-3
votes
2answers
39 views

Math word problem for 4th grade [on hold]

Adrian wants his lawn to be mown. Three men apply for the task. The first man can mow the lawn in 6 hours; the second man can mow the lawn in 4 hours; and the third man can mow the lawn in 3 hours. ...
0
votes
0answers
8 views

Vanishing cech cohomology of a concratible space.

Let $C$ be a concratible space. Is it possible to find a sheaf $F$ such that two Cech cohomology groups don't vanish? E.g. Can I find a sheaf (or a local system) and two integers $i,j$ such that ...
0
votes
3answers
30 views

How to prove the equivalence relation $A\cup B=B \Leftrightarrow A\cap B = A$? [on hold]

How to prove the equivalence relation? $$A\cup B=B \Leftrightarrow A\cap B = A$$
0
votes
1answer
32 views

Projective Geometry in $\mathbb{R}^{3}$: “Lonely lines” in source/image planes

I am reading some lecture slides about projective geometry in $\mathbb{R}^{3}$. In particular, given a source plane, $S$, an image plane, $I$, and a focal point, $f$, the issue at hand is the ...
1
vote
0answers
29 views

Combinatorics project ideas for high school students

It's that time again! Last year I asked for high school project ideas in the area of algebraic geometry, this year it's combinatorics (you can include graph theory and combinatorial game theory if you ...
1
vote
0answers
19 views

Etymology of normal extensions and subgroups

According to wikipedia, a normal extension is a splitting field of a family of polynomials, and a normal subgroup is one that is invariant under conjugation. Why are normal extensions and normal ...
1
vote
0answers
21 views

Is a dense and co-dense subset $G_\delta$ or co-$G_\delta$

Let $A \subset \mathbb{R}$ such that $A$ and $A^C$ are both dense. By Baire's Theorem at most one of $A$ and $A^C$ is $G_\delta$ (i.e. a countable intersection of open sets) I couldn't think of an ...
0
votes
0answers
12 views

On a congruence for the number of finite topologies

I am making search about "On a congruence for the number of finite topologies". I have found a paper. I guess it is written in Russian. How can I find English version of this paper ? I am also ...
3
votes
2answers
31 views

Complex hyperbolic Trigonometry

When faced with the equation $\cos{z}=\sqrt{2}$ I want to solve for z so I break it up into a sum $z=x+iy$ and get: $\cos{z}=\cos{x}\cosh{y}-i \sin{x} \sinh{y}$ equating real and imaginary parts I ...
0
votes
1answer
20 views

Commutative matrix question

I was doing my HW, and I am confused with one thing. To show that a matrix is commutative, do we need to show both $x+y = y+x$ and $xy=yx$? Or just by showing $xy=yx$ would suffice?
0
votes
1answer
34 views

For what natural number $n$ is the following inequality true: $2^n \geq 2\cdot n^2$?

Can you solve this by using induction? The inequality is true for $n = 1$, but is false until $n = 7$. After the induction step I got $$2^n \geq n^2 + 2n + 1.$$ If you take the limit as $n$ ...
-2
votes
1answer
16 views

Example of GCD=1, but… [on hold]

Give an example of three positive integers $m$, $n$, and $r$, and three integers $a$, $b$, and $c$ such that the GCD of $m$, $n$, and $r$ is $1$, but there is no simultaneous solution to: $x ≡ a ...
-4
votes
1answer
23 views

Show that the sequence $\{b_j\}$ given by $b_j = j$ as $j$ approaches infinity is not bounded [on hold]

Show that the sequence $\{b_j\}$ given by $b_j = j$ as $j$ approaches infinity is not bounded by using the definition of boundedness of a sequence. Help please.
0
votes
0answers
10 views

Classifying representations of $G = C_m \times C_n$

I have been set the following problem: Classify representations of $G = C_m \times C_n$; the direct product of two finite cyclic groups. My first thought is to rewrite $G$ in terms of its ...
0
votes
0answers
30 views

Their product is a cubic of a rational number $x$ minus $x$

It is given the integer $6$. Analyze it into two parts such that their product is a cubic of a rational number $x$ minus $x$. $$$$ Let $y$ be the one factor. The other one is $6-y$. We have ...
-2
votes
0answers
21 views

Real analysis open and closed set [on hold]

Please help me with the below question: Prove that the set $(0, 1)$ is open, $[0, 1]$ is closed, and $(0, 1]$ is neither open nor closed.
1
vote
0answers
12 views

Evaluating the surface integral side of a divergence theorem problem

Edit: I realized where my mistake was...thanks for the help! In class we were discussing a problem (page 1185 in Smith and Minton's Calculus Third Edition): Let Q be the solid bounded by the ...
0
votes
1answer
8 views

Need explanation on asymptotic running time results for various functions

I did not understand few results from the book problem. Here is the problem: Indicate, for each pair of expressions (A, B) in the table below, whether A is O, o, Ω, ω, Θ of B. Assume that k ≥ 1,  > ...
3
votes
1answer
16 views

Is there a general way to find what $Aut(C_n)$ Is Isomorphic to?

