Should I Become a Mathematician?

[Supremo]

@Mathwork,

I know you are familiar with Spivak Calculus, how about N.Piskunov Calculus. I have read somewhere in Physics Forum that Piskunov Calculus is a great book that it has chapters uncommon to other calculus book, and do not cover topics just to cover them just like some author.

Sir can you give a detailed difference (advantage) of using one over the other between Piskunov and Spivak's Calculus book for college freshman. How about the topic presentation (discussion), is it ideal for young student of average level in math. Which one is the better choice between the two.

 

[mathwonk]

i am sorry, i have not seen piskunov. is it online? but in general, it is not important which of several great books you use, just get hold of one and start thinking and working.

 

[x BlueRobot]

You mentioned there is three branches of Mathematics, what about the other areas such as Set Theory, Number Theory and Graph Theory etc.?

Graph Theory is my favorite area of Mathematics, I find Analysis and Calculus rather boring and dull.

 

[homeomorphic]

You mentioned there is three branches of Mathematics, what about the other areas such as Set Theory, Number Theory and Graph Theory etc.?

I'm guessing mathwonk probably said topology/geometry, analysis, and algebra. Those were just broad areas. Number theory could be considered part of algebra, and you'd see why if you studied enough algebra and number theory.

I think you might have to add combinatorics (including graph theory) and logic/foundations (including set theory) to the list. But with those 5, I think you could probably cover everything in broad strokes. But names and compartmentalization aren't that important, anyway. Who cares? They are just names.

Graph Theory is my favorite area of Mathematics, I find Analysis and Calculus rather boring and dull.

If you find calculus/analysis boring and dull, that hints to me that you might have a less than complete understanding of it. I wouldn't blame you for thinking certain aspects of calculus are dull, but if you look at the bigger picture and some of its applications, it's pretty nice. We shouldn't be so spoiled and judge a subject so harshly because of a few silly trigonometric integrals that we might have had to put up with. Although I'm a topologist, or maybe I should say, a failed topologist, I might have to say graph theory is arguably my favorite subject, too.

Of course, I think almost every subject in math is too complicated for my tastes once you get to research-level stuff because I don't have time to understand everything clearly and understanding clearly is exactly what I like about math (which is why I like elementary analysis, at least). The struggle for understanding is good, too, but it gets to be too much like pitting an ant against the US army at some point, in terms of that battle for understanding at the level that I desired. I at least have to have a fighting chance for it to be enjoyable. This is coming from someone with a PhD in math, so I don't think I'm the only ant out there--I think all mathematicians have become ants with respect to the entire subject. A few Fields medalists might be like big queen ants or something, but they are still awfully puny and pitiful compared to the whole subject.

 

[x BlueRobot]

I understand what you mean about Number Theory, and I do like Series within Calculus/Analysis and some other little bits and pieces of the area, but overall Analysis doesn't really appeal to me as much as other areas like Graph Theory.

 

[mathwonk]

go with what you enjoy! the fun is the main motivation in math.

 

[dkotschessaa]

Man, feel like I'm doing a 180. (Colloquially speaking). I was going down the "pure math" road. Now I am doing a project in mathematical oncology and it's really fascinating. http://moffitt.org/research--clinical-trials/research-disciplines/departments/integrated-mathematical-oncology

I'm working on differential equations (I did not enjoy this subject when I first took it) modeling of tumor growth (I have no biology background).

You just never know what's going to happen do you?

-Dave K

 

[mathwonk]

I also disliked diff eq until I read the books of martin braun , hurewicz, guterman and nitecki, and especially arnol'd.

 

[dkotschessaa]

I also disliked diff eq until I read the books of martin braun , hurewicz, guterman and nitecki, and especially arnol'd.

Thanks. I actually hated the subject so much I got rid of all materials relating to it (some good ones too) saying "I think I'll just avoid that subject for the rest of my math career." I feel very silly about that now. I just found the guterman one for 20 cents on amazon and purchased. ($4.00 shipping of course).

