Recent content by stgermaine

Hi. This is a homework question, so I can't ask or give out too much info. SO, there is a linear mapping F, and it is given that F=F^2. Can I assume that everything about F, i.e. dimension, kernel, image, etc, is exactly the same for F^2? Or does it just mean that given a vector v, F(v) =...

Hi. I just came back from the registrar and dropped the complex analysis course I was failing. I don't think I slacked off. True, it's the summer and I had a few kickbacks with my friends that I wouldn't have had during the academic year, but I really wasn't doing much else besides complex...

Homework Statement i'm using Fisher's Complex Variables for my complex analysis class and there is a proof for Liouville's theorem. It says "Set g(z)=(F(z) - F(0)) / z; Then g is an entire function" Homework Equations N/A The Attempt at a Solution I am confused by that statement...

Homework Statement Let f be an analytic function on the disc |z|<1 and satisfies |f(z)|≤M if |z|<1. Show that |f(z)| \le M \left| \frac{z-a}{1-a'z} \right| when |z|<1 where a' is the complex conjugate of a Homework Equations This section uses maximum modulus principle, but I really don't...

Hi. I am taking complex analysis over the summer and I am having a difficult time learning the concepts. I've tried reading several dfiferent textbooks, and though they sometimtes state the same theorem using different wording, different arguments, etc, I am still having a hard time...

I feel like algebra proceeded in a fairly step by step way. First you covered basic number theory. Then Euclid's algorithm, then you go into GCD and modular arithmetic, then Euler's totient theorem, etc. Complex analysis I guess does go in steps, covering complex variables first, then learning...

No, I think it's just that I totally suck at analysis. I took algebra and linear algebra (300 and 400 level courses) which had plenty of proofs. I was also taking differential equations last semester but ended up dropping it. Proofs I am fine with, but it just something about complex analysis...

Hi I am taking summer class in complex analysis and I am having a horrible time. I don't understand anything we've covered so far, e.g. Cauchy-Goursat theorem, Laurent series, series expansion, etc. The prereqs was just Calc III, which I got an A- in. The textbook isn't much help...

Hi. I'm a math major and I am considering either a CS minor or a stats minor. The question I have is how useful a CS minor would be, especially in careers outside of software development. I would have to stay an extra semester for a stats minor, but I see a stats minor as more applicable...

Hi. I'm currently a math major and I need to choose a concentration (CS or stats). I've already taken MATLAB and currently taking C++. I've noticed that upper-level courses are not about programming but are about machine learning, algorithms, cryptography, etc. I think I am capable at...

Homework Statement Find all integers x such that 7x \equiv 11 mod 30 and 9x \equiv 17 mod 25 Homework Equations I guess the Chinese Remainder theorem and Bezout's theorem would be used here. The Attempt at a Solution I can do this if the x-terms didn't have a...

Hi. I will be a math major starting nex semester as a junior. I transferred from a CC, so the only math courses I have taken are linear algebra and calc III. I only have 2 years left at the college I've transferred into and there are just so many courses I want to take. Should I be so...

k is a square modulo m?? \:Homework Statement This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m. I have no idea what "k is a square modulo m" means. Homework Equations The Attempt at a Solution I've looked it up online and found some PDF's...

1. Homework Statement [/b] Prove that the number 2^{2^{n}} - 1 has at least n distinct prime factors. Homework Equations Seems like I'd have to use Fermat numbers and its properties to solve this question. F(n) = 2^{2^{n}} + 1 F(n) = (F(n-1) - 1)^{2} + 1 F(n) = F(0)*F(1)*...*F(n-1) +2...

Homework Statement Find a formula for the sum of the elements of the nth row of Pascal's Triangle Homework Equations C(n,r) = [C(n-1,r-1) + C(n-1,r)] C(n,0) = C(n,n) = 1 The Attempt at a Solution I started with the summation of the elements in the rows n \sum^{n}_{r=0} C(n,r)...