1
vote
0answers
73 views

difference between n - 1 and n-1

I hope things are going well. I am doing some recursion stuff with databases and the text book I am reading has made it clear there is a difference between n-1 for example and n - 1. The difference ...
2
votes
1answer
57 views

What does this log notation mean?

Can someone please explain what $^2\log x$ means? Is it the same as saying $\log x^2$ or is it something completely different? Here is an image of it as an example:
3
votes
1answer
84 views

Is this notation good for the chain rule derivative?

When we take this derivative, for example: $$y = \log(\sin x)$$ We call $u = \sin x$, so we have: $$\frac{dy}{dx} = \frac{d y}{du}\frac{du}{dx} = \frac{1}{u}\cos x = \frac{\cos x}{\sin x}$$ But for ...
1
vote
0answers
36 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
1
vote
2answers
37 views

Notation for Derivatives with Respect to Time

My math teacher writes $\frac{dx}{dt}$ as $x'$, and makes us do the same for homework. (in a particle motion context, where $t$ is time) I am aware that the standard notation is usually $\dot{x}$, ...
0
votes
0answers
16 views

Representing trees in Set builder notation?

Is there a way to represent graphs and minimum spanning trees using set builder notation? e.g. I have a weighted graph of n nodes, all connected to each other in a mesh network manner. I am to ...
1
vote
0answers
26 views

Groups - Compositions

If the f is written to the right of its argument does that mean the composition of $f g$ is actually $g(f(x))$ instead of being $f(g(x))$ which is the notation I'm used to. I ask this because I read ...
1
vote
2answers
39 views

Is this a good expression of the claim using logical notation?

Four Square Theorem: Every positive integer can be written as a sum of four integer squares. Expressed in logical notation : $$\forall n>0 =a_{0}^{2} + a_{1}^{2} + a_{2}^{2} + a_{3}^{2}$$
1
vote
4answers
66 views

Surprised over notation in fundamental theorem

So I'm looking into the fundamental theorem of calculus and I'm a bit weirded out by the notation used in part two. $$ \int_{a}^b f(t) dt = G(B)-G(a)$$ Why don't we say $F(b)-F(a)$? We are just ...
0
votes
1answer
54 views

confusion about Einstein notation

I have the following expression $$ \partial_k\sigma_{ik} = \partial_i\partial_ku_k + \partial_k^2u_i $$ I know that a repeated index means summation. So for a 2D space $(x, y)$ I would get (for the ...
1
vote
2answers
83 views

What does $\alpha+\gamma$ mean when $\alpha$ and $\gamma$ are well-ordered sets?

I was asked to prove the following: let $\gamma$ be a well ordered set with the following property: for any $\alpha$ and $\beta$ well ordered sets, if $\alpha+\gamma=\beta+\gamma$ then ...
0
votes
1answer
115 views

Problem with simple Projectile motion formula

I'm really new to all this, so please don't be rude. I have here what appears to be a simple formula. Yet I cant get my head around it: $$\begin{align} y &= y_0 + v_{0y}t + (1/2)a_y t^2 \\ 0 ...
1
vote
2answers
82 views

How would one prove $[f,[\nabla^2,f]]=-2(\nabla f)^2$?

How would one prove this equation: $$[f,[\nabla^2,f]]=-2(\nabla f)^2 $$ And I'm confused that $\nabla f\nabla f$ equals $(\nabla f)^2$ or $\nabla(f\nabla f)$.
0
votes
0answers
14 views

For signature $\Sigma$ and equations $E$, what is meant by $\mathcal{T}_{\Sigma/E}$?

This notation came up in a homework problem and I'm having trouble finding its definition in our course notes. $\mathcal{T}_\Sigma$ represents the term algebra of $\Sigma$, but I'm unsure what ...
2
votes
3answers
175 views

Basic question: what does the notation $[A,B]$ mean?

If $A$ and $B$ are both matrices, what is $[A,B]$? I understand that it is a commutator and that $[A,B]=AB-BA$, but since I don't know what a commutator is, none of this information is telling me ...
1
vote
1answer
72 views

The difference between a / and ÷ use

I'm confused with the $/$ symbol meaning the same as $÷$ $4+2(8-3)÷2-1$ should equal $8$ using PEMDAS. However if using the Wikipedia's definition of the slash "Used between numbers slash means ...
1
vote
1answer
35 views

Notation for Permuting Sets

If I have some arbitrary sets $A_i : i \in I$ and I want to permute their intersections pairwise, how would I write such a permutation? Would I use some permutation tensor? Essentially I want to ...
3
votes
1answer
61 views

Help with notation in second order tensor.

