Discrete Definition and 897 Threads

hi, Zee in QFT in nut shell says "The most unsatisfying feature of field theory is the present formulation of gauge theories. Gauge symmetry does not relate 2 different physical states but the same physical state. We have this strange language with redundancy which we cannot live without" He...

Homework Statement Okay so I'm trying to teach myself the first three chapters if Grimaldi before I take a discrete math course in January. I'll probably be posting a few problems. The question is as follows: In how many ways can we select n objects from a collection of size 2n that...

Homework Statement Here is the question: how can we know that if we have discrete or continuous spectrum just by looking at the potential graph? Specifically, let`s consider the potential V(x)=-F*x (F:const) . After we solve, we can conclude wavefunctin is airy function, and so both...

1. Homework Statement Use set builder notation to give a description of each of these sets. a) { 0,3,6,9,12 } b) { -3, -2, -1,0, 1, 2, 3 } c) { m,n,o,p } 3. The Attempt at a Solution X={x l x is an odd possitive multiplier of 3 less than 12 } X is supposed...

"Pure" Mathematics vs. Applied Math vs. Discrete Math I'm approaching the point where I'm going to have to decide which four-year university I'm going to finish my Bachelor's degree at. I'm pretty much restricted to colleges in Georgia, and I am primarily looking at Georgia State and Georgia...

how do i interpret this probability distribution: \sum_{k=r}^\infty \binom{k}{r}p^k(1-p)^{k-r} where r is the number of successes, p is the probability, k trials. by looking at it, it seems like it's similar to a negative binomial distribution once you pull out a k/r. if you do some...

Been enjoying Physics Forums and this is my first question so before I ask I should I applaud everyone for the helpful friendly atmosphere. I'm trying to understand the concepts of continuity and connectedness. I have no set theory background nor physics backgrounds so I just read online...

Homework Statement A card is drawn at random from an ordinary deck of 52 cards and its face value is noted, and then this card is returned to the deck. This procedure is done 4 times all together. Let X be the total number of aces selected and Y = \cos(\pi X/2). E[Y] = ? Homework Equations...

Hi! I don't know much about QM. I'm reading lecture notes at the moment. Angular momentum is discussed. The ladder operators for the angular-momentum z-component are defined, it is shown that <L_z>^2 <= <L^2>, so the z component of angular momentum is bounded by the absolute value of angular...

Homework Statement I want to construct a truth table for the following propositions Homework Equations (a) ¬p ∨ q (b) p ∧ q ⇒ p (c) ¬p ∨ q ⇔ p ⇒ q The Attempt at a Solution Approach: 1) Determine the order of precedence: 2) Fill in the values for the operator...

Anybody know of any uses of discrete math in physics? I learned proof by induction in discrete math. Is that used to prove anything in physics? Any other examples that you can think of?

I don't understand how in quantum mechanics we have discrete and exact energy states for electron orbits but then at the same time we have a continuous probability density function for the position of an electron. This seems like a paradox (although I know it can't be) since considering a...

Hi, I have some troubles with this question. Define an operator * on R by x*y = 2xy -x -y +1 a) is * commutative? b) is * associative? I can easily see that * is commutative, but how do i test for associativity? The rule states that (x*y)*z = x*(y*z) But what is z ?

Whether or not time is discrete or continuous is unknown, and is a key idea answer that many physicists are looking for. This topi is for discussing the factors that effects whether or not ime is continuous, and effects it might have. Before i talk about whether or not time is discrete or...

Homework Statement Let X be a discrete random variable with probability mass function p given by: a ...| -1 .| 0 ..| 1 ..| 2 -----+-----+-----+-----+--- p(a) | 1/4 | 1/8 | 1/8 | 1/2 and p(a) = 0 for all other a. a.) Let random variable Y be defined by Y = X^2. Calculate the...

Geometry both discrete and continuous at once, like information--Kempf It is possible for a geometry to be both discrete and continuous. We don't know if our universe's geometry is like that, but it could be. Video of a talk at Perimeter by Achim Kempf, describing this, was put online...

