatorics and learn more combinatorial problem solving techniques (I especially liked combinatorial proofs but I still have a lot to learn in this area). I know the basics: addition rule, multiplication rule, permutations, combinations, combinations with repetition... and a little about generating functions.

1. I would like a proof based book that includes details and gives a solid justification for each derivation/step in the problem/proof (I really dislike reading math texts that would have been so much easier to understand if the author would just give more justifications)
   
2. I would like to learn a lot of the "tricks" or "ingenuity" behind these problems.

Thanks for all help!

 

[reenmachine]

I want to become a mathematician.

At 26 years old though , a lot of people are trying hard to discourage me.I will have to start from scratch (undergraduate level) and go from there.

I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on Y because you didn't learn X while X is very easy to learn but you don't know that it's X that you have to learn to solve Y so you end up trying to find X by yourself but it took centuries to humanity to solve it while it takes half an hour to learn and understand it once you have in front of your eyes. (exagerration but not so far from the truth of trying to learn by one's self).

 

[epenguin]

Hi all,

I would like to study Combinatorics and learn more combinatorial problem solving techniques (I especially liked combinatorial proofs but I still have a lot to learn in this area). I know the basics: addition rule, multiplication rule, permutations, combinations, combinations with repetition... and a little about generating functions.

1. I would like a proof based book that includes details and gives a solid justification for each derivation/step in the problem/proof (I really dislike reading math texts that would have been so much easier to understand if the author would just give more justifications)
   
2. I would like to learn a lot of the "tricks" or "ingenuity" behind these problems.

Thanks for all help!

I am aways puzzled by these requests for 'proof-based' math books. I have never found any other type, perhaps my standards are low.

I think a very helpful book is 'Introduction to Combinatorial Mathematics' by C.L.Liu (publ. McGraw-Hill).

 

[RJinkies]

okay here's my quirky list...

1 Introductory Combinatorics*- Kenneth P. Bogart

2 Mathematics of Choice: Or, How to Count Without Counting (New Mathematical Library)*- Ivan Morton Niven
[Excellent first book in combinatorics]

4 Combinatorics of Finite Sets - Ian Anderson - Dover
[An excellent and unique perspective on combinatorics]

7 Generatingfunctionology - Herbert S. Wilf
[A terrific book on discrete math and combinatorics]

8 Combinatorics: Topics, Techniques, Algorithms - Peter J. Cameron
[The book contains an absolute wealth of topics.]

12 Discrete Mathematics - Laszlo Lovasz - Springer 2003

19 Applied Combinatorics - Alan Tucker
[almost an ideal introduction to combinatorics]
[clear and friendly]

21 Principles and Techniques in Combinatorics (Paperback) - Chen Chuan-Chong and Koh Khee-Meng - World Scientific 1992 - 312 pages

24 Constructive Combinatorics (Undergraduate Texts in Mathematics) - Dennis Stanton and Dennis White - Springer 1986 - 204 pages
[Unlike other textbooks in combinatorics , this introductory book takes a very different pace.]

26 Introduction to Combinatorial Analysis - John Riordan - originally Wiley 1958/Dover 2002 - 256 pages
[a classic text on the subject]

28 Miklos Bona - A Walk through Combinatorics. 1st Edition - World Scientific 2002 - 424 pages
[the book is exciting to read - has a few typos]

29 Applied Combinatorics - First Edition - Fred Roberts - Prentice-Hall 1984 - 640 pages
[clear and straightforward]

-----if anyone has any opinions, thumbs up or thumbs down on these books, speak up
on these books or the liu suggestion...

I remember browsing roberts once, thought it was a great looking cover and it was one of the easier books to follow. Beiler's book on Number Theory spoke to me in the same way, abd i think Sprecher's book on Real Analysis which was i think a late 60s early 70s book Dover Reprinted...

all three were instantly likeable from 5 minutes browsing and were no less fascinating after 15 more minutes...

 

[Vahsek]

I want to become a mathematician.

At 26 years old though , a lot of people are trying hard to discourage me.I will have to start from scratch (undergraduate level) and go from there.

I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on Y because you didn't learn X while X is very easy to learn but you don't know that it's X that you have to learn to solve Y so you end up trying to find X by yourself but it took centuries to humanity to solve it while it takes half an hour to learn and understand it once you have in front of your eyes. (exagerration but not so far from the truth of trying to learn by one's self).

