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. M

    What kind of math notation is this?

    what kind of math language is this? $I\subset \reals$ $$\gamma_i:I_i\rightarrow M,\quad I_i\subset\reals,\quad i=1,2$$ $\sigma_{\alpha\beta}$ , let $$\rJ\sigma_{\alpha\beta}:V_{\alpha\beta}\rightarrow \Mat_{n,n}(\reals)$$ I have seen this notation thrown around in this forum, but I never...
  2. A

    Basic operations on sequences (conventional notation)

    Hi All, So here's my question: Suppose we have two sets A and B, then A \setminus B denotes their set-difference. Does there exist an equivalent operator for the case where A and B are not sets, but sequences? Otherwise, is there an operator to convert a sequence into a set...
  3. V

    What do the subscripts in thermodynamic notation mean?

    I'm having trouble understanding some of the notation used in thermodynamics. The textbook will write things like: \frac{1}{T} = \left(\frac{\partial S}{\partial E}\right)_{N,V} such as you might use in the thermodynamic temperature in the microcanonical ensemble, and it says that the...
  4. N

    The domain of a function in interval notation

    [b]1. what is the domain of the function k(y)=1/(2y+1)? Express your answer in interval notation [b]2. [b]3. I find that 0.5 is a possibility in this function, but since i have not done functions at school, i do not really know much more of this question.
  5. L

    Proving vector calculus identities using summation notation

    Homework Statement \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Equations \vec{r} = x_{i}e_{i} The Attempt at a Solution \frac{∂x_{i}}{∂x_{j}} = 1 iff i=j δ_{ij} = 1 iff i=j therefore \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Statement r^{2} = x_{k}x_{k} Homework...
  6. mnb96

    Big-O Notation Question: Polynomial with Variable Coefficients

    Hello, I have a polynomial having the form: \beta x^5 + \beta^2 x^7 + \beta^3 x^9 + \ldots = \sum_{n=1}^{+\infty}\beta^n x^{2n+3} How can I express this with Big-O notation? Please, note that I consider β as another variable (independent from x). I already know that if β was a constant I...
  7. C

    Which of the following numbers can be added directly in exponential notation?

    Which of the following numbers can be added directly in exponential notation? 1. 3x10^-4 2. 600x10 3. 32.6x10^-3 4. 0.4x10^-4 _______________________________ a. 1 and 2 c. 1 and 4 d. 2 and 4 b. 1and3
  8. B

    Exponential of an operator into bra-ket notation

    Homework Statement The question is to evaluate the expression e^-iA, where A is a Hermitian operator whose eigenvalues are known (but not given) using bra-ket algebra. Homework Equations See above. The Attempt at a Solution I have been looking around, reading the textbook and...
  9. M

    MHB Derivative Notation: Clarifying Confusion

    I am always getting mixed up on derivative notation, so I was just wondering if this below makes sense? \(f(x) = 2x^\sqrt{2}\) \(\frac{df(x)}{dx} = 2\frac{d}{dx}x^\sqrt{2}\) The first should probably just be \(\frac{dy}{dx}\), but I was wondering if the other way would work as well.
  10. M

    MHB Wave equation and weird notation

    I have $u_{tt}=u_{xx},$ $x\in\mathbb R,$ $t>0,$ $u(x,0)=0$ and $u_t(x,0)=\chi_{[-1,1]}(x).$ What does mean the last condition? In such case, how to solve the equation then? Thanks!
  11. C

    What is the Meaning of this Notation in the Context of Smooth Retractions?

    Homework Statement Here is the context: suppose f=(f_1,...,f_{n+1}) is a smooth retraction of B^{n+1} onto S^nBut what does the following statement mean? \int _{S^n}f_1df_2\wedge df_3 \wedge ... \wedge df_{n+1} Homework Equations The Attempt at a Solution
  12. B

    Where are free online classes for Scientific Notation?

