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I'm confronted with this question:
Let $V$ be an inner product space and $B=\{u_{1}, ..., u_{n}\}$ a basis of $V$.
Suppose there exists $\lambda_{1},...,\lambda_{n} \in F (=R \text{ or } C)$ such that: $$||\sum_{k=1}^{n}\lambda_{k}u_{k}||^2=\sum_{k=1}^{n}|\lambda_{k}|^2$$
Prove or disprove: $B$ is an orthonormal basis... |
Q: If we consider $\mathbb{R}$ and $\mathbb{C}$ as $\mathbb{Q}$-vector spaces, then how can we show they are isomorphic?
I know that if two vector spaces have bases with the same cardinality, then they are isomorphic. Also, Zorn's lemma tells us that every vector space has a basis.
In this case, answering my question... |
I was working through Pugh's Real Mathematical Analysis when I came across this proof:
Theorem $\mathbb{N} \times \mathbb{N}$ is denumerable.
Proof Think of $\mathbb{N} \times \mathbb{N}$ as an $\infty \times \infty$ matrix and walk along the successive counter-diagonals. This gives a list
$$(1, 1), (2, 1), (1, 2), (... |
Prove the following statement: if $\frac{p}{q} (p \in \mathbb{N}, q \in \mathbb{N})$ is a rational number that corresponds to an infinite periodic decimal fraction $\alpha$, then the rational number $10^{k} \frac{p}{q} (k \in \mathbb{N})$ corresponds to an infinite periodic decimal fraction obtained from the decimal f... |
Lets assume that we have a element, which can have value from 1 till n. (let's set it on 20 to make it easier)
And we have the Set, that consists of object, which consists of three elements $\langle e_1, e_2, e_3 \rangle$.
We have also one rule regarding to objects in the set: $e_1 \geq e_2 \geq e_3$
- example of good ... |
(not sure if "decreasing-difference" is the right way to put it - please edit away if you know the proper technical term)
From my analysis homework:
Does there exist a bounded sequence
$\{x_n\}_{n \in \mathbb{N}}$ such that
$x_{n+1}-x_n \to 0$, but the sequence
$(\sum_{i=1}^n x_i)/n$ does not have a
limit? Giv... |
I'm trying to prove that the Cauchy distribution is stable, i.e., if $X_{1}, X_{2}, ...$ are i.i.d. Cauchy random variables then $\frac{1}{n}(X_{1}+...+X_{n})$ has the same distribution as $X_{1}$ for $n \geq 1$.
I suspect the proof has something to do with characteristic functions, but haven't been able to write it ou... |
Now, I am working through a particular case in the book on smooth manifolds by John.M.Lee used in my graduate math class, let's say we have a smooth manifold X which has positive dimension. He then claims that the vector space $C^\infty$ of all smooth functions from $X \rightarrow \mathbb{R} $ will have infinite dimens... |
So when first developing the natural numbers in basic set theory, most properties are proven by induction. This is very convenient since $\omega$ is the smallest inductive set.
I saw a proof of the following proposition.
For all $n\in\omega$ and $n\neq 0$, $n\times\omega\sim\omega$.
The induction goes as let
$$
K=\... |
I'm trying to prove that every simple graph $G$ of girth $g(G)=5$ (length of smallest cycle), and minimum degree $\delta$, has at least $\delta^2 + 1$ vertices.
I tried using induction on $\delta$ without any results, and also tried to apply the pigeonhole principle, to no avail.
Help?
|
I'm studying for my Intro to Algebra class. I've reached the point where I want to understand the first Noether isomorphism theorem.
Here is the definition I was given in class:
Let $f :R \rightarrow S$ be a surjective ring homomorphism. Then we have a "commutative diagram" of ring homomorphisms.
Here is the scanned d... |
When calculating determinants it can be nice to multiply a row by a number or to add one row to another (your basic row operations). Each has an easy to understand effect on the determinant. Today I ran across a type of row operation whose effect on the determinant is a lot less clear to me.
