[quote=CRGreathouse;208844]That's fine, just explain what you know ("the quadratic formula, graphing polynomials, logarithms and exponentials, trigonometric functions"). Otherwise, it will be hard to guess what to recommend![/quote]
I understand.

Number Theory:
Euclid's algorithm.
Perfect numbers, and Mersenne numbers materials.
Some theorems in number theory.
Gauss's and Euler's criterions.
The reciprocity law.
The recidue classes.
The golden ratio and Fibbonaci's numbers.
Arithmetic functions.

Algebra:
High school's algebra.
That's why I want to improve it..

Calculus:
High school's logarithms and exponentials.
Basic Trigonometric functions.
Basic the quadratic formula.
Basic linear functions.
Basic ntegrals and derivatives.

As you see I have an high school's calculus and algebra knowledge, and I want to improve it to first's grade level.

Thanks.

I have a question:
if p_1(n) means the first prime number such that it's succsesive prime is p_1(n)+n .
Like 7,11 (n=4),
23,29 (n=6).
The question is: is there a connection between "n" for p_1(n) to
Pie(p_1(n)) (the number of smaller prime numbers)?

I have a problem with understanding "the prime number theorem", and "the twin primes theorem".
The prime number theorem, as I know, means:
For n-->infinity
Pi(n)/(n/ln(n))=1
Right?
This is becuase of the orders of these:
Pi(n) and (n/ln(n)) are equal?
But order (as I know) is not the exaxtly phrase, it is just the dominantic part of it. Yes I agree that at infinity the dominantic part is a much larger infinity than the other parts can be, for example: y=n^2+n, the order is n^2.
for x-->infinity.
But f(x)/g(x)=1
seems not exactly the right thing.
Let me examply:
But x+1/x=1
for x-->infinity.
Is right, right?
Seems still wrong to me.

The second problem is:
The twin primes theorem by Hardy-Littlewood.
I try to play with this conjecture to gain some expirience...
I'm sorry to say that, for everyone who is angry about me, I conjectured some conjectures on this area, and I try to exuse them.
I continued and got some ideas about the area of this conjecture..
I conjectured these without knowing too much about orders and the order of Pi_2(n) (which is still unknown).
Just conjectured by looking on the numbers of twin prime numbers between o to natural "n".
Still sorry for conjecturing, but wanted to say anything about it.
I keep reading and learning..

Thanks tomer.

[QUOTE=blob100;211416]I have a problem with understanding "the prime number theorem", and "the twin primes theorem".
The prime number theorem, as I know, means:
For n-->infinity
Pi(n)/(n/ln(n))=1
Right?
This is becuase of the orders of these:
Pi(n) and (n/ln(n)) are equal?
But order (as I know) is not the exaxtly phrase, it is just the dominantic part of it. Yes I agree that at infinity the dominantic part is a much larger infinity than the other parts can be, for example: y=n^2+n, the order is n^2.
for x-->infinity.
But f(x)/g(x)=1
seems not exactly the right thing.
Let me examply:
But x+1/x=1
for x-->infinity.
Is right, right?
Seems still wrong to me.[/QUOTE]

I think what you're saying is that there are still lower-order terms beside the dominant term x/log x for pi(x). Yes, there are other terms; the next one would be x/(log x)^2, then 2x/(log x)^3. There are also oscillatory components...

[QUOTE=blob100;211416]The twin primes theorem by Hardy-Littlewood.
I try to play with this conjecture to gain some expirience...
I'm sorry to say that, for everyone who is angry about me, I conjectured some conjectures on this area, and I try to exuse them.
I continued and got some ideas about the area of this conjecture..
I conjectured these without knowing too much about orders and the order of Pi_2(n) (which is still unknown).
Just conjectured by looking on the numbers of twin prime numbers between o to natural "n".[/QUOTE]

What's the question?

[QUOTE=blob100;211416]
The prime number theorem, as I know, means:
For n-->infinity
Pi(n)/(n/ln(n))=1
Right?
[/QUOTE]

Not exactly. The prime number theorem is:
For n-->infinity
Pi(n)/(n/ln(n)) --> 1

Here the notation "-->" means the [I]limit[/I] of Pi(n)/(n/ln(n)) is 1 for n-->infinity.
By definition of limit this means that for any positive real ε there exists an N such that |Pi(n)/(n/ln(n)) - 1| < ε for all n > N.

