Recent content by iironiic

I am struggling to find a way to count the number of irrational points defined recursively which satisfies specific conditions. This is the only hurdle I need to overcome, but the problem is proving itself extremely difficult. Here is my construction of a recursion. My goal is to...

Homework Statement Prove that a! b! | (a+b)!. Homework Equations Probably some Number Theory Theorem I can't think of at the moment. The Attempt at a Solution Without loss of generality, let a < b. Therefore b! | \Pi _{k=1}^b a+k. Since (a+1) ... (a+b) are b consecutive...

Homework Statement Suppose that I\subseteq J are subfields of \mathbb{C}(t_1,...,t_n) (that is, subsets closed under the operations +, - , \times, \div), and J is generated by J_1,...,J_r where I \subseteq J_j \subseteq J for each j and J_j:I is radical. By induction on r, prove that J:I is...

I have been working on a problem proposed in a math journal, and there is only one thing I need to figure out. Here it is: Let (a_n) be a sequence defined by a_1 = a and a_{n+1} = 2^n-\sqrt{2^n(2^n-a_n)} for all 0 \leq a \leq 2 and n \geq 1. Find \lim_{n \rightarrow \infty} 2^n a_n in terms...

Hello! I have applied to ~10 REUs as well. From whom I have heard so far: 1) Rejected at Emory 2) Rejected at Duluth I haven't heard from the SMALL Program yet either, but I applied for the Number Theory/Probability project.

To input something in this discussion, aside from the trivial solution, m can't be even. If m was even, the parities don't match up, so you know that m has to be odd. I'll try to figure something more later.

Yeah! I heard that teacher recommendations are substantially important in the application process, so it's really important to know your professors well. Fortunately I know my professors very well so hopefully this will help me during the application process. I have taken two classes last...

Yeah I think I'm aiming around 10, just because I'm a little inferior about my chances lol. From what I've heard, the SMALL Program at Williams and the Duluth Program (now at Emory I think) are very difficult to be admitted into. I also know that Cornell's REU program is rather selective but...

Hello! I am currently in the same exact boat as you are (except I took Calc 1-3, two semesters of linear algebra, an introductory proofs class, and probability and stats, and will be taking number theory and differential equations). Which REUs are you considering applying to for the summer?