Take an $n \times n$ matr... |
Suppose $a$, $b$, $c$, and $d$ are positive numbers and each is not equal to $1$.
If $\log_a(d)$, $\log_b(d)$, and $\log_c(d)$ are an arithmetic progression in this order, then what is $(ac)^{\log_a(b)}$ equal to?
|
I know the equation, $y = mx + b$ where $m$ is slope and $b$ is $y$-intercept, is a straight line. But I know also that $Ax + By = C$ is a straight line equation, but how does it represent a straight line?
|
Is the concept of an odd imaginary number defined/well-defined/used in mathematics? I searched around but couldn't find anything. Thanks!
|
(See edits at the bottom)
I'm trying to use Bézier curves as an animation tool. Here's an image of what I'm talking about:
Basically, the value axis can represent anything that can be animated (position, scaling, color, basically any numerical value). The Bézier curve is used to control the speed at which the value i... |
I have heard much about the numerous appearances of the ratio found in nature: 1.6180339887.
Are there any actual mathematical uses that have been found of this number? What are its advantages? Just curiosity, really.
|
I am aware of an intuitive explanation for $\operatorname{curl} \operatorname{grad} F = 0$ (a block placed on a mountainous frictionless surface will slide to lower ground without spinning), and was wondering if there were a similar explanation for $\operatorname{div} \operatorname{curl} F = 0$.
|
Could someone tell me the time complexity of a convex quadratically constrained quadratic program (QCQP)? Any references?
|
I get myself confused sometimes when to use => or =
= x + y = x + 5 = x = -5
or
=> x + y => x + 5 => x = -5
|
I have read here and in some other places that if $$(a \circ b) \star (c \circ d) = (a \star c) \circ (b \star d)$$ for all $a,b,c,d$ in a set with two binary operations $\circ$ and $\star$, then each one is a monoid homomorphism.
My problem is that I don't quite understand in what sense these are monoid homomorphisms,... |
( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix
A = [$a_{jk}$] =
$ \left[ \begin{array}{ccc}
0.1&0.5&0\\
0.8&0&0.4\\
0.1&0.5&0.6
\end{array} \right] $
where $a_{jk}$ is the f... |
After finishing a first calculus course, I know how to integrate by parts, for example, $\int x \ln x dx$, letting $u = \ln x$, $dv = x dx$: $$\int x \ln x dx = \frac{x^2}{2} \ln x - \int \frac{x^2}{2x} dx.$$
However, what I could not figure out is why we assume from $dv = x dx$ that $v = \frac{x^2}{2}$, when it could ... |
Can you give me few examples of binary operation that it is not associative, not commutative but has an identity element?
|
So I want to prove that for natural numbers $m,n,k$, if $k$ is no $0$ or $1$, and if $m<n$, then $k^m<k^n$. I jotted down the following proof, but I'm not sure how acceptable it is. I only have use of basic set theoretic properties of the naturals with addition, multiplication, and powers. I also have use of cancellati... |
Does anyone know where I can find (if they exist) full solutions to the exercises of Alan Hatcher's Algebraic Topology? Thanks.
|
How should I prove that $\mathrm{Aut}(\mathrm{PSL}(2,7)) \cong \mathrm{PGL}(2,7)$? Is this result extendible to $\mathrm{PSL}(n,q)$ where $q=p^n$?
|
Let $\Omega \in R^n$ be open, bounded and with smooth boundary. Can you prove the existence of a system of vectors that simultaneously forms an orthogonal basis both in $L^2(\Omega)$ and $H^1_0(\Omega)$?