Loosely speaking, Pi(n)/(n/ln(n)) can get as close to 1 as we want if we just make n large enough.

See more about limits at for example [url]http://mathworld.wolfram.com/Limit.html[/url].

[quote=CRGreathouse;211425]I think what you're saying is that there are still lower-order terms beside the dominant term x/log x for pi(x). Yes, there are other terms; the next one would be x/(log x)^2, then 2x/(log x)^3. There are also oscillatory components...



What's the question?[/quote]
There are three questions:
First: I'm I able to conjecture?
Second: can anyone give me some info about this theorem?
Third: Will you help me with my conjectures and tell me why are these false or true (it will help me to understand my mistakes or non-mistakes).
Fourt: I saw that how we continue with larging "n" in the prime number theorem, Pi(n)/(n/ln(n)) becomes less 1.
Can u explain?

[QUOTE=blob100;211493]There are three questions:
First: I'm I able to conjecture?
Second: can anyone give me some info about this theorem?
Third: Will you help me with my conjectures and tell me why are these false or true (it will help me to understand my mistakes or non-mistakes).
Fourt: I saw that how we continue with larging "n" in the prime number theorem, Pi(n)/(n/ln(n)) becomes less 1.
Can u explain?[/QUOTE]

Here is a 3/4 answer to the first question:

Yes, but they might be so off that they stop being conjectures before you even make them. In mathematics a conjecture is an unproven proposition that appears correct. It requires a lot of knowledge and insight to make a conjecture without being arrogant. It is best not to use the word conjecture, but rather state claims, questions or opinions. (I think this has been said enough many times now.)

[quote=rajula;211500]Here is a 3/4 answer to the first question:

Yes, but they might be so off that they stop being conjectures before you even make them. In mathematics a conjecture is an unproven proposition that appears correct. It requires a lot of knowledge and insight to make a conjecture without being arrogant. It is best not to use the word conjecture, but rather state claims, questions or opinions. (I think this has been said enough many times now.)[/quote]
Thanks for answering me.
So how to call these?

[QUOTE=blob100;211502]Thanks for answering me.
So how to call these?[/QUOTE]

What is the [b]question[/b]????

It is a theorem that lim n-->oo pi(n)/ (n/log(n)) = 1.

It is also a theorem that better approximations to pi(n) exist than
n/log(n). In particular, li(x) = integral from 2 to x of dz/log(z) is a
better approximation. We can even give a bound for the amount of
error in the approximation.

It is also known that p(i) - li(x) changes sign infinitely often.

It is also know that p_n > n log(n) for ALL n > 1. (proved in a
deservedly famous paper by Rosser and Schoenfeld) p_n is the n'th prime.
The same paper proved pi(n) > n/log(n) for all n > 17.

This can even be improved to p_n > n(log(n) + loglog(n) - 1)

What do you want to know?

[quote=R.D. Silverman;211503]What is the [B]question[/B]????

It is a theorem that lim n-->oo pi(n)/ (n/log(n)) = 1.

It is also a theorem that better approximations to pi(n) exist than
n/log(n). In particular, li(x) = integral from 2 to x of dz/log(z) is a
better approximation. We can even give a bound for the amount of
error in the approximation.

It is also known that p(i) - li(x) changes sign infinitely often.

It is also know that p_n > n log(n) for ALL n > 1. (proved in a
deservedly famous paper by Rosser and Schoenfeld) p_n is the n'th prime.
The same paper proved pi(n) > n/log(n) for all n > 17.

This can even be improved to p_n > n(log(n) + loglog(n) - 1)

What do you want to know?[/quote]
Thanks for answering.
Others explained what you've said.
The question was about how to call a proposition which wasn't exused and were conjectured?
The second question was: if to post my new propositions here even though I'm just me (not a proffesional mathematicain, etc.)?

[quote=cmd;211510]Tomer, play now ???

We have four types of frogs that jump distances with ever exactly alike ...
first type, frogs type "b"
second type, frogs type "d"
third type, frogs type "p"
fourth type, frogs type "q"

and only two individual frogs special the "[B]y[/B]" and "[B]j[/B]" ...

interested in knowing how to behave when "all" jump along a straight line, infinite?[/quote]

Do these frogs jump on the straight line, or random walk?