I'm asked to describe $Aut(C_{21}),Aut(C_{24})...$ as a product of cyclic groups - but I'm wondering is there a general way to do this?
1
vote
1answer
18 views

$3$-edge coloring of Georges Graph

Accoring to Wolfram|Alpha, Georges Graph $\hskip1.7in$ is 3-edge colorable. Does anybody have a actual 3-edge coloring in form of three sub-matrices of the adjacence matrix: $$A_1+A_2+A_3=A $$ I ...
2
votes
1answer
37 views

Presentation of a group isomorphic to $A_4$

I have a group $G$ defined by $G = \langle x,y,z|x^2 = y^3 = z^3 = xyz \rangle$ and we know that $a$ $=$ $xyz$ belongs to the centre of $G$. But im struggling to show that $\frac{G}{\langle a\rangle} ...
2
votes
1answer
22 views

Origin of period function model of primes

There is a web page attributed to Omar Pol, "Sobre el patrón de los números primos: Determinación geométrica de los números primos y perfectos." ("On the pattern of primes: Geometric Determination of ...
0
votes
2answers
14 views

Need help with a conic tangent question? (Hyperbolics)

I need to find the equation of the tangent to the hyperbola $$\frac{x^2}{6}-\frac{y^2}{8}=1$$ at the point $(3,2)$. I tried doing it by substituting for $y$ but the algebra is not nice at all and I ...
1
vote
1answer
34 views

Solving a ln divided by a ln.

I am having trouble figuring out how to calculate this. Thank you for your help. $$.926 = \frac{ln(1+.8u)}{ln(1+u)}$$ What does $u$ equal?
3
votes
0answers
19 views

Automorphisms of Abelian groups

Let $A$ be a free Abelian group and $N$ a characteristic subgroup of $A$ such that $A/N$ is finite. I also know that $Aut(A/N)$ and $Aut(N)$ are both finite. I have to prove that $Aut(A)$ is finite. ...
0
votes
0answers
17 views

Geometry of Spans in $\Bbb{R}^2$ and $\Bbb{R}^3$

I'm having difficulty figuring out how to approach the following Geometry of Spans questions. I only seem to understand the "span of a single vector" ones. How would I go about explaining the others? ...
2
votes
5answers
135 views

How can one know every Cauchy sequence in a complete metric space converges?

I am new to Cauchy sequences. I stumbled onto them in the process of learning what a Hilbert space is. As I understand it, a Cauchy sequence is a sequence whose elements become arbitrarily close to ...
0
votes
2answers
20 views

How is the Set of all Polynomials Equal to the Following Union?

Given that $P(F)$ is the set containing all polynomials with coefficients from field $F$, I am given the following: $W_1$ is the set of all polynomials $f(x)$ in $P(F)$ such that for: ...
1
vote
0answers
6 views

Determine if there is a node in a binary postorder anti-sorted tree with key $k$

A binary postorder anti-sorted tree is a binary tree for which the post-order traversal gives the keys that are saved at the nodes of the tree in descending order. Present a pseudocode for the most ...
0
votes
1answer
28 views

Founding maxima or minima to a function

$g(x)=e^{x-1}+x^{2}-3+2x$ How can I find when this function has maxima and minima? I found the derivative but I can't understand how find the solution when $g'(x)=0$. It's high school material.
2
votes
0answers
17 views

Prove or disprove $\nu(E)=\lambda(f(E))$ is a measure provided that $f$ is nondecreasing and satisfies the N-condition.

Suppose $f$ is a non-decreasing continuous function from $[a,b]$ to $\mathbb{R}$, and $\lambda$ is the Lebesgue measure in $\mathbb{R^1}$. Also, $f$ satisfies the property that $f$ maps Lebesgue ...
-1
votes
0answers
11 views

Solve this problem involving Geometric Brownian Process

The price of a stock follows a geometric Brownian process with annual expected return rate of 20% and volatility 50%. The initial stock price is 10 euros. Compute the probability that the stock price ...
3
votes
2answers
34 views

Why we throw away the units in the definition of irreducible elements?