Can you generalize this construction to obtain a simultaneous orthogonal basis for $H^0(\Omega),\cdots,H^k_0(\Omega)... |
The first equation is $m_1x_1 + m_2x_2 + \cdots + m_{n}x_{n} = K$, and then
$x_1 \geq x_2 \geq x_3 \geq \cdots \geq x_{n-1} \geq x_{n}$. Rather than solving is there any method which can tell me if this is solvable or not. All the numbers numbers are positive intgers or zero.
|
I am currently working on source material for a math-related software project with my mother, who has a PhD in Elementary Education and specializes in math education. While she has quite a strong fundamental understanding of the current techniques and topics taught to children at an early grade school level, I am relat... |
The union of a sequence of $\sigma$-algebras need not be a $\sigma$-algebra, but how do I prove the stronger statement below?
Let $\mathcal{F}_n$ be a sequence of
$\sigma$-algebras. If the inclusion
$\mathcal{F}_n \subsetneqq \mathcal{F}_{n+1} $ is strict, then
the union
$\bigcup_{n=1}^{\infty}\mathcal{F}_n$
... |
Does there exists a function $f \in C^2[0,\infty]$ (that is, $f$ is $C^2$ and has finite limits at $0$ and $\infty$) with $f''(0) = 1$, such that for any $g \in L^p(0,T)$ (where $T > 0$ and $1 \leq p < \infty$ may be chosen freely) we get
$$
\int_0^T \int_0^\infty \frac{u^2-s}{s^{5/2}} \exp{\left( -\frac{u^2}{2s} \rig... |
If the complex numbers $0$, $z_1$, $z_2$ and $z_3$ are concyclic, prove that $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear.
I really can't seem to get anywhere on this problem, but all I've deduced is that there might be some relationship between circle geometry properties and the arguments of the com... |
I am currently studying Herbrand's Theorem and wonder in which form it would hold for intuitionistic logic. I guess in intuitionistic logic we will have only one witness.
To be practical I am experimenting with the following derivation, which is classically valid:
$$\lnot p(a) \rightarrow p(b) \vdash \exists x p(x)$$
B... |
I've doing a bit of self study on the Fourier Transform and I keep coming across "basis function", I have attempted to understand the theory behind it, but I'm finding a lot of explanations go into more maths concepts that I'm not fully understanding.
I'm wondering if someone can in simple english give me an explanatio... |
Does the slope depend on how the y of a straight line changes or on both x and y?
For example, A straight line 2x - y = 0 passing through origin has a slope m = 2.
Now, when
x = 1 | y = 2
x = 2 | y = 4
x = 3 | y = 6
It looks like the value of y is increasing by 2, which is confusing me because m = 2.
In case 2,... |
What is a good graphing software ? The one that has the ability to accept an equation (linear, quadratic, etc.) from users and output a graph for that equation (software equivalnet of T1-84 graphing calculator).
|
I can calculate the derivative of a function using the product rule, chain rule or quotient rule.
When I find the resulting derivative function however, I have no way to check if my answer is correct!
How can I check if the calculated derivative equation is correct? (ie I haven't made a mistake factorising, or with one... |
Let $G$ be a compact (Hausdorff) group and $V$ a faithful (complex, continuous, finite-dimensional) representation of it. (Hence $G$ is a Lie group.) Is it true that every irreducible representation of $G$ occurs as a summand of $V^{\otimes n} \otimes (V^{\ast})^{\otimes m}$ for some $m, n$? (The original question only... |
Which of the following are true?
1:for every positive integer m, there is a positive integer n such that m+n+1 is a perfect square.
2:for every positive integer m, there is a positive integer n such that mn+1 is a perfect cube
3:for every positive integer m, there is a positive integer n such that m+n+1 is a perfect cu... |
Inspired by a paper (from 2001) entitled Pi is Wrong:
Why is $\pi$ = 3.14... instead of 6.28... ?
Setting $\pi$ = 6.28 would seem to simplify many equations and constants in math and physics.
