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I have been trying to do this for quite a while, but generally speaking the partially relevant information I could find on the internet only dealt with the question: "How does on convert a recurrence relation into... well, a non-recurrence relation?"
Let's start of with a simple example: $f(n) = 34n^3+51n^2+27n+5$. Ho... |
If $(X, \lt)$ is a well-ordering I can show by transfinite recursion over the ordinals that the function $f(x) = \text{ran} f |_{\hat{x}}$ exists (where $\hat{x} = \{ y : y \lt x\}$).
I have obtained $f$ this way, Let $V$ be the class of all sets and $F:V \to V$ be a class-function, then there is a unique $G:ON \to V$ ... |
The n-dimensional cone, with vertex at the origin, central angle, $\alpha$ and central axis in the direction of the unit vector $\xi$ is defined to be all those points, $x\in {R^n}$ whose dot product with $\xi$ is |$x$|$cos(\alpha)$. How would I find parametric equations for this surface?
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Given a long exact sequence of the form
$$
\dots\to A'_n \to B'_n \to C'_n
\,\xrightarrow{\omega_n}\,
A'_{n-1} \to B'_{n-1} \to C'_{n-1}\to \dots\qquad (*)
$$
is there a way to recover a short exact sequence of complexes $\mathcal A=\{A_n,\partial_n^A\}$, $\mathcal B=\{B_n,\partial_n^B\}$, $\mathcal C=\{C_n,\parti... |
let $S(k), k\geq 0$ a discrete random process. Suppose $S(N)$ is with probability one either 100 or 0 and that $S(0)=50$. Suppose further there is at least a sixty percent probability that the price will at some point dip below 40 and then subsequently rise above 60 before time $N$.
How do you prove that $S(k)$ cannot... |
I am finding with some formulas for my web application. I need a formula that counts the number of values between two number, e.g. there are four numbers (3,4,5,6) between 2 and 7
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If i know the means and standard deviations of 2 sets of data, and i know the slope of the regression line, how can I find the correlation?
edit
Sample 1
SD: 12.37
Sample 2
SD: 7.00
Slope of regression line: 0.789
|
Find an equation of the parabola with focus at point $(0,5)$ whose directrix is the line $y=0$. (Derive this equation using the definition of the parabola as a set of points that are equidistant from the directrix and the focus)
Ok this one is killing me. My textbook has this
An equation of the parabola with focus $(0... |
I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology.
I have decided to fix this lacuna once for all. Unfortunately I cannot attend a course right now. I must teach myself all the stuff by reading books.
Towards this purp... |
Question: Let $a, b \in \mathbb{R}$ with $a < b$ and let $f: [a,b] \rightarrow [a,b]$ continuous. Show: $f$ has a fixed point, that is, there is an $x \in [a,b]$ with $f(x)=x$.
I suppose this has to do with the basic definition of continuity. The definition I am using is that $f$ is continuous at $a$ if $\displaystyle ... |
Let $Y_1,\dots,Y_n$ be independent and identically distributed random variables such that for $0 < p < 1$, $P(Y_i = 1) = p$ and $P(Y_i = 0) = q = 1-p$.
A. Find the moment-generating functions for the random variable $Y_1$.
B. Find the moment-generating functions for $W = Y_1 + \dots + Y_n$.
C. What is the distribution ... |
It can be shown by simple induction that $\dfrac{\mathrm d^n}{\mathrm dx^n}\left(\dfrac1{x}\right) = \dfrac{(-1)^n n!}{x^{n+1}}$.
But what about the nth integral of $\dfrac1{x}$? Finding the first few primitives, I can't discern a pattern.
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Let $Y$ be a binomial random variable with $n$ trials and probability of success given by $p$. Show that $n-Y$ is a binomial random variable with $n$ trials and probability of success given by $1-p$.
I understand why this is true, and can explain in logically, but I just don't know how to prove it in mathematical terms... |
I feel like this should have a rather simple solution using logarithms, but I don't quite know where to start.
Basically, every day I am going to multiply a given quantity by $r$, where $r < 1$.