I have seen recently this notation: $$F=F_{ij}\,e_i\otimes e_j $$ Where $F_{ij}=\frac{\partial x_i}{\partial X_j}$ is the tensor matrix: $$ F=\left[ {\begin{array}{cc} ...
1
vote
1answer
178 views

What is this strange symbol called :=?

I want to Google it but I don't even know what to call it. It looks like some sort of assignment used in computer science or math. Here it is again := It is ...
0
votes
2answers
113 views

Atiyah-MacDonald 5.10

The problem says: Let $f:A\rightarrow B$ be a ring homomorphism and let $f^{*}:\operatorname{Spec}(B)\rightarrow \operatorname{Spec}(A)$ be the mapping associated with $f$. And then comes the ...
0
votes
1answer
68 views

Tree graph intuition + mathematical notation

Let $T$ be a tree with at least two vertices. Consider a path of maximal length in $T$. Prove that the start and end point of this path have degree 1 by contradiction : If we let the start and ...
0
votes
3answers
42 views

Reference a vector component

If I have the following cartesian vector: $$ \vec{v_1} = \pmatrix{1 \\ 2} $$ How would I reference the second vector component of: $$ \vec{v_1} $$ Is it okay to do it this way: $$ \vec{{v_1}_y} = 2 ...
0
votes
2answers
190 views

Evaluating using BRA KET Notation?

Evaluate $\langle 0 \mid x^3 \mid 1\rangle$, assuming that all the wave functions you encounter are normalized eigenfunctions of the harmonic oscillator Hamiltonian, without Mathematica, Maple, or ...
0
votes
2answers
298 views

Proper Use Of Notation? (Determine whether the function is surjective)

Determine whether the function $f: Z×Z→Z$ is onto if a) $f(m,n)=m+n$. b) $f(m,n)=m^2+n^2$ c) $f(m,n)=m$. d) $f(m,n)=|n|$. e) $f(m,n)=m−n$. I was able to answer these ...
0
votes
1answer
66 views

Put the $i$th term to be the coefficient of $x^i$: A question about Mathematical notation and sequences

Take $u(x)$ and $v(x)$ to be integer polynomials, and then interpret them as sequences in the obvious way: i.e. you put the $i$th term to be the coefficient of $x^i$. $u(x)=x-2$, $v(x)=3x^2+x$. The ...
1
vote
1answer
94 views

What does the expression $A^c$ mean in this context?

In a maths question, I had $A$ with a superscript of $c$, like this: $$A^c$$ What does this mean? In a Venn Diagram $A =$ to 5 and 6.
3
votes
1answer
173 views

When using sigma notation, why is “1” put as value?

First of all, I never really learned exactly what Sigma notation is, and although I understand the basics, there are some things that are confusing me. I'm trying to convert the following algorithm to ...
1
vote
1answer
42 views

Notation issue regarding differential equations

I am given the following problem: Find a basis of solutions for the equation: $u^{iv} + 2u'' + 3u = 0$ The notation is an exact duplicaticate of what our professor used in his notes. Does anybody ...
3
votes
1answer
110 views

Strange Notation: $f(x,y) = \ln (x + \text {s} \space \overline {x^2 + y^2} $)

I am currently working on my first calculus assignment of the quarter, and immediately ran into a strange notation which neither my teacher discussed nor is it mentioned in any previous parts of the ...
1
vote
2answers
108 views

What does this syntax mean: “$f^{-1} : N_{10} \Rightarrow N_b $ is the inverse of $f: N N_{b} \Rightarrow N_{10}$?”

I'm trying to solve this but I haven't seen syntax like this before. Can someone please explain the syntax? http://i.imgur.com/GO1Ki.png The image is Show that the one-to-one function $f^{-1} : ...
0
votes
1answer
107 views

Don't understand the notation for this group theory question

Could someone explain the notation in this question to me so I can have a go at answering it. Show that $SO_3(\mathbb{F_2}) = \{M \in SL_3(\mathbb{F_2})|M^{-1} = M^t\}$, where $M^t$ is the transpose ...
1
vote
2answers
85 views

Prove that $\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$

prove the $$\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$$ for all n greater or equal to 2. $\pi$ should be a big pi from $i=2$ to $n$ for $(1-1/i^2)$. I'm really confused about the $\prod$ function. ...
1
vote
1answer
127 views

How can this algorithm be expressed in mathematical terms?