Is there an intuitive reason we relate the circumference of a circle to its diameter instead of its radius, or was it an arbitra... |
For which integral values of $n$ can a set $(1,2,3,...,4n)$ be split into $n$ disjoint $4$-element subsets $(a,b,c,d)$ such that in each of these sets $a=(b+c+d)/3$ ?
|
I'm finding it hard to find a derivation of the DFT from books, was wondering if someone can point me to some resources or attempt to explain it here.
|
Prove:
$$\int_0^\infty x^{2n} e^{-x^2}\mathrm dx=\frac{(2n)!}{2^{2n}n!}\frac{\sqrt{\pi}}{2}$$
Thanks!
|
Let $f:R \rightarrow R'$ be a ring homomorphism that is epic in the category of rings. Let $M,N$ be $R'$-modules. Why is it that a homorphism $h:M \rightarrow N$ is $R'$-linear if and only if it is $R$-linear? I have used this result in specific cases in the past (and know why it's true),e.g., if $f$ is the usual map o... |
I have sample data like in above format along X, Y axis. Now what i would like to do is to devide it in "n" number of slabs having fixed values. Now how do i achive this in mathematics(statistics).
Please guide me to good and simple tutorial so that i can understand it. I would like to use this in computer algorithm ... |
The question is:
When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank?
|
I have to solve a problem which states that $(m,n) = 1$, but I have no idea what this means. Maybe, the problem itself will help:
Suppose $m, n \in \mathbb{Z}$, with $n > 0$ and $(m,n) = 1$. Show that:
$$\left \{ e^{2 \pi i m k/n}: 0 \leq k < n \right \} = \left \{ e^{2 \pi i j/n}: 0 \leq j < n\right \}$$
Thanks a lot ... |
In localization of a ring $R$ or a module $M$ over $R$ at a multiplicative subset $S$ of $R$, we define an equivalence relation on $R\times S$ or $M\times S$ and define addition and multiplication on equivalence classes. I think, if you don't define an equivalence relation, and define addition and multiplication in the... |
I have to solve find the value of
$$\sum_{k=1}^{n/2} k\log k$$
as a part of question.
How should I proceed on this ?
|
For which $m$, $n$ (if any) is the following true: if $M$ and $M'$ are smooth manifolds of dimension $n$, and $\Phi$ is a bijection from $M$ to $M'$ such that for any subset $S$ of $M$, $\Phi(S)$ is an embedded submanifold of $M'$ of dimension $m$ iff $S$ is an embedded submanifold of $M$ of dimension $m$, then $\Phi$ ... |
How would I solve this:
Multiply: $(4 + x)(x^2 + 2x +3)$
|
I'm looking for reasonably real, non-abstract applications modeled by quadratic equations where both solutions make sense. I'd like them to be accessible to high school algebra students.
One I come up with is firing a bullet through a sphere -- the two solutions correspond to the entry and exit points of the bullet, th... |
I have difficulties in showing the series $f(x)=\sum_{n=1}^\infty \frac{\cos(\sqrt{n}x)}{\sqrt{n}}$ is divergent at every real numbers $x$.
However I cannot find any elementary methods to do this. Can anyone help me on this?
Thanks.
|
how can i determine wether a circle can be circumscribed about a quadrilateral?
|
Suppose that the population of cats in a has a rate of growth proportional to the population itself. Write down a differential equation for the population $P (t)$ at time $t$ ?
|
Consider the $n$-sphere $S^n$ and the real projective space $\mathbb{RP}^n$. There is a universal covering map $p: S^n \to \mathbb{RP}^n$, and it's clear that it's the coequaliser of $\mathrm{id}: S^n \to S^n$ and the antipodal map $a: S^n \to S^n$. At first I thought I might use this fact and invoke abstract nonsense ... |
There are two proofs of Nielsen-Schreier that I know of. The theorem states that every subgroup of a free group is free. The first proof uses topology and covering space theory and is rather elegant. The second uses combinatorial techniques on a free group of words with no relations.
Is there a more algebraic proof whi... |
I need to brush up my knowledge about quadric surfaces and conics. I find myself understanding things better when I work with problems. Do you know any good textbook or website with problems about these topics? Thanks!
|
Heres the "Link", my issue circled in red. Can anyone tell me how they get this this step?; How does $6s_k = 6(5^k-1)$? What rule are they using here?