Obviously, if $r$ is 0.5, then my half-life $n$ is 1 day. (This is also stated to remove any ambiguities on what counts as a ... |
Suppose $k,k'$ are fields such that $k\subset k'$ and $x_1,x_2,...,x_n,t$ are indeterminates over $k'$. Suppose we have a homomorphism of rings given by $f:k[x_1,x_2,...,x_n]\to k[t]$, where $$x_1\to f_1(t)$$ $$x_2\to f_2(t)$$ $$\vdots$$ $$x_n\to f_n(t)$$ Let the kernel of this map be $I$.
What can be said about the ... |
As I understand, martingale is a stochastic process (i.e., a sequence of random variables) such that the conditional expected value of an observation at some time $t$, given all the observations up to some earlier time $s$, is equal to the observation at that earlier time $s$.
A sequence $Y_1, Y_2, Y_3 ...$ is said to ... |
In a set of lecture notes, there is an example of calculating the group $E_\text{tors}$ of an elliptic curve. This is the example:
Let $E$ be the elliptic curve
$$y^2=x^3-5x+4.$$
The curve has discriminant
$$\Delta=16(4\cdot 125 - 27\cdot 16)=2^6\cdot 17.$$
Therefore, if $[a:b:1]$ is a torsion point, we mus... |
How can I prove that $\gcd(7^{79}+5,7^{78}+3) = 4$ ? This was a question on a past exam, so the naive euclidean algorithm doesn't seem to suffice.
I'm not really sure where to start with this.
Note: This is exam prep, not homework.
|
Consider large (100,000+ vertices, say) graphs, which we think of as representing some population with edges representing some form of symmetric relation. They might be the Friend graph of Facebook, mathematicians with the collaboration relation, or a large computer network.
These networks have the property that the... |
Background: Let $n$ be an integer and let $p$ be a prime. If $p^{e} || n$, we write $v_{p}(n) = e$. A natural number $n$ is a sum of two integer squares if and only if for each prime $p \equiv 3 \pmod 4$, $v_{p}(n)$ is even. Every natural number is a sum of four squares. A natural number $n$ is a sum of three squares i... |
Let $X$ be a topological space such that every open cover has a finite refinement. Then is $X$ compact, or is there a counterexample?
Let $X$ be a topological space such that every open cover has a locally finite subcover. Then is $X$ compact, or is there a counterexample?
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I was reading this question, and I idly wondered if there could be spaces that were globally Euclidean, but locally not, and couldn't think of any circumstances in which that might be the case.
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The Question: Are there any ways that "applied" mathematicians can use Homology theory? Have you seen any good applications of it to the "real world" either directly or indirectly?
Why do I care? Topology has appealed to me since beginning it in undergrad where my university was more into pure math. I'm currently in... |
Let $X1,X2$ be independent random variables with $P[Xi = 0] = P[Xi = 1] = \frac{1}{2}$ for $i = 1, 2$. What is the random variable set $A1 = \{X1 = X2\}$ mean? I came across this representation in the book but not sure what this means.
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One of false beliefs in this question on Math Overflow is "If f is a smooth function with df=0, then f is constant". What is a counterexample to this statement? Can it be made correct by adding some restriction, e.g. that f is a function from reals to reals?
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The category of simplicial presheaves on a small Grothendieck site $\mathcal{C}$ can be given a model structure by defining weak equivalences and cofibrations sectionwise. It's called the (global) injective model structure and has a mapping space functor $\operatorname{Hom}$, given by $\operatorname{Hom}(X, Y)_n =\oper... |
The definition of Gauss-Manin connection involves de Rham cohomology. Surely, Gauss didn't work with de Rham cohomology as we know it.
So, what was the context in which Gauss came up with this idea?
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Let Let $E \rightarrow X$ be a vector bundle on a manifold $X$. Let $\cal E$ be the sheaf of sections of $E$. Let $\cal F$ be a subsheaf of $\cal E$, and let $F$ be the etale space of $\cal F$. What is an example that the map $F \rightarrow E$ might not be an injection on all fibers?