Regards,

Dave K

 

[dkotschessaa]

Just got Gutermen and Nitecki. If this book had been my introduction to Differential Equations, my perspective would have been much different.

I am finding all too often that my experience of a particular area of mathematics has to do with how I am introduced to it. Kind of a shame in a way.

 

[dkotschessaa]

Most spot-on quote from my cousin, a geophysicist.

"Anything worth doing research-wise, requires you to learn a bunch of stuff that you've never thought about before just to get to the point where you understand the problem you're trying to solve."

I keep reading it over and over...

 

[x BlueRobot]

Most spot-on quote from my cousin, a geophysicist.

"Anything worth doing research-wise, requires you to learn a bunch of stuff that you've never thought about before just to get to the point where you understand the problem you're trying to solve."

I keep reading it over and over...

Science and Mathematics is like solving lots of little problems, which eventually lead to a solution to a much larger problem.

 

[dkotschessaa]

I'm not sure if it's kosher to post in a thread asking for another thread to be answered. But darn the torpedoes, if anyone, including mathwonk, could look at my recent thread First Year Math graduate school - Full of possibility!. I post a lot of threads that don't get a reply, so I'd like if this is not one of them.

Thanks

Dave K

 

[x BlueRobot]

I never used to like Pure Mathematics, but when I started to think of it as more of a puzzle, then I started to enjoy the subject much more.

 

[homeomorphic]

I never used to like Pure Mathematics, but when I started to think of it as more of a puzzle, then I started to enjoy the subject much more.

I would agree with that. I don't mind my math being pure if it's something I can sit down and solve in a couple hours, or even a few days, or up to a week or two. As a brain-teaser it's great. But if it's something I have to devote my life to and read hundreds and hundreds of pages of stuff (plus, trying to get by with a minimal conceptual understanding of it, since there isn't time to really process it all) and work on stuff that takes several years to solve, that's where the problem comes. At that point, I have realized, I need external motivation beyond it being having a brain-teaser to solve. It took me a PhD in pure math to realize that.

Also, a lot of the point isn't just solving puzzles, but wrapping your head around cool ideas.

 

[x BlueRobot]

I given myself a little research project on Bull Graphs, I've been doing labeling problems for the last few days. I'm going to check my conjecture that Bull Graphs can be prime labeled tomorrow.

What area of Mathematics do you specialize in?

 

[mathwonk]

remember, EVERYTHING is interesting if seen in the right perspective, which usually comes from an introduction at the hands of someone who loves and understands it.

 

[homeomorphic]

What area of Mathematics do you specialize in?

Not sure if you mean me or mathwonk. Mathwonk does algebraic geometry. I wrote my dissertation in topological quantum field theory, but I don't really do much math any more. I'm just trying to become a programmer, now. To the extent that I still do math, it's mostly probability, statistics, financial math, theoretical computer science, and a tiny bit of graph theory, and very much on the applied side of it all (and nowhere near research level). I've been meaning to learn more about numerical methods but haven't gotten around to it, yet. So much to do, so little time. The idea of specializing in something is sort of repugnant to me.

 

[Philip]

Hypertorus Exploration and Mathematics

Well, I'm certainly not sure what I want to do. I've been a professional bike mechanic for 14 years ( the kind you pedal ), and I've made some interesting mathematical discoveries. Lately, in the last 7 months, it seems that I have acquired knowledge of far-reaching things, into unexplored territory. These things are known about theoretically, but I'm not sure to what extent.

And, it seemed by accident, or pure chance that I would be able to learn it. On a quiet forum, somewhere on the internet, is a funny-looking notation system, called toratopic notation. It was made by others, before I joined. It just so happens to stand for the equations of multidimensional toroids. By reducing the implicit surface equation for, say a circle, sphere, and torus, we can get something like:

circle : (II) : x^2 + y^2 - R1^2 = 0

sphere : (III) : x^2 + y^2 + z^2 - R1^2 = 0

torus : ((II)I) : (sqrt(x^2 + y^2) - R1)^2 + z^2 - R2^2 = 0

The end result is a combinatoric sequence of surfaces of revolution. By repeating these rotations into various hyperplanes, one can build a notation sequence for a shape, which converts into an implicit surface equation.

