What is Notation: Definition and 1000 Discussions

In linguistics and semiotics, a notation is a system of graphics or symbols, characters and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an arbitrary meaning, created to facilitate structured communication within a domain knowledge or field of study.
Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like mathematics, physics, chemistry and biology, but can also be seen in areas like business, economics and music.

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  1. J

    What are the different forms of Fourier notation and how are they connected?

    The Fourier integrals and series can be written of 3 forms (possibly of 4): the "real cartesian": a(ω)cos(ωt) + b(ω)sin(ωt) the "real polar": A(ω)cos(ωt - φ(ω)) where: A² = a² + b² sin(φ) = b/A cos(φ) = a/A tan(φ) = b/a the "complex polar" A(ω)exp(iφ(ω))exp(iωt) And my...
  2. H

    How to define a set without set builder notation

    How do you define a set without using set builder notation? For example, let's say that I want to define set S as: S={x ∈ ℕ ∣ 0<x<5} Then S={1,2,3,4} However, suppose that I wanted to define S without set-builder notation, as below? ∀x(x ∈ ℕ ^ 0<x<5 ⟺ x∈S ) Would these two...
  3. U

    Vector calculus identities proof using suffix notation

    I must become good at this ASAP. Homework Statement prove \vec{\nabla}\cdot (\vec{a}\times\vec{b} ) = \vec{b} \cdot(\vec\nabla\times\vec{a}) - \vec{a}\cdot(\vec\nabla\times\vec{b}) Homework Equations \vec a \times \vec b = \epsilon_{ijk}\vec a_j \vec b_k \vec\nabla\cdot =...
  4. Isaacsname

    Can somebody help me re-write this with traditional notation ?

    I apologize if this is the wrong section This is an integral written with the first 7 digits of pi, reversed, I think... Can somebody write this out with traditional notation ? I am still learning the basics of integrals, so I am completely unsure of how to write it out...
  5. D

    Matrix notation for Lorentz transformations

    I'm having some confusion with index notation and how it works with contravariance/covariance. (v_{new})^i=\frac{\partial (x_{new})^i}{\partial (x_{old})^j}(v_{old})^j (v_{new})^i=J^i_{\ j}(v_{old})^j (v_{new})_i=\frac{\partial (x_{old})^j}{\partial (x_{new})^i}(v_{old})_j...
  6. S

    Translating set notation to english

    I've been trying to think of the grammatically correct way to translate A\cupB and A\capB. So, let's say A is the set of all animals and B is the set of all boats. Then, A\cupB is the set of all entities which are either animals or boats (or both). And A\capB is the set of entities...
  7. S

    Inverse matrix notation question

    I'm hoping that you can help me settle an argument. For a matrix \textbf{M} with elements m_{ij}, is there any sitaution where the notation (M_{ij})^{-1} could be correctly interpreted as a matrix with elements 1/m_{ij}? Personally I interpret (M_{ij})^{-1} in the usual sense of an inverse...
  8. E

    Notation question for probability measures on product spaces

    I asked this in the logic&probability subforum, but I thought I'd try my luck here. ... Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to...
  9. E

    Notation question for probability measures on product spaces

    Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to some probability measure q(\cdot|a) on (B,\mathcal B). Then there is a unique probability...
  10. A

    Really a Question about Notation

    Homework Statement Form negation and then either prove statement or negation: \forally \in { x | x \in Z, x>=1}, 5y^2+5y+1 is a prime number. The Attempt at a Solution Answer given: \existsy \in { x | x \in Z, x>=1} such that 5y^2+5y+1 is not prime. The negation is true...
  11. Rococo

    On the index notation used in Lorentz transformations

    I understand how contravariant 4-vectors transform under a Lorentz transformation, that is: ##x'^μ= \Lambda^\mu~_\nu x^\nu## [1] and how covariant 4-vectors transform: ##x'_\mu=(\lambda^{-1})^\nu~_\mu x_\nu##. [2] Now, I have come across the following relations...
  12. T