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Classify up to similarity all 3 x 3 complex matrices $A$ such that $A^n$ = $I$.
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I'm reading the Algebra book by Knapp and he mentions in passing that an orthonormal set in an infinite dimension vector space is "never large enough" to be a vector-space basis (i.e. that every vector can be written as a finite sum of vectors from the basis; such bases do exist for infinite dimension vector spaces by ... |
I'm modeling a process with a Markov chain like this:
$$
Pr(i \rightarrow i) = \alpha,
Pr(i \rightarrow i+1) = \beta,
Pr(i \rightarrow i+2) = \gamma
$$
All other probabilities are zero.
Is there any way to calculate the expected number of steps it takes to reach state $n$ from state $0$? So far, all I've come up i... |
The book Irresistible Integrals by George Boros and Victor Moll on page 204 has the following identity
$\displaystyle \frac{1}{1+x}=\prod_{k=1}^{\infty}\left(\frac{k+x+1}{k+x} \times \frac{k}{k+1}\right)$
How does one derive this?
Thanks.
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How do I show that the product $$\biggl(4 - \frac21\biggr) \cdot \biggl(4 - \frac22\biggr) \cdot \biggl(4 - \frac23\biggr) \cdots \biggl(4 - \frac2{n}\biggr)$$ is an integer for any $n \in \mathbb{N}$.
Source: www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf
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Problem:
From the deck of the 52 cards,cards are drawn randomly without replacement.What is the probability of drawing a king of hearts at the third attempt? If it was drawn at the 15th attempt, what is the probability ?
I have solved the first by finding P(getting the card at third attempt) = P(not getting at first) ... |
It seems like I am facing some confusion while handling with inequalities,I was doing some tasks where it is asked to find the interval of the variable,after some steps I deduced the the necessary expression but I am facing some problem while trying to deduce the final expression.
Consider for example:
$$a^2 \ge 8;... |
To state the context, I am familiar with the Hopf-Rinow theorem.
My request is three fold,
I would like to know of general classes of geodesically incomplete spaces. I basically want to see lots of examples for this.
I want to know of techniques of proving and testing for geodesic incompleteness or completeness.
I ... |
I would like to gain intuition how "singular" a distribution can be.
Let $X \in \mathbb R^n$ be open, $\mathcal D(X)$ be the smooth test functions on $X$ with canonical LF topology, and let $\mathcal D'(X)$ be the topological dual of $D(X)$.
Let $\Psi \in D'(X)$. Can the singular support of $ \Psi$, i.e. the complement... |
Suppose that $R$ is a ring, $I$ and $J$ are ideals, and $R=I+J$. Can we conclude that $R/J$ is free?
|
It's well known that under some "weak" hypothesis, such as finitely generated, the support of an A-module is closed in Spec(A). It is true also in the most general case?
|
Problem:
The probability that a man who is 85 years. old will die before attaining the age of 90 is $\frac13$. A,B,C,D are four person who are 85 years old. what is the probability that A will die before attaining the age of 90 and will be the first to die ?
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Is there a procedure/algorithm for calculating sums of the form
$$ \sum_{n_1,\ldots,n_r >0} \frac1{L_1(n_1,\ldots,n_r)^{m_1} \ldots L_r(n_1,\ldots,n_r)^{m_r}} $$
where
$$ L_i(n_1,\ldots, n_r) := a_{1,i} n_1 + \ldots + a_{r,i} n_r $$
for some $a_{i,j} \in \mathbb C$. How would one go about evaluating this sum to sa... |
We have a random variable $Y$ that has a uniform distribution on the interval $[1,5]$. The cost of delay is given by $U = 2Y^2 + 3$. Use the method of transformations to derive the density function of $U$.
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This might be an elementary question, but I am just beginning to learn logic theory.
From wikipedia article on Gödel's incompleteness theorems
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated f... |
Is there a general way to show whether the limit $$\lim_{n \to \infty}\frac{\mathrm d^n}{\mathrm dx^n} f(x)$$ converges to some expression?