Going beyond 3D, we have many more possible shapes, per dimension:

4D:
(IIII) - x^2 + y^2 + z^2 + w^2 - R1^2 = 0
((II)II) - (sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2 - R2^2 = 0
((II)(II)) - (sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 - R2^2 = 0
((III)I) - (sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2 - R2^2 = 0
(((II)I)I) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2) - R2)^2 + w^2 - R3^2 = 0

5D:
(IIIII) - x^2 + y^2 + z^2 + w^2 + v^2 - R1^2 = 0
((II)III) - (sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2 + v^2 - R2^2 = 0
((II)(II)I) - (sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 + v^2 - R2^2 = 0
((III)II) - (sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2 + v^2 - R2^2 = 0
(((II)I)II) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2) - R2)^2 + w^2 + v^2 - R3^2 = 0
((III)(II)) - (sqrt(x^2 + y^2 + z^2) - R1a)^2 + (sqrt(w^2 + v^2) - R1b)^2 - R2^2 = 0
(((II)I)(II)) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2)^2 + (sqrt(w^2 + v^2) - R1b)^2 - R3^2 = 0
((IIII)I) - (sqrt(x^2 + y^2 + z^2 + w^2) - R1)^2 + v^2 - R2^2 = 0
(((II)II)I) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2) - R2)^2 + v^2 - R3^2 = 0
(((II)(II))I) - ((sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 - R2)^2 + v^2 - R3^2 = 0
(((III)I)I) - (sqrt((sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2) - R2)^2 + v^2 - R3^2 = 0
((((II)I)I)I) - (sqrt((sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 ) - R2)^2 + w^2) - R3)^2 + v^2 - R4^2= 0