Hi Reenmachine,
I would recommend you to pursue the math degree. It seems to me that this is what you really want and you don't seem to be money-minded or overly ambitious( I've read your other posts). And I must warn you that I'm only a high school student, so you don't have to take me too seriously.
As a matter of fact, I wanted to be both a physicist and mathematician. But I had to choose, so I chose physics, believing that I can quench my thirst for maths on my own. Anyway, so I'm encouraging you to do it as I have similar pursuits too.
Best of luck.

 

[RJinkies]

reenmachine - I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on...

Well what things have you been trying to learn, or maybe what textbook or math puzzle book are you attempting?

There are a lot of people who hit the getting stuck roadblock, and it's quite natural, but with almost anything in math and physics, with a bit more patience and simply spending more time on something, and going back regularly, even if 10-30 min a week, you can snap out of it.

Sometimes it takes weeks, sometimes years but if your interest is there, you'll self-study one day. Just knowing a little piece well, and being interested enough to come back to the book for 30 minutes at a time, and then browsing again, every week for another 30 minutes, you can kickstart the habit

a. where you'll get a better grasp of ideas and concepts from just random browsing and getting the 'gist of things' far more than you might realize

b. actually saying, maybe i'll start on this book properly, at the beginning and go for being slow and complete, but trying extra hard to being consistent with your reading or pondering of examples, and realizing that you don't need to get far. Be patient, spend more time with things.A lot of hurdles with self-studying math can just be something so simple as not realizing that you needed to spend three times as long reading that article/chapter fragment. that 14 minutes didnt work, but 71 minutes unlocked some secrets...

im still kicking myself for not reading sherman stein's calculus book in the house, when i was still struggling with algebra. I got frustrated with the book that some chapters were crystal clear and a few just seemed 'unclear' to me. I gave up.

Also i didnt realize how important it was to just try out what the author *really* intended.

If he wrote 36 pages for chapter one, why not read *all* 36 pages?

Why not read it slowly enough to give the author a 'decent' chance?

Maybe his examples are extremely extremely useful, figure those out *deeply*

Hey, why did the author plop 64 questions at the end? Gee that's a lot! Wait a minute, what happens if i did all 64 of them?

That's the sort of thing that broke things for me with self-study.

Don't fall into the trap that the school system teaches you, the bad habit that it always needs to be a race. Make one chapter of that textbook, your life. Forget about the whole book. Drop the idea that you need to rush through the book and skim through 70% of it, sure a lot of teachers do that to cram things into 12 weeks or 15 weeks ,but why should you?

Make sure you got math books that are slightly easy to read, and some that actually do challenge you too. One day some subjects will be eye-opening if you can read one math book, and then slowly, use 2 more textbooks to read together...

So you're seeing some ideas open up in three different ways, and see how each explanation is unique...

What's murky in one book, can be clearer in another book.

but real accomplishment is when you can read all three chapters in all three books, and they all start to help each other, rather than feel like three different universes, all frustratingly different and confusing.If you are fascinated with something, don't let friends or teachers get you down. You might be interested in something, but who says that you got to be an expert from day one with it?And who says that self-study isn't so hot when you do it randomly...

If you got a book, you start at the beginning. There's nothing random at all about taking an extremely small sliver of it and trying to learn it well. Take small bites, take a lot time to chew, eat regularly...

 

[reenmachine]

reenmachine - I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on...

Well what things have you been trying to learn, or maybe what textbook or math puzzle book are you attempting?

There are a lot of people who hit the getting stuck roadblock, and it's quite natural, but with almost anything in math and physics, with a bit more patience and simply spending more time on something, and going back regularly, even if 10-30 min a week, you can snap out of it.

Sometimes it takes weeks, sometimes years but if your interest is there, you'll self-study one day. Just knowing a little piece well, and being interested enough to come back to the book for 30 minutes at a time, and then browsing again, every week for another 30 minutes, you can kickstart the habit

a. where you'll get a better grasp of ideas and concepts from just random browsing and getting the 'gist of things' far more than you might realize

b. actually saying, maybe i'll start on this book properly, at the beginning and go for being slow and complete, but trying extra hard to being consistent with your reading or pondering of examples, and realizing that you don't need to get far. Be patient, spend more time with things.A lot of hurdles with self-studying math can just be something so simple as not realizing that you needed to spend three times as long reading that article/chapter fragment. that 14 minutes didnt work, but 71 minutes unlocked some secrets...

im still kicking myself for not reading sherman stein's calculus book in the house, when i was still struggling with algebra. I got frustrated with the book that some chapters were crystal clear and a few just seemed 'unclear' to me. I gave up.

Also i didnt realize how important it was to just try out what the author *really* intended.

If he wrote 36 pages for chapter one, why not read *all* 36 pages?