What about repeatedly integrating an expression $n$ times as $n \to \infty$?
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Is the function $\frac{e^z-1}{e^z+1}$ analytic?
I tried using $\mathop{\lim}\limits_{z\to a} \frac{f(z)-f(a)}{z-a}$, but I didnt really know what to use for $a$.
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I have a non-linear ODE that I need to linearise.
I could go about linearising the trig terms using Taylor series...but not sure about a square root of the form:
$$\sqrt{(A+C)^2 + B -2 * \cos (\alpha - \theta)}$$
Thanks.
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Suppose we have a countable set of objects $\{x_i|i \in [1..m]\}$ in a metric space $(\mathbb R^n,d_n)$ and a map ($F$) mapping the objects to objects in a metric space $(\mathbb R^1,d_1)$. For each pair of objects we can define an error:
$$
e_{ij} = \frac{d_m(x_i,x_j)}{d_1(F(x_i),F(x_j))}
$$
Let $e_{ii}$ be 1.
It... |
Suppose that we have two varieties of algebras $A$ and $B$, whose operators all have arities less than some regular cardinal, and such that every $B$-algebra (please correct me if this is not the usual notation) is also an $A$-algebra. It is known that the forgetful functor from the category of $B$-algebras to that of ... |
What is the rationale behind saying that $|x|=1$ implies $x=\pm 1$?
|
Bill Dubuque has answered several questions by indicating that some form of "telescoping" is taking place. See this post and the links provided by Bill for more information.
I have never heard of "telescoping" until I read a few answers on here by Bill which refer to this notion. It seems fairly straightforward, basi... |
Let $m$ be a positive integer. Define $N_m:=\{x\in \mathbb{Z}: x>m\}$. I was wondering when does $N_m$ have a "basis" of two elements. I shall clarify what I mean by a basis of two elements: We shall say the positive integers $a,b$ generate $N_m$ and denote $N_m=<a,b>$ if every element $x\in N_m$ can be written as $x=\... |
I'm looking for a good book on distribution theory (in the Schwartz sense), I have the basic knowledge as given in Grafakos' Classical Fourier Analysis, but I want to know more about it. Is the reference still Laurent Schwartz' Théorie des distributions? That book is hard to obtain, it seems to be only available in Fra... |
I've read that the formula A if and only if B is a formulation of the equivalence
that can be decomposed in A if B (the implication B -> A) and in A only if B (the implication A -> B).
I don't agree with the second part : for me it looks like that A only if B is the translation of ¬B -> ¬A (I know that it's the contra... |
I came across this problem. If $X_1,X_2, \ldots, X_n$ is an iid sequence with uniform distribution on [-1,1] and we define a new random variable like this:
$Y_n = \frac{\sum X_k}{\sum(X_k^2 + X_k^3)}$
How do I use the strong law of large numbers to show that $Y_n$ is normal and find its mean and variance? The uniform ... |
The pullback is a subset of the cartesian product in the category of commutative rings with unit.
What is the pullback in the category of commutative $k$-algebras? Is it the same set as in rings?
|
I need to find the function c(k), knowing that
$$\sum_{k=0}^{\infty} \frac{c(k)}{k!}=1$$
$$\sum_{k=0}^{\infty} \frac{c(2k)}{(2k)!}=0$$
$$\sum_{k=0}^{\infty} \frac{c(2k+1)}{(2k+1)!}=1$$
$$\sum_{k=0}^{\infty} \frac{(-1)^k c(2k+1)}{(2k+1)!}=-1$$
$$\sum_{k=0}^{\infty} \frac{(-1)^k c(2k)}{(2k)!}=0$$
Is it possible?
|
WolframAlpha is confusing me. I'm working on two different integral problems, and with each one, for some reason, Wolfram switches the signs of the answer.
http://www.wolframalpha.com/input/?i=integral+dx/(x^.5(x-1))
http://www.wolframalpha.com/input/?i=integral+(x-1)/(x^2-4)
For the first one, they get $\log[1 - \sq... |
Is it correct to say that the number of circles in an Apollonian gasket is countable becuase we can form a correspondence with a Cantor set, as their methods of construction are similar?