6D:
(IIIIII) - x^2 + y^2 + z^2 + w^2 + v^2 + u^2 - R1^2 = 0
((II)IIII) - (sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2 + v^2 + u^2 - R2^2 = 0
((II)(II)II) - (sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 + v^2 + u^2 - R2^2 = 0
((II)(II)(II)) - (sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 + (sqrt(v^2 + u^2) - R1c)^2 - R2^2 = 0
((III)III) - (sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2 + v^2 + u^2 - R2^2 = 0
(((II)I)III) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2) - R2)^2 + w^2 + v^2 + u^2 - R3^2 = 0
((III)(II)I) - (sqrt(x^2 + y^2 + z^2) - R1a)^2 + (sqrt(w^2 + v^2) - R1b)^2 + u^2 - R2^2 = 0
(((II)I)(II)I) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2)^2 + (sqrt(w^2 + v^2) - R1b)^2 + u^2 - R3^2 = 0
((III)(III)) - (sqrt(x^2 + y^2 + z^2) - R1a)^2 + (sqrt(w^2 + v^2 + u^2) - R1b)^2 - R2^2 = 0
(((II)I)(III)) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2)^2 + (sqrt(w^2 + v^2 + u^2) - R1b)^2 - R3^2 = 0
(((II)I)((II)I)) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2a)^2 + (sqrt((sqrt(w^2 + v^2) - R1b)^2 + u^2) - R2b)^2 - R3^2 = 0
((IIII)II) - (sqrt(x^2 + y^2 + z^2 + w^2) - R1)^2 + v^2 + u^2 - R2^2 = 0
(((II)II)II) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2) - R2)^2 + v^2 + u^2 - R3^2 = 0
(((II)(II))II) - ((sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 - R2)^2 + v^2 + u^2 - R3^2 = 0
(((III)I)II) - (sqrt((sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2) - R2)^2 + v^2 + u^2 - R3^2 = 0
((((II)I)I)II) - (sqrt((sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 ) - R2)^2 + w^2) - R3)^2 + v^2 + u^2 - R4^2= 0
((IIII)(II)) - (sqrt(x^2 + y^2 + z^2 + w^2) - R1a)^2 + (sqrt(v^2 + u^2) - R1b)^2 - R2^2 = 0
(((II)II)(II)) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2 + w^2) - R2)^2 + (sqrt(v^2 + u^2) - R1b)^2 - R3^2 = 0
(((II)(II))(II)) - (sqrt((sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2) - R2)^2 + (sqrt(v^2 + u^2) - R1c)^2 - R3^2 = 0
(((III)I)(II)) - (sqrt((sqrt(x^2 + y^2 + z^2) - R1a)^2 + w^2) - R2)^2 + (sqrt(v^2 + u^2) - R1b)^2 - R3^2 = 0
((((II)I)I)(II)) - (sqrt((sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2)^2 + w^2) - R3)^2 + (sqrt(v^2 + u^2) - R1b)^2 - R4^2 = 0
((IIIII)I) - (sqrt(x^2 + y^2 + z^2 + w^2 + v^2) - R1)^2 + u^2 - R2^2 = 0
(((II)III)I) - (sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2 + v^2) - R2)^2 + u^2 - R3^2 = 0
(((II)(II)I)I) - ((sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 + v^2 - R2)^2 + u^2 - R3^2 = 0
(((III)II)I) - (sqrt((sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2 + v^2) - R2)^2 + u^2 - R3^2 = 0
((((II)I)II)I) - (sqrt((sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 ) - R2)^2 + w^2 + v^2) - R3)^2 + u^2 - R4^2= 0
(((III)(II))I) - ((sqrt(x^2 + y^2 + z^2) - R1a)^2 + (sqrt(w^2 + v^2) - R1b)^2 - R2)^2 + u^2 - R3^2 = 0
((((II)I)(II))I) - ((sqrt((sqrt(x^2 + y^2) - R1a)^2 + z^2) - R2)^2 + (sqrt(w^2 + v^2) - R1b)^2 - R3)^2 + u^2 - R4^2 = 0
(((IIII)I)I) - (sqrt((sqrt(x^2 + y^2 + z^2 + w^2) - R1)^2 + v^2) - R2)^2 + u^2 - R3^2 = 0
((((II)II)I)I) - (sqrt((sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2 + w^2) - R2)^2 + v^2) - R3)^2 + u^2 - R4^2= 0
((((II)(II))I)I) - (sqrt(((sqrt(x^2 + y^2) - R1a)^2 + (sqrt(z^2 + w^2) - R1b)^2 - R2)^2 + v^2) - R3)^2 + u^2 - R4^2 = 0
((((III)I)I)I) - (sqrt((sqrt((sqrt(x^2 + y^2 + z^2) - R1)^2 + w^2 ) - R2)^2 + v^2) - R3)^2 + u^2 - R4^2= 0
(((((II)I)I)I)I) - (sqrt((sqrt((sqrt((sqrt(x^2 + y^2) - R1)^2 + z^2) - R2)^2 + w^2) - R3)^2 + v^2) - R4)^2 + u^2 - R5^2 = 0

As you can see, these are very large and complex surfaces of revolution, the basic concept behind a hypetorus. The number of hypertori in each dimension is 1,1,2,5,12,33,90,261, etc, which is the A000669 integer sequence on the OEIS. These equations and notations are defining discrete hypershapes in an n-dimensional Euclidean plane.

