Hi
I've recently decided to become a math major, as it's the subject that I've enjoyed the most and had the most exposure to during high school.
During high school, the AP Calc classes and a Calc III course I took at a local CC came to me quite naturally. I just followed along to the...
Honors analysis is known to be one of the hardest math courses....people that I've talked to advised me not to take it unless I'm really up for it. I'll be taking a 400 level stats course next semester..maybe it'll come up there.
Searching the course catalog doesn't really show any courses that focus on measure theory. Honors analysis syllabus shows that it covers Lebesgue measure and integration.
I'm just starting out, so I don't know too much about the courses. What kind of courses would focus on measure theory?
Two courses in Algebra (Linear algebra, intro to algebra, computational algebra, number theory, matrix group, applicable algebra)
Two courses in analysis (analysis, manifolds and differential forms, intro to diff eq, applied complex analysis, Waves and fourier series, Intro to partial diff...
Hi. I am a math major that got started late. I started taking prerequisites during my sophomore year (which I'm finishing this year). I'll be taking some courses in algebra and analysis next year. There are some courses that can fulfill my major requirements, but some are theoretical and some...
Hi. I'm currently a sophomore and I am doing a math major with a concentration in statistics. I'm a bit overwhelmed by the amount of courses there are for the major.
I haven't taken any math classes during my first year, and I just finished up linear algebra (intro level; will be taking upper...
Hi. I'm planning on doing a double major with psychology and mathematics.
My parents are opposed to this, and they think that I should major in psychology and do premed. They are doctors and all their doctor friends are employed and having a good life in general. The only people that they know...
I know what you are trying to say but in terms of rational numbers, there are no factors in common between 24 and 49, but according to this problem, there might be a factor that is a quadratic integer in Q[sqrt3]. The question is which numbers do we know is a factor or not? Since 3 is not...
The idea for this program is derived from Euclid's algorithm...i just need to see if a number is an integer or not
If I fix the loop to while and increase the upper bound of the counter to say 35, woudl this program help me see if b contains decimals or not?
Hi
I wanted to make a program that would check if a number if it was an integer or not in Java. here's the source code:
import static java.lang.Math.*;
public class gcd {
public static void main(String [] args) {
double a = 1;
double b =1;
double c = 1...
Homework Statement
Prove unique factorization for hte set of polynomials in x with integer coefficients
Homework Equations
The Euclidean algorithm may be of some use
The Attempt at a Solution
Let's say that the polynomial is of the form anx^n + a(n-1)x^(n-1) ... a1x + a0
There...
The 'hypothenuse' seems to play a role in that
1
-8 -7
28 -16 9
-7 - 1 = -8
-7 - 9 = -16
As far as the other numbers go I havent gotten them yet, but just putting this out there as a possible stepping stone
For the theorem that states that in quadratic field Q[sqrt d], if d is congruent to 1 mod 4, then it is in the form (a + b sqrt d)/2 and if it's not, it's in the form a + b sqrt d where a and b are rational integers, is it saying that if a and b are rational integers and the quadratic number are...
I COULD use the euclidean algorithm, but I wouldn't know where to start, as these numbers are rational primes, and I need to find solutions in Q[sqrt 3]
Hi.
I need to find the GCD of two numbers in Q[sqrt 3]. Let's suppose these two numbers are 12 and 35. How would you go about finding the GCD of those in Q[sqrt 3]?
thanks~
I'm making a quick comment
Euler's totient function IS multiplicative. Someone said it's only for coprimes but there's a general form where the 2 numbers dont have to be coprime
phi(mn) = phi(m)phi(n) * d/phi(d)
where d is the GCD of m and n.
Let m = f1^a1 * f2^a2 ... fk^ak where each fk is a prime (basically the prime factorizatin of m)
Let n = p1^a1 * p2^a2 ... pk^ak where each pk is a prime. The k or each ak has no connection to the prime factorization of n. I'm just making a general prime factorization of numbers.
Let d equal...
If the OP's question is why phi(2n) = phi(n) when n is odd, I think my explanation is clear enough,.... see post #5.
please feel free to ask questions and dont say stuff like even numbers have no factor of two.
@Mensanator
ϕ(2m) = 2ϕ(m) ONLY IF m is even thats where's the mystery. And i think I did a pretty good job explaining it in post #5 if anyone is interested...
The formula for euler's function ϕ(n) is given by
ϕ(n) = n (1-1/p1) (1 – 1/p2) … (1 – 1/pk)
where n is prime factorized into p1a1p2a2...pkak and each pk is a prime.
Assume n is an odd number. None of the pk will be an even number. When n is multiplied by 2, the prime factorization of n will...