Why not read it slowly enough to give the author a 'decent' chance?

Maybe his examples are extremely extremely useful, figure those out *deeply*

Hey, why did the author plop 64 questions at the end? Gee that's a lot! Wait a minute, what happens if i did all 64 of them?

That's the sort of thing that broke things for me with self-study.

Don't fall into the trap that the school system teaches you, the bad habit that it always needs to be a race. Make one chapter of that textbook, your life. Forget about the whole book. Drop the idea that you need to rush through the book and skim through 70% of it, sure a lot of teachers do that to cram things into 12 weeks or 15 weeks ,but why should you?

Make sure you got math books that are slightly easy to read, and some that actually do challenge you too. One day some subjects will be eye-opening if you can read one math book, and then slowly, use 2 more textbooks to read together...

So you're seeing some ideas open up in three different ways, and see how each explanation is unique...

What's murky in one book, can be clearer in another book.

but real accomplishment is when you can read all three chapters in all three books, and they all start to help each other, rather than feel like three different universes, all frustratingly different and confusing.If you are fascinated with something, don't let friends or teachers get you down. You might be interested in something, but who says that you got to be an expert from day one with it?And who says that self-study isn't so hot when you do it randomly...

If you got a book, you start at the beginning. There's nothing random at all about taking an extremely small sliver of it and trying to learn it well. Take small bites, take a lot time to chew, eat regularly...

I wrote a super long answer but it got erased as soon as I clicked on send. :(

Thanks for answering me btw , lot of good advices in your post.

I'll make a longer one later but for the moment:

I currently have no math book because I'm scared of getting a book I won't understand due to lack of math background.What I do in the meantime to keep my brain from getting rusty is doing some math puzzles I find on the internet here and there.Sometimes I can't solve them and this is where I try to learn new concepts to help me solve these problems , but organizing what I need to learn and where to learn it is very hard.This is why I might just be better off going back to school.

I destroyed my high school math programs back in the days with a 98.5% average out of about 36 exams.Unfortunately calculus (or at least Calcul Infinitésimal in french , which I think is calculus) wasn't part of it.This is my next target , any suggestions to self-teach calculus?

One thing about my high school math years is that while I scored very high , I don't feel like the program was in my favor because it was too easy for the other students to score somewhat high (like 85-90%).To make an analogy a lot of students knew a single path to get to the answer while I knew the entire map.I was known as a very creative math student.I always tried to understand the concepts in depth , not just mesmorizing the formulas and technics.If they would have put two trickier/tougher questions at the end of every exam which would count for at least 10% the standard would have been fairer to people who make the effort to understand the entire map instead of mesmorizing a single path , a path that ideally wouldn't be enough to answer those two hypothetical trickier/tougher problems I'm talking about.

One thing I'm scared of right now is if I go back to undergraduate they'll force me to at least a year of ''general studies'' where math isn't the only focus.This would be a major waste of time for someone my age trying to contribute to math in the long run.I don't know all the details yet of what is expected of me before entering a math program but I have a meeting with a math department person next month and we shall see.If I have to take some french classes or social sciences classes for a year it'll be very frustrating in my situation.

Another thing about self-teaching , 3 years ago I didn't speak a word of english , I learned it by myself discussing on message boards so I've seen the possible success self-teaching can bring.

Sorry for the short reply , can't believe my long one got deleted :X

 

[zapz]

hey guys just a quick timeline type question. If I want to do a phd in math, when should i play to take the general gre and the subject gre? i figure i should take the subject test twice, or at least have the time to be able to. so any idea why i take try to take the tests?

 

[reenmachine]

Not sure if it's the right place to ask , but I will probably study in Montreal and I would prefer to do it in french.

What is the reputation of the Université de Montréal in math?

I know McGill has a good reputation but I rarely hear about UdeM and I was wondering.

 

[andrewkg]

Hello I saw it in an earlier post o. Here, but does anyone know if the humongous book of calculus problems is a good book to start calculus with. Or does anyone have any other good texts. Also if possible not a 1200 page book.

 

[mathwonk]

Univ de Montreal has Andrew Granville, and outstanding number theorist. I don't know the other faculty but if Andrew went there it should be good.

 

[reenmachine]

Univ de Montreal has Andrew Granville, and outstanding number theorist. I don't know the other faculty but if Andrew went there it should be good.

thanks!

 

[reenmachine]

I edited this post as I don't think it was the right place to discuss such a subject.

I still have a dumb question for mathematicians , is your ph.d thesis likely to be good original work? I mean will the work on your ph.d be more or less at the same mathematical level as your future researches?