Once the equation is derived, one can reduce it to a 3D equation, as a cross section of the hypertorus. Then add rotate and translate parameters to move the slice around. I put these enormous functions into a great program, CalcPlot3D. It handles 3D implicit graphing quite well. While exploring the various functions for a shape, I'll see fascinating things happening all the time. That notation system can be used to interpret cross sections abstractly, too. By removing the uppercase " I " you make a cut, by setting that dimension to zero. Take 6D hypertorus (((II)I)((II)I)) for example:Dimensional Map of (((II)I)((II)I)) Hyperplane Intercepts

XYZWVU 6D Hyperplane
(((II)I)((II)I)) - 1x tiger duotorus
-------------------------------------
XYZWV 5D Intercepts
(((II)I)((I)I)) - 2x tigritoruses (((II)I)(II)) in 1x1x1x2x1 vert column
(((II)I)((II))) - 2x tigritoruses (((II)I)(II)) in major1 concentric pairs
--------------------------------------
XYZW 4D Intercepts
(((I)I)((I)I)) - 4x tigers ((II)(II)) in 2x1x2x1 vert square
(((II)I)((I))) - 4x ditoruses (((II)I)I) in 1x1x1x4 vert column
(((II))((II))) - 4x tigers ((II)(II)) in concentric maj1/maj2 pairs
(((I)I)((II))) - 4x tigers ((II)(II)) in maj2 concentric pairs in 2x1x1x1 line
(((II)I)(()I)) - empty
--------------------------------------
XYZ 3D Intercepts
(((I)I)((I))) - 8x torii ((II)I) in 4x1x2 vertical rectangle
(((II))((I))) - 8x torii ((II)I) in 2 concentric maj pairs along 1x1x4 vertical column
(((I)I)(()I)) - empty
(((II)I)(())) - empty
((()I)((II))) - empty
----------------------------------------
XY 2D Intercepts
(((I))((I))) - 16 circles in 4x4 squareUsing the notation sequence (((II)I)((II)I)), the implicit equation can be derived like this:

(((II)I)((II)I)) = 0
((II)I)((II)I) = 0
((xy)z)((wv)u) = 0
((x + y) +z) + ((w + v) +u) = 0
((x + y -R1a) +z -R2a) + ((w + v -R1b) +u- R2b) -R3 = 0
((x + y -R1a)^2 +z -R2a)^2 + ((w + v -R1b)^2 +u- R2b)^2 -R3^2 = 0
((sqrt(x + y) -R1a)^2 +z -R2a)^2 + ((w + v -R1b)^2 +u- R2b)^2 -R3^2 = 0
((sqrt(x + y) -R1a)^2 +z -R2a)^2 + ((sqrt(w + v) -R1b)^2 +u- R2b)^2 -R3^2 = 0
(sqrt((sqrt(x + y) -R1a)^2 +z) -R2a)^2 + ((sqrt(w + v) -R1b)^2 +u- R2b)^2 -R3^2 = 0
(sqrt((sqrt(x + y) -R1a)^2 +z) -R2a)^2 + (sqrt((sqrt(w + v) -R1b)^2 +u) -R2b)^2 -R3^2 = 0
(sqrt((sqrt(x^2 + y^2) -R1a)^2 +z^2) -R2a)^2 + (sqrt((sqrt(w^2 + v^2) -R1b)^2 +u^2) -R2b)^2 -R3^2 = 0

Establish diameter values for non-intersection, and make 3D equation from cut (((II))((I))) :

(sqrt((sqrt(x^2 + y^2) - 2)^2 + 0^2) -1)^2 + (sqrt((sqrt(z^2 + 0^2) - 2)^2 + 0^2) -1)^2 = 0.4^2

Establish rotate + translate parameters:

(sqrt((sqrt((x*sin(b) + a*cos(b))^2 + (y*sin(d) + c*cos(d))^2) - 2)^2) -1)^2 + (sqrt((sqrt(z^2 + (y*cos(d) - c*sin(d))^2) - 2)^2 + (x*cos(b) - a*sin(b))^2) -1)^2 - 0.3^2 = 0

 

[homeomorphic]

So, what kind of future can this hold? Are there any other groups investigating this field of discrete high dimension geometry? I know Algebraic Topology is a related field, and I would love to be able to write the language for these shapes and concepts. It's pretty wild stuff!