$s_{k+1} = 6s_k - 5s_{k-1} = 6(5^k -1)-5(5^{k-1}-1)$
Thanks everyone! -Kyle
|
Given a matrix $A\in D^{n\times (n+1)}$ where $D$ is an integral domain, the system $Ax=0$, where $x\in D^{n+1}$, has a nontrivial solution (which can be proved looking at the field of fractions of $D$).
Would this result still be true if instead of $D$ we had a general ring $R$ with identity? Does $R$ need to be commu... |
How does one averages a function over a solid angle? I'm used to do this with conventional angles but it's the first time I come across this problem with a solid angle.
In my specific problem, the function is only dependent on the azimuthal angle, which should simplify the problem somewhat and the average is over $4\p... |
Why do we have dy/dx with the regular d, and 'del y/del x' with the 'funny' d? I can easily find definitions for each expresion, but the definitions appear to be logically equivalent. However, they are informal enough that it is possible that I am not understanding the definitions properly.
Specifically, can anyone s... |
If one has a quasiprojective complex variety X, there is a natural map from the algebraic Picard group to the analytic Picard group. Is this map either injective or surjective?
I assume the latter is not true, but couldn't think of an example (nor a definitive opinion for the former question) If you take a normal c... |
I need your help with this:
Let $f$, $p$, and $g$ be a polynomials in $F[x]$, assume that $f$, $g$, and $p$ are nononzero.
If $\gcd(f,p)=1$ and $fg$ is divisible by $p$,
I need to prove that $g$ is divisible by $p$.
Thanks.
|
editing signal in frequency domain and converting back to time domain
the code is matlab / open source octave code
Greetings All
I would like to be able to edit different aspects of a signal
(frequency, magnitude) in the frequency domain is this possible?
I do know about fft and ifft which work great but I'm a little... |
If $M$ is Noetherian, any submodule $N \neq M$ can be written as a finite intersection of intersection-indecomposable ones.
I just don't know how to begin with the proof of this proposition.
Very kind of you for reading or answering.
|
I have always been interested in cryptology, but struggled with Algebra as a kid. As a result I know the basics of how the Diffie-Hellman Key Exchange (DH from here on) works, but I don't know why it does. I know that by two similar algorithms with two private numbers, both parties come to the same conclusion.
Why?
(I ... |
I came across an exercise in this book where the question was to define a collection of sets and the union operator as a group. The two parts of the question were to (1) find the identity element and (2) find the inverse element.
Assuming some collection of sets that's closed over set union $\mathcal{X}$ and some eleme... |
How to prove that the only subgroup of the symmetric group $S_n$ of index 2 is $A_n$?
Why isn't there other possibility?
Thanks :)
|
Suppose we have P, a string denoting a C program which takes in a natural number as input and outputs at most one natural number. Prove that it is impossible (unsolvable) to determine that P has infinite range.
In other words, show that it is impossible to determine whether $\mid\{y\in N | \exists x \in N.(P\ outputs\... |
I have a system of equations with two equations containing the Lambert $W$ function as follows,
$$\begin{cases} x = 1 - W_0(\frac{C_1 e^{y + 1}}{y + 1}) \\ y = 1 - W_0(\frac{C_2 e^{x + 1}}{x + 1}) \end{cases}$$
I have already solved the system numerically using a simple iterative method. A gentleman told me that the an... |
Is there any problem which is in NP but not in NP-Complete?
Is there any possibility that this problem is analogous to P=NP problem, if so is there any problem which is in NP, but currently there is no proof or disproof about its NP-Completeness?
|
Consider the principal bundle $S^7$ with base space $\mathbb{C}P^3$ (3-dimensional complex projective space) and fiber $S^1\cong U(1)$. Can someone write to me the bundle projection $\pi:S^7\rightarrow\mathbb{C}P^3$ explicitly?
|
Let's say I've got a plane P, a point A and a vector V, how do I find the distance from A to P moving along the direction to which V points?