    Understanding Dirac notation - Product of ops. is product of matrices

    Homework Statement This makes intuitive sense to me, but I am getting stuck when trying to read the Dirac notation proof. Anyway, the author (Shankar) is just demonstrating that the product of two operators is equal to the product of the matrices representing the factors. Homework Equations...
  13. C

    Interval notation for series converging

    Homework Statement So I solved this problem ∑ (-1)^n (x+5)^n by finding the sum of the series to be 1/(x+6), which was correct. I am stuck on the second part of the problem asking for interval notation. It says: Determine, in interval notation, the values of x for which the series converges...
  14. Math Amateur

    MHB Ring Theory texts and "right notation" for maps/functions

    I would like members views on right notation for maps/functions. I am thinking of studying some material in some of the chapters of the book: Introduction to Ring Theory by P. M. Cohn Cohn claims his book is suitable for 2nd and 3rd year undergraduates and the book seems to have some really...
  15. Matt atkinson

    Suffix Notation Help: Nabla Vector Calculation

    Homework Statement Show that the equation \nabla \times \vec{p} = -\frac{\vec{B}}{r^3} + 3\frac{\vec{B} \bullet \vec{r}}{r^5}\vec{r} Where ; \vec{p} = \frac{\vec{B} \times \vec{r}}{r^3} \vec{r}=(x_1 ,x_2 ,x_3) and \vec{B} is a constant vector. and r is the magnitude of \vec{r}...
  16. A

    Cauchy Stress Tensor: Equilibrium Equations

    ''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.'' \sigma_{ij,j}+F_i=0 I would appreciate if you could write out what it means. Also there is this notation which I don't understand: \frac{\partial}{\partial y_j}\sigma_{ij}(x,y)
  17. I

    Looking for a specific math notation

    I'm trying to write a contracted general equation for an expandable equation. Just like there's the summation symbol for sums, is there something for multiplying terms? for example.. how do i contract the following? $$C_{i}C_{ii}C_{iii}C_{iv}C_{v}...$$?
  18. S

    Expectation value for momentum operator using Dirac Notation

    Question and symbols: Consider a state|ε> that is in a quantum superposition of two particle-in-a-box energy eigenstates corresponding to n=2,3, i.e.: |ε> = ,[1/(2^.5)][|2> + |3>], or equivalently: ε(x) = [1/(2^.5)][ψ2(x) + ψ3. Compute the expectation value of momentum: <p> = <ε|\widehat{}p|ε>...
  19. D

    Extremely Simple Notation Question on a Circuit

    I cannot for the life of me remember what to do with the diode: It is a DC Current hooked up to one resistor in series with a pair of resistors in parallel drawn vertically, but then the diode is hooked up to (on paper) the top two ends of the parallel resistors? It's aligned horizontally...
  20. N

    Understanding Index Notation and Tensor Operations in Vector Calculus

    Homework Statement Hi I have a vector v. According to my book, the following is valid: \frac{1}{2}\nabla v^2-v\cdot \nabla v = v\times \nabla \times v I disagree with this, because the first term on the LHS I can write as (partial differentiation) \frac{1}{2}\partial_i v_jv_j =...
  21. M

    Angular momentum using unit-vector notation

    Homework Statement At one instant, force F: 4.0j N acts on a 0.25 kg object that has position^vector^V : (2.0t - 2.0k) m and velocity vector /: (-5.0i + 5.0k) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b)the torque acting on the object...
  22. J

    Confusing max(min(f(x,y)) notation?

    I'm working on some MIT OCW for probability theory, and I've come across some confusing notation in the assignmnet. Look at exercise 3 here: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-436j-fundamentals-of-probability-fall-2008/assignments/MIT6_436JF08_hw01.pdf...
  23. A

    How to Perform Operations on Big O Terms?