What about if we apply the Apollonian gasket construction inside of a fractal like the Koch snowflake? (I think that will still be co... |
Suppose I have acquired 103,304 customers for a transaction-based business at 12 months into the business and their number has increased at a monthly rate of 40% (from month 1, in which 2,551 customers were acquired). Assume 103,304 represents the total number of new customers (active or dead) acquired over the 12 mont... |
If given 2 lines $\alpha$ and $\beta$, that are created by
2 points: A and B
2 plane intersection
I want to find shortest distance between them.
$$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 \\ P_2=x_2X+y_2Y+z_2Z+C=0\end{array}\right.$$
$$A=\left(x_3;y_3;z_3\right)$$
$$B=\left(x_4;y_4;z_4\right)$$
$$\alpha =n_1\... |
I'm curious to whether you guys have any tips on book concerning classical euclidean geometry. I'd like somewhat of an advanced treatment, around the same level as Coxeter's "Geometry revisited". I'd however want something more comprehensive, therefore I'm asking you for tips!
Hopeful for answers ^^
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So, I am a graduate student who is certain that he does not want to do analysis (I think...). What are the most exciting fields in mathematics right now? It seems to me that very generally, they are algebraic geometry and algebraic topology, with the latter being specifically concerned with homotopy theory (something... |
I'm trying to solve exercise 2614.1 from Demidovich's famous book of exercises on Analysis. Having solved the bit about convergence, I'm now stuck in trying to prove that a series of terms $a_n\geq 0$ is divergent if there exists $N$ such that $(1-\sqrt[n]{a_n})\frac{n}{\log{n}} \leq 1$ for all $n>N$. I've been trying ... |
I've been spinning my wheels on this for an embarrassing amount of time. This is not for an assignment, I'm just studying.
Three balls are placed at random in
three boxes. There is no restriction
on the number of balls per box; list
the 27 possible outcomes of this
experiment.
I could only come up with 10 whe... |
$x=t^2-3$
$y=9t$
Assume that a point moves in (x,y) plane according to the above parametric equations. Find for which $t$ the velocity is equal to 9.
I have an idea about this problem, but I'm not sure how to work with it. If we are given the position functions, then the derivative is the velocity. The derivative of... |
The permanent can be interpreted as the number of perfect matchings in bipartite graphs.
Is there a similar graph-theoretic interpretation of the determinant?
|
My undergraduate number theory class decided to dip into a bit of algebraic geometry to finish up the semester. I'm having trouble understanding this bit of information that the instructor presented in his notes.
Here it is in paraphrase (assume we are over an abstract field k)
We take a polynomial in k, $f =Y^2 - X^... |
According to wikipedia the right quotient of a regular language with ANY other language is regular. I have not been able to find a proof of this fact. All the sources talk about quotient with another regular language. Can somebody point me to a proof?
P.S. Definition from Wikipedia: The right quotient (or simply quotie... |
I have two faces ($S_1$ and $S_2$), each bounded by a series of Vertex $V$. These two faces may or may not intersect. In addition to that there are two vertical faces $S_3$ and $S_4$, that connect between $S_1$ and $S_2$ vertically, as shown in the below diagram. The question is how to find the polyhedrons that are for... |
I am wondering how to find the Zariski Cover of the Grassmannian over $\mathbb{C}$. I was hoping some reference would go through this calculation. I was recently told that it was not too hard, so I wondered if it was written somewhere.
Any reference that does this, or at least gives an introduction for how to calculat... |
such a RSA algorithm.
|
I am trying to understand why $1^{x}=1$ for any $x\in\mathbb{R}$
Is it OK to write $1^{x}$? As the base 1 should not equal 1 for $1^{x}$ to be an exponential function?
Is $1^{x}=1$ just because it is defined to be so?