I'm not sure, but it seems like a bit of a stretch to say algebraic topology is a related field. You could certainly apply algebraic topology techniques to the figures to tell them apart topologically (or homotopically), but that seems pretty tangential to what you're doing, and modern algebraic topologists generally seem to work on very algebraic stuff, like cobordism spectra, algebraic K-theory, or stable homotopy theory, which is pretty far removed from making computer plots of algebraic equations, and are very difficult to describe to the layman.

You might want to check out this subject, though:

http://en.wikipedia.org/wiki/Computational_geometry

There are probably other branches of math that could be relevant, but I'm not exactly sure where you want to go with it, and I'm not an expert on all nooks and crannies of math. I can tell you, it's probably a nook or a cranny you'll have to find if you want to just continue on that theme alone.

 

[Philip]

Yeah, you're probably right. It's a very small and specific thing, but who knows what the outcome may be. I've come across some interesting papers on the subject of " Hypertoric Varieties" : http://pages.uoregon.edu/njp/su.pdf . It describes the combinatorial nature in polynomials, which solve into exact roots as the intercepts. It's much more in-depth than I understand, but speaks of some familiar things. For discrete hypersurfaces, the topic itself seems so new, since there's no +5D hypertorus discussion or visuals anywhere else, other than one place: http://hddb.teamikaria.com/forum/viewforum.php?f=24 . Youtube has probably 5 people making hypertorus vids.

I can't find much more research on them other than what Mr. Proudfoot writes about. The animations are just a recreational math thing, in artistic form. It's the deeper understanding that I'm after now. I'd like to explore the maths that define them, and other related methods. It was quite an effort in learning the notation, and the shapes/concepts it stands for. Where, there seems to be so many high-level maths that barely get into their particulars. It makes me think if it's something novel and unexplored.

 

[sunny79]

Man, feel like I'm doing a 180. (Colloquially speaking). I was going down the "pure math" road. Now I am doing a project in mathematical oncology and it's really fascinating. http://moffitt.org/research--clinical-trials/research-disciplines/departments/integrated-mathematical-oncology

I'm working on differential equations (I did not enjoy this subject when I first took it) modeling of tumor growth (I have no biology background).

You just never know what's going to happen do you?

-Dave K

Dave! For an undergrad who is a math major wanting to pursue this path how would one go about it?

Here is another link...
http://mathematicalneurooncology.org

 

[sunny79]

Dave! My plan is to pursue a pure math track in undegrad while taking a good bunch of science classes and then either go to grad school for applied mathematics and follow it up with phd or medical school ( interested in radiation oncology a very technical specialty)
https://sites.google.com/site/jacobgscott/theoretical-biology

What were your experiences as a math major in undergraduate?What advice would you give to an upcoming math major? I am not a math whizz but I love math with a passion and am a hard worker. Also what do the top graduate schools look at when they accept you in their program?

 

[dkotschessaa]

Dave! For an undergrad who is a math major wanting to pursue this path how would one go about it?

Here is another link...
http://mathematicalneurooncology.org

I got kind of lucky because we have Moffitt here, which is the only hospital that has a dedicated mathematical oncology department. Of course it wasn't all luck. I kept emailing them about internship possibilities until they gave me one.

For you, I'd say try to get some background in biology (maybe double major) and learn some "scientific" programming, like matlab. Mathematically, differential equations (both partial and ordinary) are the big thing.

There are people doing mathematical oncology in other places, just not with a dedicated department. See if you can find these people and tell them you'd like to help. They might have some sort of project sitting around that is not high priority but that you can work on.

-Dave K

 

[dkotschessaa]

Dave! My plan is to pursue a pure math track in undegrad while taking a good bunch of science classes and then either go to grad school for applied mathematics and follow it up with phd or medical school ( interested in radiation oncology a very technical specialty)
https://sites.google.com/site/jacobgscott/theoretical-biology

What were your experiences as a math major in undergraduate?What advice would you give to an upcoming math major? I am not a math whizz but I love math with a passion and am a hard worker. Also what do the top graduate schools look at when they accept you in their program?