I have found a solution to a basic problem using an algorithm, but I'm having a bit of a hard time expressing this algorithm in terms of discrete math. ...
1
vote
1answer
190 views

little o notation with natural logs

I'm having trouble with little o notation. Help me show that: $2(n^2 + 100n)\log^5n = o(n^2\sqrt{n})$. It is the last hwk on my sheet and I don't understand it, if someone can help me with ...
0
votes
0answers
63 views

Is this a correct translation from recursive function to math notation?

I have this recursive function, written in Java. Assignment is to translate it to mathematical notation. ...
1
vote
2answers
76 views

What is '+' in set notation

In set $T = \{(0+2)^{i+5}|\space i \in \mathbb{N}\}$, what is the meaning of the $(0+2)^{i+5}$?
4
votes
1answer
237 views

Field extensions, inverse limits, notation and roots of unity

I'm hoping I can get some assistance with a revision problem and also a notational issue I'm not sure about (although it may not be standard). I seem to remember going over this or something similar ...
3
votes
1answer
300 views

Disproving a big O equation

As a homework assignment I am trying to prove/disprove the next statement: Let $f(x)=O_a(g(x))$, then $\forall A,B\in\mathbb{R}\rightarrow A\cdot f(x)=O_a(B \cdot g(x))$ Which I think is wrong ...
1
vote
2answers
2k views

Notation : What is the meaning of the (mod n) in factoring algorithms?

Pretty much every thing is in the title, really! I'm trying to come up with an efficient algorithm to factorize large integer as an homework for a parallel programming course. I've seen a few pages ...
1
vote
1answer
480 views

Sequence Notation

I have come across the following in the book "Principles of Program Analysis" by Nielson, Nielson and Hankin to represent a sequence and I am unsure of what its constituent parts mean. Obviously ...
2
votes
2answers
212 views

$(fg)(x)$ and $f(g(x))$. Commutability in Limits

Is there a difference between $(fg)(x)$ and $f(g(x))$? From my lecture slides $\lim\limits_{x\to a} (f(x)+g(x)) = \lim\limits_{x\to a} f(x) + \lim\limits_{x\to a} g(x)$ Then in the next slide, it ...
1
vote
1answer
71 views

Question Concerning The Solution Of A Differential Equation

Here's another question from Advanced Engineering Mathematics by Greenberg [Ex 1.2 Q5]: For what values of the constant $\lambda$ will $y = \exp(\lambda x)$ be a solution of the differential ...
1
vote
4answers
189 views

Understanding the $\equiv$ symbol

I am trying to understand a wierd symbol in a book and I am failing. The symbol is this '$\equiv$'. I understood that if I have $32\equiv 2\bmod15$ means that if I divide $32$ with $15$ I will get ...
1
vote
3answers
284 views

What is the “limit point of a function?”

I am asked to prove that Show that a sequence $x: \mathbb{N} \to \mathbb{R}$ has a limit point iff there $\lim_{n\to\infty} x(n)$ exists as a limit point of a function from a subset of metric ...
2
votes
1answer
187 views

What is the meaning of a small o in between function names? i.e (f o g)

I am helping with homework. I am stumped here - What is the meaning of the small round circle, or small "o" in question 19 (that I underlined) and question 20
0
votes
0answers
181 views

Interval Notation With Gaps

I have $A = (-10, -4)$ and $B = (3, 8)$. And I am trying to write the answer to $A \cup B$. I know the answer is $(-10, -4)$ and $(3, 8)$ but I am unsure how to write an interval range where there is ...
1
vote
1answer
150 views

Cover & Thomas textbook notation

Exercise 2.27 in Elements of Information Theory (2nd ed.) reads: Let $\mathbf{p} = (p_{1}, p_{2}, \ldots, p_{m})$ be a probability distribution on $m$ elements (i.e., $p_{i} \geq 0$ and ...
1
vote
1answer
123 views

PEDMAS in RPN needed?

In RPN do we still have to take into note the PEDMAS rules? For example these questions: 3 – 4 * 2 3 * 4 – 2 3 * (4 – 2) (3 – 4) * 2 3 – 4 + 2 Answers 342*- ...
3
votes
1answer
730 views

Determine if function is little-o, little-omega or big-theta

Let $f(n) = n^3(5+2\cos(2n))$ and $g(n) = 3n^2+4n^3+5n$. Given these two functions, I must determine the appropriate symbol where the underscore is: $f(n) \in \_(g(n))$ So, first thing to do is take ...
1
vote
1answer
118 views

rational functions notation in Dummit&Foote

A problem in Dummit and Foote states: Let $k$ be a field and let $k(x)$ be the field of rational functions in $x$ with coefficients from $k$. Let $t \in k(x)$ be the rational function ...