If possible please refer me to a book or article that discusses this topic.
|
If you sum an expression over an uncountable set
$\sum_{x\in \mathbb{R}}f(x)$, then do we need $f(x)=0$ on all but a countable subset in order for the sum to have a finite value?
If not can you give an example of a function everywhere nonzero that has a transfinite sum with a finite value?
Possible keywords: Transserie... |
If I have term -5 and I want to change its sign to opposite can I say that I'm negating its sign?
|
The problem:
Given a Fibonacci number,find its index.
I am aware of the standard solution 'generate-hash-find'. I am just curious if there is some inverse system of matrix exponentiation or some other mathematical method that gives the solution.
|
If a Diophantine equation is: exists v, p(x,v) = 0 (where v is a vector of finitely many integers) for some polynomial p, is there a Turing machine which prints out all values of x?
|
A while ago I was dreaming up point-set topology exam questions, and this one came to mind:
Is $\mathbb Q\setminus \{0\}$ homeomorphic to $\mathbb Q$? (Where both sets have the subspace topology induced from the standard topology on $\mathbb R$.)
However, I couldn't figure this out at the time, and I'm curious to see w... |
There is a direct relationship between equivalence relations and partitions.
Is there a way to simply use an equivalence relation's definition to get the matching partition? And what about the other way around?
|
I have been looking for a proof of the statement:
"Assume the Generalized Riemann Hypothesis. Let $d$ be a fundamental discriminant and $\chi_d$ the associated primitive quadratic character. Then, $$L(\tfrac{1}{2},\chi_d)\geq 0."$$
Can anyone point me in the right direction or give a reference? Thanks a lot!
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What's the thing with $\sqrt{-1} = i$? Do they really teach this in the US? It makes very little sense, because $-i$ is also a square root of $-1$, and the choice of which root to label as $i$ is arbitrary. So saying $\sqrt{-1} = i$ is plainly false!
So why do people say $\sqrt{-1} = i$? Is this how it's taught in the ... |
When asked to evaluate $\int_{a}^{\infty}f(x)dx$, you split the interval based on the improper points.
If there is another improper point other than $\infty$, at $b$, we will write: $\int_{a}^{\infty}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx+\int_{c}^{\infty}f(x)dx$ and ask whether each of the integrals on the right... |
I was thinking about some problem involving quantifiers (the existencial and universal quantifiers) and I noticed how it might resemble probability in a sense. They both assume a variable and its domain, and put restrictions on some predicate of that variable over that domain.
For an example if you didn't get me yet, w... |
Let's say I have two numbers that I know to have been normalized- 39, 12. How do I calculate the percentage difference between them? Is it the same as if they hadn't been normalized? ie: (12/39) * 100
|
I just read through a proof of the Compact Uniformization Theorem, and I follow it up to the very last line. The proof is:
Compact Uniformization Threorem. If $X$ is a compact regular space, then the neighborhood filter $\mathcal{N}_\Delta$ of the diagonal $\Delta\subset X\times X$ is a uniform structure on $X$.
Suppos... |
I have to test for convergence of the series:
$\displaystyle \sum\limits_{n=1}^{\infty} \sin\Bigl(\frac{\pi}{n}\Bigr)$
What i did was
\begin{align*}
\sin\Bigl(\frac{\pi}{n}\Bigr)+ \sin\Bigl(\frac{\pi}{n+1}\Bigr) + \cdots & < \pi \biggl( \frac{1}{n+1} + \frac{1}{n+2} + \cdots \biggr) \\ &= \pi \biggl( \sum\limits_{... |
How can one find if a function $f$ is infinitely differentiable?
|
Define a quadtope P as a polytope which is the convex hull of a set Q of convex quadrilaterals, any pair of which intersect in at most one vertex, and are in maximally general position, or, a k-fold pyramid over such a convex hull. (So, a pair of quadrilaterals from Q with a common vertex subtends a 4-dimensional subpo... |
I am trying to figure out the fundamental group (actually simply connected or not will suffice) of the following quotient space of $SO(3)$:
Let $X = SO(3)/E$, where $E$ is the equivalence relation defined as follows:
$E \equiv M \sim {S_{A}}^{i} * M * {S_{B}}^{j}$ where ${S_{A}}^{i} \in $ Crystallographic point group $... |
I know this is a silly question, but I've tried to find an answer using my TI-89 calculator, Maple and wolframalpha but none of those could tell me whether
$$\int_0^\infty |\cos(x^2)| \mathrm dx$$
converges or diverges.
