What Proves More Math Formulas and Theorems?

Calculus or Combinatorics? My belief is that arithmetic is the sacred ground of mathematics, and since, to me, combinatorics is closer to arithmetic, combinatorics proves more formulas and theorems.

As an engineering student, I have taken four calculus courses, but I've never studied combinatorics, and barely even know what it is. I do know that you can prove a TON of formulas and theorems with calculus. I strongly suspect that it proves more formulas/theorems than combinatorics, but I don't know that for certain.

All math to me is arithmetic. I get mad when people use algebra and calculus.

I swear its a conspiracy to complicate something that doesnt have to be.

i do not know how algebra seems like a conspiracy to you.

To say you get mad when people use algebra is to get mad at yourself.

Posting on this website, you are sending the information you want displayed to the world through many different alegbra and logic equations.

This is the most relevant example at this exact moment, but there are other times I am sure you unwittingly use algebra and calculus. Its just that other people have done extra work so that you wont have to think as hard about math.

---Pineapple

GreatTech,

to respond to you, I have never taken a course in Combinatorics, although I am currently taking a Calculus AB class.

Could you give us a few examples of theorems solved through combinatorics, so we can see what you are refering to?

---Pineapple

Originally posted by pineappleupsidedown
i do not know how algebra seems like a conspiracy to you.

To say you get mad when people use algebra is to get mad at yourself.

Posting on this website, you are sending the information you want displayed to the world through many different alegbra and logic equations.

This is the most relevant example at this exact moment, but there are other times I am sure you unwittingly use algebra and calculus. Its just that other people have done extra work so that you wont have to think as hard about math.

---Pineapple

And do you know how algebra is implemented in computer hardware? As arithmetic.

The binary computer langauge is all arithmetic. There is no "algebra" behind the scenes that makes this message board posting possible.

Algebra is still useful, I like algebra. But it is overly complicated in how it is taught.

Calculus is useless.

Originally posted by ImplementOfWar
Calculus is useless.

If you want to live like a primative, yes it would be useless. Have trouble in math classes do we?

All branches of mathematics are related to some degree. So, you can't really say which proves more theorems. The calculus is a method of calculating areas, and finding the rates of change, but behind it is a whole area of theoretical mathematics, called analysis. Combinatorics foundation is built upon what is called abstract algebra.

Basically, Analysis concerns itself with the best approximations of what cannot be precisely known. For instance consider the sequence [3, 3.1, 3.14, 3.141, 3.1415, 3.14159, 3.141592, ...]. Each number gets successively closer to PI. However, we can never write an exact decimal for PI. You can similarly visualize this by considering C=2*PI*r for a circle. You can approximate a circle by drawing equilateral shapes with 3,4,5,... sides, and taking the ratio of a point from the center to the edge, and the circumference.

In abstract algebra, we are more concerned with operations, like mulitiplication, addition, and subtraction. However, we can also be concerned with things like how many different ways are there to rotate a wheel. For instnace, if you have 60-sided ferris wheel, and you rotate it past 40 people, and then you rotate it past another 30 people, how far will all the seats be from where they started? Each different type of rotation can be considered a member of a group, and two rotations multiplied together would make up the other rotation.

Originally posted by crontab
All branches of mathematics are related to some degree. So, you can't really say which proves more theorems. The calculus is a method of calculating areas, and finding the rates of change, but behind it is a whole area of theoretical mathematics, called analysis. Combinatorics foundation is built upon what is called abstract algebra.

Basically, Analysis concerns itself with the best approximations of what cannot be precisely known. For instance consider the sequence [3, 3.1, 3.14, 3.141, 3.1415, 3.14159, 3.141592, ...]. Each number gets successively closer to PI. However, we can never write an exact decimal for PI. You can similarly visualize this by considering C=2*PI*r for a circle. You can approximate a circle by drawing equilateral shapes with 3,4,5,... sides, and taking the ratio of a point from the center to the edge, and the circumference.

In abstract algebra, we are more concerned with operations, like mulitiplication, addition, and subtraction. However, we can also be concerned with things like how many different ways are there to rotate a wheel. For instnace, if you have 60-sided ferris wheel, and you rotate it past 40 people, and then you rotate it past another 30 people, how far will all the seats be from where they started? Each different type of rotation can be considered a member of a group, and two rotations multiplied together would make up the other rotation.

I think your post might mislead people to think that Combinatorics is about approximating values or optimizing.
Combinatorics is basically what the name suggests- a system for counting a certain number of combinations. It is the basis for game theory.

For ex: How many ways can you arrange the word " MISSISSIPPI" or how many outfits can you make from 4 shirts, 2 pants, and 4 ties etc etc.

Also, I wouldnt really say that the foundation of combinatorics lies in Linear algebra.

Like crontab states, linear algebra deals with more simple functions and builds up from there. You wanna prove thms and equations, linear algebra would be a good start. Calculus is really used to apply the formulas and theorems to real life problems.

Originally posted by ImplementOfWar

Originally posted by pineappleupsidedown
i do not know how algebra seems like a conspiracy to you.

To say you get mad when people use algebra is to get mad at yourself.

Posting on this website, you are sending the information you want displayed to the world through many different alegbra and logic equations.

This is the most relevant example at this exact moment, but there are other times I am sure you unwittingly use algebra and calculus. Its just that other people have done extra work so that you wont have to think as hard about math.

---Pineapple

And do you know how algebra is implemented in computer hardware? As arithmetic.

The binary computer langauge is all arithmetic. There is no "algebra" behind the scenes that makes this message board posting possible.

Algebra is still useful, I like algebra. But it is overly complicated in how it is taught.

Calculus is useless.

I agree with you on algebra, and I do think they teach mathmatics ridiculosuly in a way too complicated manner in the US. They have made so overly simple, but the problems in homework and tests always tend to made more complicated. I understand most algebra, but I get lost in geometry and took math tutoring for years while in public school. So I think the deal Clinton broke with the UNESCO people for the public schools, is useless to say the least, if most adults only understand math up to my level, and math is the biggest GPA maker for most schools and thier curriculums.