Thread: The Most "Important" Math Discipline

If you decided to master an area of math, which one would it be? Algebra, trigonometry, calculus, linear algebra, and probability and statistics are all very important. I think I'd like to master calculus.

Jagella

I think you made an excellent choice, but why stop there? I think linear algebra would be an excellent second choice. Not only is it important in its own right, but it would be very helpful in mastering calculus.

As I learn more maths, one thing is clear to me: that concepts from one branch provide a deeper insight into other branches. Thus, to master one branch, one really needs to master them all. Category theory is perhaps the one branch of mathematics that attempts to unify all the other branches of mathematics, including itself.

Master algebra in it's entirety, and most higher maths will be easier than if otherwise. jocular

I really enjoy geometry and the different types of it. Interesting. I also like abstract algebra. I'm not sure what I would pick.

Originally Posted by KJW

I think you made an excellent choice, but why stop there? I think linear algebra would be an excellent second choice. Not only is it important in its own right, but it would be very helpful in mastering calculus.

Thanks. Linear algebra is on deck for my planned math studies.

Jagella

Originally Posted by KJW

As I learn more maths, one thing is clear to me: that concepts from one branch provide a deeper insight into other branches. Thus, to master one branch, one really needs to master them all. Category theory is perhaps the one branch of mathematics that attempts to unify all the other branches of mathematics, including itself.

In any branch of math, π times the diameter of a circle equals its circumference, 2 + 2 = 4, and x^2 = 1 has the solution set {1, -1}. It's rather arbitrary to call one branch calculus when it's geometry, trigonometry, and algebra applied to some situations.

Jagella

Originally Posted by jocular

Master algebra in it's entirety, and most higher maths will be easier than if otherwise. jocular

Algebra is very important. It may well be the most important discipline in math aside from arithmetic.

Jagella

Originally Posted by anticorncob28

I really enjoy geometry and the different types of it.

Geometry is very important! It may be the least abstract field of math.

Jagella

Originally Posted by Jagella

Originally Posted by KJW

As I learn more maths, one thing is clear to me: that concepts from one branch provide a deeper insight into other branches. Thus, to master one branch, one really needs to master them all. Category theory is perhaps the one branch of mathematics that attempts to unify all the other branches of mathematics, including itself.

In any branch of math, π times the diameter of a circle equals its circumference, 2 + 2 = 4, and x^2 = 1 has the solution set {1, -1}. It's rather arbitrary to call one branch calculus when it's geometry, trigonometry, and algebra applied to some situations.

Perhaps, but I was thinking more along the lines of something like treating a correlation function from statistics as a dot product of two unit vectors from vector algebra.

Originally Posted by KJW

Perhaps, but I was thinking more along the lines of something like treating a correlation function from statistics as a dot product of two unit vectors from vector algebra.

That's a good example of how math disciplines overlap a lot. When you study probability, you calculate some probabilities using a normal curve. The area under that curve is the probability of an event, and that area can be found by using a definite integral from calculus.

So it's all "math" although we may call it something else.

Jagella

Originally Posted by Jagella

Geometry is very important! It may be the least abstract field of math.

Geometrical Drawing and Perspective (Technical Drawing) is a useful tool for conceptualizing applied maths.

Originally Posted by Laurieag

Originally Posted by Jagella

Geometry is very important! It may be the least abstract field of math.

Geometrical Drawing and Perspective (Technical Drawing) is a useful tool for conceptualizing applied maths.

I tend to think that applied maths is more the subject it is applied to than mathematics itself.

In any branch of math, π times the diameter of a circle equals its circumference

Two words: non-Euclidean geometry.

Originally Posted by anticorncob28

In any branch of math, π times the diameter of a circle equals its circumference

Two words: non-Euclidean geometry.

OK, you got me on that one. Pi times the diameter of a circle on a flat plane equals its circumference.

Have you studied non-Euclidean geometry? What's it like?

Jagella

Er... whichever you enjoy the most?

OK, you got me on that one. Pi times the diameter of a circle on a flat plane equals its circumference.

Have you studied non-Euclidean geometry? What's it like?

I tried inventing my own geometry, but lost interest in it. I've never gotten into too much details about hyperbolic geometry (what I'd probably study if I had to take non-Euclidean geometry), but it's not as difficult as I once imagined. I believe it's a geometry where Euclid's first four postulates are true, and the fifth is false, thus proving once and for all that it is impossible to prove Euclid's fifth postulate from the other four. btw, does anybody know a formula of the form z = f(x, y) that creates a hyperbolic surface where the rules of hyperbolic geometry apply?

Learn the ruler. A ruler that is fatter on one side is also helpful. Rulers are good for measuring things.

Originally Posted by anticorncob28

OK, you got me on that one. Pi times the diameter of a circle on a flat plane equals its circumference.

Have you studied non-Euclidean geometry? What's it like?

I tried inventing my own geometry, but lost interest in it. I've never gotten into too much details about hyperbolic geometry (what I'd probably study if I had to take non-Euclidean geometry), but it's not as difficult as I once imagined. I believe it's a geometry where Euclid's first four postulates are true, and the fifth is false, thus proving once and for all that it is impossible to prove Euclid's fifth postulate from the other four. btw, does anybody know a formula of the form z = f(x, y) that creates a hyperbolic surface where the rules of hyperbolic geometry apply?

You're looking for an embedding of the hyperbolic plane. IIRC, you can't embed it in less than 5 euclidean dimensions, which would mean your z would be f(x,y,z,u,v) (or something similar). I'm pretty sure I've gotten some of my terminology wrong though, because there are ways to embed the hyperbolic plane in two dimensions (Poincare disk model) but not with the usual euclidean distance metric.