Homework Statement Homework Equations Σ(n*2/5*(3/5)^(n-1)=5/2 The Attempt at a Solution First I found the number of tosses needed to get heads, but I don't understand how to interpret this in the E[X] formula. I know that my p(x)=.40 what is my x ? "tails for the first time"...

Homework Statement If I want to know how many ways there are to distribute 11 chocolate chip cookies to 50 children, is there any way to do this without brute force? Homework Equations The Attempt at a Solution

how is discrete metric space given by d((x1,x2,...xn)(y1,y2,...yn))=0 if xi=yi else 1 disc is complete

given a function F(x) = 1 ,x=1 2 ,x=2 3 ,x=3 The above function is a 3 pointed graph. it is continuous . Is it just because every point has a specific value..please someone explain this..??

I am trying to explore a number of things regarding the entropy of random strings and am wondering how a character set of random size would affect the entropy of strings made from that set. Using the following formula, I need to take the log of a discrete random variable H = L\log_2 N...

The distribution function of a random variable X is given by: F(x) = 0 if x <-3 3/8 if -3 <= x < 0 1/2 if 0 <= x < 3 3/4 if 3 <= x <4 1 if x => 4 Calculate E(X) and E(X2 - 2|X|) Well I'm at a loss of E(X) although once I know this the other should be fairly simple.. Ive got...

a) Let f:N*N->Q be defined by f(m,n)=(m-3)/n. Determine if f is injective or surjective. b) Show that if f:A->B and g:B->C are both bijective, then the composition (g o f):A->c is also bijective. Solve the recurrence relations a(r)-5a(r-1)+6a(r-2)=2^r+r (r,r-1,r-2 are all subscripts)

I am not sure how to answer the following question, which I have posed to myself to better understand the method: "Suppose two six-sided dice are rolled together N times. What is the uncertainty in the number of times any given total appears on the dice?" For example, what is the...

Experiments in nuclear magnetic resonance for example, demonstrate that precessing atomic nuclei do it so smoothly. At the same time, atoms have discrete magnetic moments presumably associated with spins. Would anyone care to comment on the difference?

Discrete hellmann-feynman theorem ?? The Helmann-Feynman theorem states that : derivative of eigenvalue with respect to a parameter = eigenfunction dagger * derivative of operator with respect to parameter * eigenfunction (assuming that the eigenfuncitons are normalized, otherwise the...

The question is to find the difference equation relating u(k) and y(k), which are input and output respectively. H(Z) is given as H(Z) = \frac{1+(1/2)z^{-1}}{(1-(1/2)z^{-1})(1+(1/3)z^{-1})} Solution that is given: y(k)-\frac{1}{6}y(k-1)-\frac{1}{6}y(k-2) = u(k)+\frac{1}{2}y(k-1)...

Homework Statement Find all pairs of integers a, b such that their GCD and LCM are 14 and 168 respectively. Homework Equations a x b = gcd(a,b) x lcm(a,b) (useful?) The Attempt at a Solution confused...

Homework Statement Find the remainder of dividing 2(562009)-3. Homework Equations Let m be a positive integer. If a\equivb (mod m) and c\equivd (mod m), then a + c \equiv b + d (mod m) and ac\equivbd (mod m). The Attempt at a Solution Using ac\equivbd (mod m): (2 mod...

Homework Statement Find the discrete Fourier transform X[k] = DFTn {x[n]} of the following periodic sequences x[n] = x[n - N] with period N: (a) For n = 0 . . .N - 1 we have x[n] =\delta[n]. (b) For n = 0 . . .N - 1 we have x[n] = \mu[n] -\mu[n - K] with K < N. (c) x[n] = cos( (2*pi*M*n)/N...

In statistics I learned how to do this problem one way, & in discrete mathematics I learned how to do it another way, but the answers don't jive. So I'm wondering if I'm doing something wrong. Below is the question. A bakery produces six different kinds of pastry. If the different kinds of...

Hey, new member here. Been viewing this forums for a long time now and used this forum as a resource for help with homework. Anyways, wasn't sure where to put this problem. I am having trouble setting up the problem. How many ways can we rearrange the letters in DISCRETE so that the E’s...