Also, once I've got that, how do I get the point of intersection between the line indicated by V and the plane?
Thanks
P.S.: of course this is in an N-dimensional case
|
$e^{i \pi} = -1$. I get why this works from a sum-of-series perspective and from an integration perspective, as in I can evaluate the integrals and find this result. However, I don't understand it intuitively.
Intuitively, what this means to me is that if you rotate pi radians around a unit circle, you will end up exac... |
I'm interested in finding sums of the form
$\sum_i{\sum_j{(-1)^{N-i+j}} }$
where $N$ can be supposed to be constant.
I'm using the difference calculus to help solve these sums efficiently. I believe that I can simulate this sum as
$\sum_i{\sum_j{cos(\pi(N-i+j))}}$
I'm attempting to simulate the sum, since I'm having t... |
One property of Euler graphs is that if a graph with $n \geq 3$ vertices and more than $n$ edges has an Euler circuit, then it has more than two simple cycles.
How can we prove it?
|
I have come across the terminology $\mathbb{Z}[X] \stackrel{\mathrm{quot.}}{\to} \mathbb{Z}$ where $\mathbb{Z}[X]$ is the ring of integer polynomials in
$\mathbb{Z}$
I am wondering what this quotient map is. From wikipedia:
"..given a (not necessarily commutative) ring $A$ containing $K$ and an element $a$ of $A$ that... |
Suppose $R$ is a local ring with maximal ideal $m$ and suppose $M$ and $N$ are $R$-finitely generated modules. Let $f,g: M \rightarrow N$ be an $R$-module homomorphism. If $f$ is an isomorphism and $g(M) \subset mN$ why is $f+g$ in fact an isomorphism? I think this might follow by Nakayama's lemma but I don't see this... |
The upper Minkowski dimension of a compact set $A$ in $\mathbb{R}$ is defined as
$$
\overline{\dim}_M = \inf \{ \epsilon > 0 : \text{ there is a constant } C(\epsilon) \text{ such that } \mu(A_\delta) \leq C(\epsilon) \delta^{1-\epsilon} \text{ for all } \delta > 0 \}
$$
Here $\mu$ is the Lebesgue measure and ... |
I have some homework problems from Greene and Krantz' Function Theory of One Complex Variable. They come from Chapter 5. I definitely do not want answers, just light prodding in the right direction.
Let $f_j: D(0, 1)\to\mathbb C$ be
holomorphic and suppose that each
$f_j$ has at least $k$ roots in $D(0,1)$, cou... |
I have a hypothesis about regular polygons, but in order to prove or disprove it I need a way to determine whether an expression is rational. Once I boil down my expression the only part that could be irrational is:
$$S_N = \cot \frac{\pi}{N} \text{ for } N\in ℕ_1 ∖ \left\{1, 2, 4\right\}$$
Is there at least one such $... |
I am wondering if there is a strict argument about the probabilities of Christmas (Dec. 25) on Monday, Tuesday, ..., Sunday. My experiments give:
Sunday 0.145
Monday 0.14
Tuesday 0.145
Wednesday 0.1425
Thursday 0.1425
Saturday 0.14
Friday 0.145
It looks that they are not equal. :)
My question is:
1) How to obtain th... |
A right angled triangle has side lengths labeled as so.
A common geometric construction that shows three squares sitting upon the sides of a right triangle with lengths A, B, and C
However unlike in this diagram $a = b$.
How can $a$ be calculated given $c$?
Would $a = c \cdot d$ where $d$ is a constant?
|
All the definitions I can find of a limit (with functions from R to R) define something like:
"as x approaches a, f(x) approaches L"
Where x is treated as a variable that is quantified over in the definition.
Whereas many of these books then go on to use expressions of the form:
"as g(x) approaches a, f(x) approaches L... |
I am trying to write a physics simulator and have had a problem for weeks now.