    Is there a standard algorithm or procedure that defines addition, multiplication of big O terms. I want definitions for problems like:- 1) (x-1) * O(x) 2) O((x-a)2) where a is some positive number etc. Since I want to implement this on a computer I would prefer some algorithm or paper...
  24. M

    Understanding Dirak Notation: Exploring State Determination with Eigen Kets

    I have the following question for anyone who can help: Suppose in Dirak notation i have the following state: /ψ> = 2 /u1> + /u2> where /u1>,/u2> are the two first eigen kets of energy of the infinite square well. That means <x/u1>= Asin(π x /L) and <x/u1>= Asin(2 π x /L) which gives ...
  25. P

    MHB Polynomial including Sigma Notation

    Hello everyone! I have this polynomial: $p(x) =$ 1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k - I'm supposed to show that this polynomial must have at least one positive real root. - I'm supposed to show that this polynomial has no negative real roots. - And I'm supposed to show that if $z$ is...
  26. ThomasMagnus

    Integrating Velocity When in Unit Vector Notation

    Homework Statement Say for example, a particles velocity was given by the following equation: \vec{V}(t) = (2t2-4t3)\hat{i} - (6t +3)\hat{j} + 6\hat{k} If I wanted to find the displacement of the particle between t=1s and t=3s, could I just integrate like this? \int \vec{V}= (2t3/3...
  27. L

    Show that the dot product is linear: Bra-ket notation

    Homework Statement Show that the dot product in two-dimensional space is linear: <u|(|v> + |w>) = <u|v> + <u|w> The Attempt at a Solution I feel like I'm missing some grasp of the concept here ... I would think to just distribute the <u| and be done in that one step, but I'm being...
  28. J

    MHB A question regarding Big Theta notation

    I'm brand new to this website, and couldn't figure out how to start a new thread, but I also have a question about Big Theta notation. Is big-theta(x/y) = big-theta(x)/big-theta(y)? I know big-o(x/y) = big-o(x)/big-o(y), but I don't know if big-omega(x/y) = big-omega(x)/big-omega(y). I can...
  29. M

    How does Franke's condensed notation simplify structural synthesis?

    Franke's "condensed notation for structural synthesis" in this pic I don't understand how we can labelled some lines as 0s and others as 1s.
  30. B

    Complex Made Simple: Notation on Disks

    Hello, I'm reading "Complex Made Simple" by David Ullrich. He has these notation for disks D(z_0,r) = \left\{ z \in \mathbb{C}: |z-z_0|< r \right\} \bar{D}(z_0,r) = \left\{ z \in \mathbb{C} : |z - z_0| \leq r \right\} I understand that these sets are to be the open and closed disks with...
  31. U

    A^c Notation in Matrix: Exploring the Unknown

    Homework Statement What is meant by A^c notation in matrix, where A is any arbitrary matrix?The Attempt at a Solution I've searched all over the internet and reference books that I have but none of them gives information about this thing. Please help me.
  32. N

    Dirac Notation and Hermitian operators

    Homework Statement Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the...
  33. O

    Quick question about bra-ket notation

    Homework Statement On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say: Homework Equations H |n> = E_n |n> So: <n| H = <n| E_n H is Hermitian. So: Why is this? The Attempt at a Solution...
  34. I

    Changing bases (with bra-ket notation)

    http://i.imgur.com/ORtBJdT.jpg i don't understand why the old base is written in terms/as a linear combination of the new bases. wouldn't i want to map my coordinates from old to new not new to old?.. here's what my textbook says about it, can you guys interpret this for me, i still don't...
  35. I

    Bra-ket notation and other linear algebra stuff

    forgive the messiness; i take bad notes in class. http://i.imgur.com/VmW8Ubg.jpg towards the middle of the page where it says "this is equivalent to..." and then my professor wrote what follows but i thought the row vector should be complex conjugates? ie, the red writings are not actually...
  36. S

    What is Interval Notation and How is it Used?

    [a;b[ I want to do a problem with this but i can't find anything about it, if anyone can help me it'd be very useful, thank you. :) The one i want to do exactly is [20;30[ , in case anyone is wondering.
  37. cactusblanket

    Acceleration of a Charged Particle in 3D Vector Notation

    Homework Statement Hi there! Here is a problem from our 1st year course. We have covered the basics on charges and Coulomb's Law. However our prof said he designed the following question to be "deliberately obscure"! Two charges of 4.00μC are fixed in space, Q1 at (0,0,0) and Q2 at...
  38. S

    What does \sum\limits_{i\neq j}^N a_i a_j mean in summation notation?