In the book "Abstract Algebra" by Dummit, the definition of irreducible element in an integral domain $R$ goes like this. Suppose $r\in R$ is nonzero and is not a unit. Then $r$ is called irreducible ...
0
votes
1answer
43 views

Universe as a finite 3-manifold without boundary

My question is soft and imprecise, as I know very little differential topology. Nevertheless, I hope it makes some $\epsilon>0$ of sense. Assume the Universe is a 3-manifold without boundary, ...
0
votes
2answers
33 views

Level curves for “unsolvable” integral

Problem: Sketch the level curves of g defined by $$g(x,y)=\int_x^y{e^{-t^2}dt}$$ (The error function does not need to be used here). Attempts at solution: (1) Apparently we could take $y=x$, then ...
1
vote
1answer
38 views

There exist uncomputable integer numbers?

This question came from the answer I've given to the question An easy example of a non-constructive proof without an obvious "fix"?. Rereading my answer I had some doubt about the ...
2
votes
1answer
21 views

What variables is $\delta$ dependent on in the epsilon-delta definition of continuity?

The definition of continuity is: $f$ is continuous at $a$ if: Given any $\epsilon>0 $, $\exists \delta > 0$ st. $|x-a|<\delta \implies |f(x)-f(a)|< \epsilon$ $\delta$ obviously depends ...
0
votes
1answer
31 views

What books do you recommend on mathematics behind cryptography?

I am currently reading the Book Understanding Cryptography from Cristof Paar. I am enjoying the book but i don't like to scratch the surface when it comes to cryptography. I would like do dig a little ...
0
votes
0answers
3 views

Regular expression building: Comment delimited strings

I'm attempting to build a regular expression that will accept only strings of the form: ...
1
vote
1answer
21 views

Reduce this third order ordinary differential equation to first order to use Runge Kutta

The ODE I'm workin with is $$\dddot{x} + t^2\ddot{x} + 4x = 0$$ with $$x(0)=1, \dot{x}(0)=0, \ddot{x}=-1$$ I've written a very basic program in C++ to use the RK4 method to approximate a solution to ...
0
votes
0answers
19 views

Abelian torsion group of rational points of an elliptic curve

I want to find the abelian group of rational points $E(\mathbb{Q})_{\text{torsion}}$ of the elliptic curve $y^2=x^3+8$. $$E(\mathbb{Q})_{\text{torsion}}=\{P \in E(\mathbb{Q}) | P \text{ of finite ...
0
votes
1answer
40 views

Computing $\mathrm{gcd} (100!, 3^{100})$

I am trying to compute $\mathrm{gcd}(100!,3^{100})$. I am still not sure how to reach an answer but I feel that Wilson's Theorem (i.e., $(p-1)!\equiv -1 \bmod p, p$ prime) and Fermat's Little theorem ...
0
votes
0answers
4 views

Solve 1D wave equation on half-line using method of images

I'm trying to solve $\theta_t - D\theta_{xx} = f(x,t)$ on the half-line $0 < x < \infty$ for $0< t < \infty$ given boundary and initial conditions $\theta(0,t) = h(t)$, $\theta(x,0) = ...
0
votes
3answers
15 views

Propositional logic problem: Sales, expenses and happiness of the boss

Either sales will go up and the boss will be happy, or expenses will go up and the boss won’t be happy. Therefore, sales and expenses will not both go up. I know the solution is that the ...
0
votes
0answers
13 views

How do I prove that a given probability distribution is Gaussian

I am trying to plot the distribution of a random variable $x$. I got this distribution by marginalising a wishart distribution. When I plot the distribution curve of $x$, it looks like bell shaped ...
1
vote
2answers
22 views

Can someone help me prove that $\tau(n)$ is odd [duplicate]

Can someone help me prove that $\tau(n)$ is odd if and only if $n$ is a perfect square. So basically I have to prove that $\tau(n)$ is odd iff $n = k^2$ for some integer $k$.
0
votes
0answers
15 views

Equivalence of Definitions of completion of metric space

I've come across two different definitions for a completion of a metric space and am trying to figure out why they are equivalent. The definitions are: 1) Let $(X,d)$ be a metric space. Then ...
-1
votes
0answers
12 views

Practicing mathematical proofs in preparation for another course and could use some help [on hold]

I'm starting a course on Algorithms and the professor wants to test our induction and proof knowledge. Problem is, our prerequisite courses never focused on such material. I'm hoping someone could ...
1
vote
1answer
20 views

No generic is definable in a perfect notion of forcing of a model of Peano Arithmetic

I would like to prove Lemma 6.1.2.2 from The Structure of Models of Peano Arithmetic by Kossak and Schmerl. Let $\mathcal{M}$ be a countable model of Peano Arithmetic and $\mathbb{P}=\langle P, \le ...
0
votes
0answers
22 views

How do I specify a function without a defined argument?

A function $f$ with the argument $x$ is commonly written $f_x : A\to B, x\mapsto f(x)$, or $f_x : \mathbb{R} \to \mathbb{R}, x\mapsto x^2$, but say I don't want to specify the argument, how would I ...

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