I have two oriented bounding boxes in 3D space. An oriented bounding box is just a box of any dimension, location, and orientation. I am able to tell when these two boxes are intersecting by using the separating axis theorem.
However once t... |
I want to ask if there is a non-zero function like this:
$f:D^{n}\rightarrow [-a,a]$ for some $a\in \mathbb{R}$. In other words $f$ is bounded.
such that $$f(\frac{Ax+By}{A+B})=\frac{Af(x)+Bf(y)}{A+B}$$ for some fixed $A,B\in \mathbb{R}-\mathbb{Q}$. And $$f(\partial D^{n})=0$$
This question originated from one of my m... |
Let $X$ be an infinite set of cardinality $|X|$, and let $S$ be the set of all finite subsets of $X$. How can we show that Card($S$)$=|X|$? Can anyone help, please?
|
Good day,
Does anybody know where I could find a recursive contour plotting algorithm which is compliant with breaks and discontinues in the objective function? Recursive subdivision should be done only in those places where more sample points are needed to get a plot with smooth contours.
|
I am trying to prove a set is convex. This is a problem from Boyd's Convex Optimization text.
The set is $\{\hat{x} + tv | \alpha t^2 + \beta t + \gamma \leq 0\}$. This is actually an intersection of a line and a set, the line can be thought of as the part before the | symbol, and the original set contributed the part ... |
I have a question about the words "acyclic" and "exact." Why does Brown use the term "acyclic" instead of "exact" in his book Cohomology of Groups? It seems to me that these two terms exactly coincide. Are there examples(or topics in math) in which being acyclic means being sth1 and being exact means being sth2, and wh... |
I have the first point is (0, -100) and the second point is (7500, -250), and the maximum point is at (x, 210).
Is it possible to find X or the equation of the parabola using this information alone?
If so how?
|
First time here, more frequent over at StackOverflow. So not sure if calculator questions are accepted here, but I'll ask.
Is there a quick way to solve problems like this in the ti-83:
82% shot success rate out of 7 shots taken, find odds of exactly 3 shots going in, more than 5 shots going in. (I know how to do the... |
Is $ax^3 + bx^2 +cx + d$, for which $a$, $b$, $c$, $d$ are integers, subset of P3. I got that it was a subspace but the book got that it wasn't a subspace and now I'm confused.
|
$F$ is an extension field of a field $K$.
Let $F$ be an algebraic closure of $\mathbb{Z}_p $ ($p$ prime). Show that
$(i)$ $F$ is algebraic Galois over $\mathbb{Z}_p$
$(ii)$ The map $\alpha:F\rightarrow F$ given by $u\mapsto u^p$ is a nonidentiy $\mathbb{Z}_p$-automorphism of $F$.
$(iii)$ The subgroup $H=\langle \alp... |
I know that there are isomorphic projective varieties which have nonisomorphic coordinate rings, but I'm a little mystified as to "why" this is the case. Why doesn't a usual functoriality proof go through to prove this, and is there any insight into this other than that the definitions just work out this way?
|
I am having trouble in proving the pointwise convergence of $$ g(x)=\sum_{n=1}^\infty \frac{\sin(\sqrt{n}x)}{n}$$ for all real numbers $x$ using elementary methods (e.g. integral test, Weierstrass M-test, Abel's Test, Dirichlet's Test, Comparison with Riemann sum, etc.).
Can someone help me on this?
|
Let's say I'm specifying a circular arc with the following information:
x1,y1,x2,y2,radius,direction
and that I have 2D boundaries of:
minX = -5, minY = -5, maxX = 5, maxY = 5
how can i tell if the arc will go outside the boundaries?
so, for example, an arc with these values would go outside the bounds:
-4.5,0,-4.5,4,2... |
I know the order of a group is the size of the group, ie the number of elements.
But what does it mean for an element of that group to have order?
Also, what are the precise definitions for
1) "element of a finite order of a
group" and
2) order of an element of
a group (assuming that the element has
finite ... |
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