    Hi I have a textbook which uses the notation: \sum\limits_{i\neq j}^N a_i a_j I can't find anywhere what this actually means. Is it equivalent to: \sum\limits_{i}^N \sum\limits_{j}^N a_i a_j where j can't equal i? Thanks.
  39. J

    I don't understand <u|A|v> notation

    u and v are vector or whatever in that base, and A is an operator. What does <u|A|v> mean?
  40. I

    What is the significance of complex conjugates in Bra-ket notation?

    so I'm fine with the kets, e.g, |a>.. but i don't understand what the bras are. the kets are basically just a column vector right? ie the components (with the direction) of the vector being described. but what is the bra? this was given to us in class: <a|=a1<e1|+a2<e2|= (a1* a2*) (where e1...
  41. T

    What does Z_2^5 mean in linear algebra notation?

    I know how to solve linear systems but I came across this question where I've never seen the notation before. I searched all over the internet but still couldn't figure it out. The question asked to find all solutions in Z_{2}^{5} of a linear system. I'm guessing that Z^5 means all integers on...
  42. J

    Ideal Gases dealing with scientific notation

    I am not sure how to properly use the scientific notation in this problem. I have attempted to solve it several different ways to no avail. A house has a volume of 1.45 x 10(4)m(3). At 20.0° C and 740 mm Hg, the air fills the house. If the temperature and pressure increase to 35.0°C and...
  43. N

    Index Notation for Rank-2 Tensor with Summation

    Homework Statement I have the following rank-2 tensor T = \nabla \cdot \sum_{i}{c_ic_ic_i} I would like to write this using index notation. According to my book it becomes T_{ab} = \partial_y \sum_{i}{c_{ia}c_{ib}c_{iy}} Question: The change \nabla \rightarrow \partial_y and c_i...
  44. binbagsss

    Quick question, index notation, alternating tensor.

    Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1. The soluton is: ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123} where g_{\alpha\beta} is the metric tensor. I am struggling to understand the last equality. Many thanks for any assistance.
  45. binbagsss

    Index notation/ Tensors, basic algebra questions.

    Ok I have T_{ij}=μS_{ij} + λ δ_{ij}δS_{kk}. I am working in R^3. (I am after S in terms of T) . I multiply by δ_{ij} to attain: δ_{ij}T_{ij}=δ_{ij}μS_{ij} + δ_{ij} λ δ_{ij}δT_{kk} => T_{jj}=δ_{jj}λS_{kk}+μS_{jj} * My question is , for the LH term of * I choose T_{jj} rathen than T_{ii}. I...
  46. binbagsss

    Quick question, index notation, alternating tensor.

    Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1. The soluton is: ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123} where g_{\alpha\beta} is the metric tensor. I am struggling to understand the last equality. Many thanks for any assistance.
  47. E

    Tensor Notation and derivatives

    Hi folks. Hope that you can help me. I have an equation, that has been rewritten, and i don't see how: has been rewritten to: Can someone explain me how? Or can someone just tell me if this is correct in tensor notation: σij,jζui = (σijζui),j really hope, that...
  48. S

    Interval Notation: Clear Explanation

    Can anyone please give a succinct and clear description on this? I'm a little confused...
  49. skate_nerd

    MHB Proving vector calculus identities w/ tensor notation

    I have an vector calculus identity to prove and I need to use vector notation to do it. The identity is $$\vec{\nabla}(fg)=f\vec{\nabla}{g}+g\vec{\nabla}{f}$$ I tried starting with the left side by writing $\vec{\nabla}(fg)=\nabla_j(fg)$. Now I look and that and it really looks like there is...
  50. P

    Eigenfunctions and dirac notation for a quantum mechanical system.

    QUESTION A quantum mechanical system has a complete orthonormal set of energy eigenfunctions, |n> with associate eigenvalues, En. The operator \widehat{A} corresponds to an observable such that Aˆ|1> = |2> Aˆ|2> = |1> Aˆ|n> = |0>, n ≥ 3 where |0> is the null ket. Find a complete...
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