Many people believe that spacetime is discrete but what evidences have they ?? in one of issues of 'Scientific of American' explained that if space time was discrete then depending of the energy of light and since spacetime would be discrete the 'effective' space of light would not the same...

Homework Statement Find E(XY), Cov(X,Y) and correlation(X,Y) for the random variables X, Y whose joint distribution is given by the following table. X 1 2 3 Y -1| 0 .1 .1 0| 0 .5 .6 1| .2 0 0The Attempt at a...

Homework Statement (Answers: (a) 0.3233 (b) 2 (c)(i) 0.6489 (c)(ii) 0.1669 (c)(iii) 0.2369) Homework Equations Formulae for Discrete Probability Distributions The Attempt at a Solution I don't know how to solve part (b) only. For (b), I have no idea. Is it using...

Homework Statement At a school sports day, the timekeeping group for running events consists of 1 chief judge, 1 referee and 10 timekeepers. The chief judge and the referee are chosen from 5 teachers while the 10 timekeepers are selected from 16 students. (a) How many different...

It seems like there should be a discrete-time discrete-space analog to the Schrodinger equation. For example, you can apply the classic explicit finite difference method to the heat equation and get a simple binomial or trinomial tree relationship in a lattice. When I try that with the...

Homework Statement Suppose that we play the following game. You are given a pile of N matches. You break the pile into two smaller piles of m and n matches. Then you form the product 2mn and remember it. Next, you take one of the piles and break it into two smaller piles (if possible), say of...

If m and n are positive integers, (mn)!=m!n! Prove or disprove. its so obviously true i can't prove it. anyone help? -also- Prove: The square root of a prime integer is an irrational number. any help?

Homework Statement Hi all. I am given the following discrete mapping: x_{n+1}=f(x_n)=x_n+r-x_n^2 for r>0. Objective: Find the r, where a period doubling takes occurs. Attempt: First I find the fixed points: These are x=-\sqrt{r} (which is unstable for all r) and x=\sqrt{r} (which is...

My professor stated that the following orthogonality condition holds: \sum_{n=0}^N cos(2\pi mn/N)cos(2\pi kn/N)=0 where m != k, and 0<= m,k < N. I couldn't prove this, so I plugged in specific values: N=4, m=1, k=3. I found that the sum equals 2. Likewise for other situations where...

Suppose a,b,c,d are integers and a DOES NOT equal c. Suppose that x is a real number that satisfies the equation: (ax+b)/(cx+d)=1 Must x be rational? If so, express x as a ratio of two integers. I have no idea how to begin this problem.

Is it true that the discrete energy level of schrodinger's equation is due to boundary condition? What is the definition of boundary condition?

I've been noticing that several new technologies (SSDs, integrated batteries, etc.) are using wear-leveling algorithms but I've never actually seen one; is there a model or set of nicely arranged equations out there? I'm trying to find a general method that can be applied to a wide range of...

Homework Statement In the following you are given a 5-card hand from a 52 card deck. a) given that you have at least one ace, what is the probability you have at least 2 aces? b) given that you have the ace of diamonds, what is the probability that you have another ace? c) given that you...

Hi, I'm trying to plot the coefficients of a Fourier series as a discrete plot. Does anyone know how I could go about doing this? I have mathematica 6 so DiscretePlot isn't there like in 7... Any help would be great!

Dear "Physics Forum", Hello! I'm Sarah. Yeah, I'm new here and starting to love this forum. I'm having a hard time proving if a statement is true or false in discrete math. For example, For all X, there's a Y (x+y=x). This question is easy and the answer is true by letting y as 0 and x for...

Hello, can anyone help me with the following problem: The discrete Fourier transform (DFT) in matrix form can be done as follows F=M*f where f are the space domain samples, F are the spatial frequency domain samples and M is the DFT matrix containing the exp(j*...) terms. To compute the...

Hello, I'm looking for a decent Discrete Mathematics book.. Well, - Discrete Mathematics & Its Applications. - Discrete Mathematics With Its Applications. Are the top-sellers and the top-rated books @ Amazon on this field. Has anyone read any of them? Recommendations? Pros & Cons? I'm...

Hello, What about gauging discrete groups ? (C, P, T (??), Flavour Groups, Fermionic number symmetry...)