Not much time to answer this now (Grad school!) but I see nothing wrong with your plan, though you might also look at bioinformatics for grad school. (maybe).

 

[sunny79]

Dave! Currently I am in sophomore year. While pursuing a pure math and statistics track. I am also fulfilling all the science courses requirement for medical school including upper division courses, namely biology. Initially, I had considered majoring in biomathematics but felt that the amount of math which the degree offers isn't enough. I would love to get more tips from a fellow math major like yourself. My current goal is to ace all my math classes, take grad level courses in undergrad, try getting in research, perhaps attend Budapest semesters of mathematics and maybe, just maybe compete in Putnam and place well.

 

[David Carroll]

Re: The general "Should I become a Mathematician?" question.

I prefer pure math to any of the hard sciences for several reasons.

1) Math is morally neutral.

It is impossible to get angry doing math. You can sometimes get very frustrated but you can't get angry. Philosophy used to be my bag, but I found myself getting increasingly angry at the world because there exist too many people in the world who adhere to the "wrong" philosophy. Or who adhere to the right philosophy but for wrong reasons. You can't get angry at someone who believes that there exist zero's of the Riemann Zeta function that have a non-trivial real part of some value other than 1/2. But you can get VERY angry at someone who believes that Israel should be annihilated as a state.

If you hold to a mathematical position that is wrong, you are subject to the epithet "Idiot". But if you hold a philosophical/scientific/historical position that is wrong, you are subject to the epithets "Bigot", "Commie", "Terrorist", "Sexist", "Homophobe", AND to the epithet "Idiot".

Save yourself, O people, from this!

Furthermore, millions of people have been imprisoned, killed, persecuted, tortured, and defrauded for the sake of scientific, historical, or economic theories (see Hitler, KKK, Pol Pot, etc.). No one has ever been imprisoned, killed, persecuted, tortured, or defrauded for the sake of a Math theorem.

2) There are no such thing as opinionated mathematicians. Only wrong ones.

3) Math is the most democratic of all the branches of knowledge.

If you want to prove a math theorem, all you need is a pen and a piece of paper. You can be a beggar on the streets of Kansas City or Calcutta and if you submit such a theorem to the right journal, you are famous overnight. Try submitting a theory of physics, economics, or microbiology when you are a beggar on the streets of Kansas City or Calcutta. You won't even have the benefit of hearing the laughs aimed at you.

No stuffy philanthropist is needed to fund your equations written on notebooks.

I could go on and on, but I'll leave it at that.

 

[mathwonk]

The original title of this thread, chosen by its starter, was "Who wants to be a mathematician?"

 

[homeomorphic]

1) Math is morally neutral.
2) There are no such thing as opinionated mathematicians. Only wrong ones.
3) Math is the most democratic of all the branches of knowledge.

1) Math can't really be cut off from the sciences because there are extremely rare instances in which things trickle down from math and eventually become "useful". Not to mention there are evil mathematicians like me who actually care primarily about contributing something useful to society, rather than being paid to sit around and play abstract games.

2) Go read Doron Zeilberger's blog for a counter-example. There's more to math than raw facts and theorems.

3) What are the odds that a beggar would be able to acquire anything even remotely approaching the ultra-specialized knowledge required to publish in today's top math journals? There are rumors that certain branches, like combinatorics might not require as much background knowledge. I have a PhD from a highly ranked program, left whole classes of math majors in the dust as an undergrad, and I'm pretty sure my odds would have been slim to zero to contribute anything meaningful if I had stayed in academia. Also, aside from people like Wiles or Perelman who get media coverage, no one really gets famous in math anymore.

These kinds of things actually could have a great impact on whether someone wants to be a mathematician.

 

[David Carroll]

I'll only briefly reply since the powers-that-be might consider this thread to have taken a philosophical tangent (which is, ironically, breaking the very rules I myself set out to lay down in the previous post).

A wrench is morally neutral. The fact that I can take this wrench and bop somebody upside the head with it doesn't negate the wrench's moral neutrality.