Read about discrete math | 14 Discussions | Page 1

  1. I

    I Discrete Optimization Problem?

    Consider the expression: $$A = \frac{ M! }{ r_1!\ r_2! }$$ where M = r_1 + r_2 , where r_1 = (M - 2r_2) $$A = \frac{ (r_1 + r_2)! }{ r_1!\ r_2! } \\ \ \\ \ = \frac{ ((M-2r_2) + r_2)! }{ (M-2r_2)!\ (r_2)! } \\ \ \\ \ = \frac{ (M-r_2)! }{ (M-2r_2)!\ r_2! } $$ Then, for a...
  2. R

    Broken Stick Math Discussion

    Here's a math question I've been thinking about lately. We have a stick of length one which is broken in one spot (with that spot chosen randomly and uniformly). Of the two broken pieces we take the one on the right and break it into two pieces in the same manner as before. With our three...
  3. I

    A Finding the bounds of a ratio

    Sorry in advance if I've posted in the wrong section. given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}## where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}## How would you go about finding the bounds of something like this, or determining if it even has any? ##( \...
  4. P

    [Discrete] Prove that |nZ| = |Z| for any postive integer n

    I have been studying discrete mathematics for fun and I am kind of stuck on this bijection problem. 1. Homework Statement I wanted to apologize in advance if i put this homework question in the wrong part of the forums. Discrete Math and much logic math is a computer science type math of...
  5. Kartik Yadav

    Big-Oh proof

    To prove that n log n is big oh of log(n!), I did: n log n <= C log(n!) n log n/ log(n!) <= C Let k = 1 n > k, so for n = 2 2 log 2 / log 2 <= C 2 <= C C is an element of [2, infinity) Taking C = 2 and k = 1 can we say, n log n <= 2 log(n!) and hence n log n is big oh of log(n!) ?
  6. J

    MATLAB 3D Diffusion Equation in MATLAB

    Hi guys, I have functioning MATLAB code for my solution of the 3D Diffusion equation (using a 3D Fourier transform and Crank-Nicolsen) that runs just from the command window and automatically plots the results. However, it seems like my solution just decays to zero regardless of what initial...
  7. K

    Negation for proposition

    my attempt. Let P = At least one a and at least one b Let Q = r=a/b Hence the proposition is simplified to, For all r where P Then Q Negation: Not all r where P Then Q = Atleast one R When Not(P Then Q) Not(P Then Q) = P And Not Q Hence Atleast one R When Not(P Then Q) = Atleast one R When...
  8. Dewgale

    Discrete Independent Study of Discrete Mathematics

    Hi all, Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject? Thanks!
  9. S

    Problem with rectangles

    <<Mentor note: Missing template due to originally being posted in other forum.>> So, my professor gave a problem which stated: Given a 15 x 20 rectangle, prove that if 26 points are chosen, at least one pair will be at most five units away. What I said was to split the rectangle into 12 5x5...
  10. Extreme112

    Combinatorics Questions

    Homework Statement How many ways can you select 10 jellybeans from colors Red, Blue, Green so that at most you only have 4 Green jellybeans? Homework Equations ... 3. The Attempt at a Solution [/B] # of ways = # of ways to pick 1 Green + # of ways to pick 2 Green + #of ways to pick 3...
  11. Extreme112

    Help with simplifying boolean expression

    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > (A+B)&(C+D) + (A+B)&(C+D)' + C (A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans (A+B)&[(C+D)+(C'&D')] + C by Distributive I'm just wondering if I did anything wrong in this simplification or if it...
  12. eseefreak

    Discrete math study strategy - Tips and advice!

    Hi everyone, I haven't been successful in Discrete Math this semester. I have finished all of the calculus I-III series and I did very well. I want to know if anyone can give me some tips on how to study for my final coming up in a few days. Now, I understand that is a vague question but I am...
  13. eseefreak

    Reflexive, Symmetric, Transitive - Prove related problem

    Homework Statement Let A=RxR=the set of all ordered pairs (x,y), where x and y are real numbers. Define relation P on A as follows: For all (x,y) and (z,w) in A, (x,y)P(z,w) iff x-y=z-w Homework Equations R is reflexive if, and only if, for all x ∈ A,x R x. R is symmetric if, and only if, for...
  14. H

    Discrete Math Question

    Prove the following theorem: Theorem For a prime number p and integer i, if 0 < i < p then p!/[(p− i)! * i] * 1/p Not sure how to go about this. I wanted to do a direct proof and this is what Ive got so far. let i = p-n then p!/[(p-n)!*(p-n)] but that doesnt exactly prove much.
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