Thus, I'd be very happy if someone could help me out and tell me, whether the given integral conver... |
I was trying to understand the notion of a connection. I have heard in seminars that a connection is more or less a differential equation. I read the definition of Kozsul connection and I am trying to assimilate it. So far I cannot see why a connection is a differential equation. Please help me with some clarification.... |
The Mathematica code is here.
Consider the heat conduction problem with Neumann (constant flux) at both boundaries of a solid slab. A constant radiant heat flux is imposed on one surface (derivative = -1) and the other surface is thermally insulated (derivative = 0).
If you increase the flux of the heat at one boundary... |
Given an elliptic curve $y^2 = x^3 + ax + b$ over a finite field $\mathbf{F}_p$, how can I retrieve the value of $y$ given the value of $x$?
My knowledge in this area is quite limited, so I understand this question might seems silly.
I'm currently working on an application that uses an elliptic curves library and I sa... |
I am attempting to write a function (programming, not mathematics) which calculates the shortest distance between two points on a toroid. I got the following formula from StackOverflow, but I don't recognize the min portion. Can someone explain that to me, please?
sqrt(min(|x1 - x2|, w - |x1 - x2|)^2 + min(|y1 - y2|,... |
I'm doing a multiple choice exercise and I'm stuck at a question, where there are two possible answers (may be both or none correct).
Consider the differential equation
$$y''+y'+y=0$$
for $y(x)$. Which of the following statements are true?
The set of complex solutions forms a two-dimensional complex vector space.
Th... |
Anyone know of an online tool available for making graphs (as in graph theory - consisting of edges and vertices)? I have about 36 vertices and even more edges that I wish to draw.
(why do I have so many? It's for pathing in a game)
Only tool available to me right now is MS Paint and it would be very messy.
Edit:
I'm ... |
Motivation
I have a prior on a random variable $X\sim \beta(\alpha,\beta)$ but I need to transform the variable to $Y=\frac{X}{1-X}$, for use in an analysis and I would like to know the distribution of $Y$.
Wikipedia states:
if $X\sim\beta(\alpha,\beta)$ then $\frac{X}{1-X} \sim\beta^\prime(\alpha,\beta)$
Thus, the ... |
It seems so. $\mathbb{Q}_p(\zeta_p)$ is a $p-1^{th}$ extension of $\mathbb{Q}_p$ which doesn't extend the residue field; and so is $\mathbb{Q}_p(p^{\frac{1}{p-1}})$. However I can't see how to express $\zeta_p$ in $\mathbb{Q}_p(p^{\frac{1}{p-1}})$ or how to express $p^{\frac{1}{p-1}}$ in $\mathbb{Q}_p(\zeta_p)$.
Can yo... |
I am Computer science student so pardon me if I am asking this in a wrong place!
My inspiration of learning maths is mainly due to algorithms and its feels to me that without mathematics I am not justifying my computer science degree, I am trying to work on my rusty math since last two years but until now I am not muc... |
Suppose I know the values of a continuous function on $[a,b]$ in some finite number of points $x_0,x_1 \ldots x_n$. I can form the Lagrange interpolating polynomial, $p$. I am curious if there is any interesting estimate of the expression $|f(x)-p(x)|$ for an arbitrary point $x$ that does not assume $f$ is smooth? (Per... |
Given a collection of points $P \subset \mathbb R^3$, a crude characterization of the "shape" of $P$ is sometimes given by the principal components. We construct a covariance matrix, e.g., if $P$ is discrete, $C = \displaystyle\sum_{p\in P} (p - \mu)(p - \mu)^\intercal$, where $\mu = \displaystyle\frac1{|P|}\sum_{p\in ... |
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