    I am new to astronomy and astrophysics, can anyone point to a great free online place to learn scientific notation? I am quite obsessed with learning the math, but unfortunately have not the funds to attend a proper school. Unfortunately I work for a cheap employer who doesn't even pay for work...
  13. G

    Question about notation (hyperplanes)

    Homework Statement I have a question for which I'm supposed to show that a function maps into "a hyperplane {u in ℝ5:u5=1}". Does this mean that the target space is the set of vectors in ℝ5 such that the dot product of u with itself (5 times) is 1? Doesn't seem right... Any clarification is...
  14. I

    Infix to Reverse Polish notation

    I have to convert.. X=A+((B+C)*D)-E to reverse polish notation I think it's... BC+D*A+E- Is this correct?
  15. C

    What is the correct notation for plugging in 0 to an anti-derivative?

    Homework Statement I need to plug 0 into an anti-derivative of f, and I'm wondering whether it can be written as: y = \int f(0)dx or do I HAVE to write it as: F(x) =\int f(x)dx y = F(0) Homework Equations See 1. The Attempt at a Solution See 1.
  16. V

    What does this notation mean ?

    What does this "(12)" represent in the number 0. (12)22293 93645 534? what does this bracket say ??
  17. J

    MHB Converting Summation Notation to Closed Form for Linear-Geometric Series

    I have the following summation and I'm attempting to remove the summation notation. It appears to be the sum of a geometric series but I'm having a great deal of trouble with it. X is an unknown constant. $$\sum\limits_{i=2}^n (n - (n-i))x^{n-i}$$ Thanks.
  18. D

    How can I write a Fibonacci sequence using summation notation?

    Homework Statement I have trouble with the summation notation. \sum_{i=0}^{k}\binom{k}{i}f_{n+i} How do I write this as a sequence based on the definition of Fibonacci sequence? Homework Equations Definition: f(0)=0 f(1)=1 f(n)=f(n-1) + f(n-2) for n>=2 Example: f(2) = f(1) +...
  19. R

    Interval Notation for Set Intersection and Union

    Homework Statement Consider the following intervals: A = [-3,5), B = (3,8), C = (0,4] Find: A\capB and A\capC The Attempt at a Solution I thought that: A\capB=(3,5) and that A\capC=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A\capB=[-3,8)...
  20. B

    Set-Theoretic Notation Kuratowski

    I'm not sure if I'm on the right track with any of this, but any insight would be greatly appreciated. I have worked out what I believe to be the correct answer, but I really don't have any idea. Express <a, b, c> =df <<a, b>, c> in terms of the set-theoretic notation only, using the...
  21. B

    Set-Theoretic Notation Kuratowski

    Hi, I am trying to work through ordered triples and quadruples, and I want to make sure I am on the right track. Given Kuratowski's set-theoretic definition of ordered pairs: <x,y> = df {{x},{x,y}} it seems that the definition of <a, b, c> = df <<a, b>, c> would be <a, b, c> = df{{a}, {a...
  22. N

    Separable Equation - Notation Question w/ Infinitesimals

    Please see below link for the two different styles of solving a separable equation. http://en.wikipedia.org/wiki/Separation_of_variables#Ordinary_differential_equations_.28ODE.29 Which one is more proper? Why? My DE teacher told me that strictly speaking it's wrong to use the first method...
  23. L

    Understand Summation Notation & Clear Confusion

    I am trying to understand summation notation and there are a few inconsistencies in my head that I would like to clear up. Suppose C is an m*n matrix and \vec{x} is a 1*m row vector. Then, \vec{x}C = \sum_{i} x_{i}C_{ij} = \sum_{i} C_{ij}x_{i} = \sum_{i} {C_{ji}}^Tx_{i} = C^T \vec{x}...
  24. R

    Involving Landau's 'big oh' notation

    (don't have an answer yet) We say that two sequences f,g are f=O(g) if-f there is a c>0 such that |f(n)|<c|g(n)| uniformly as n tends to infinity. If g(n)>2, does f=O(g) imply lnf=O(ln(g))?
  25. T

    Quick question about notation for normalisation

    Just a quick question, I'm looking to express the normalisation condition formally mathematically, is this acceptable: 1=\int_R|\psi|^2 \ \mathrm{d}\tau For a particle in 3 dimensional region R.
  26. L

    What is the product rule for finding a derivative in calculus?

    It's been a while since I've done calculus and now a simple derivative is stumping me. This is the issue: d(xf)/dx= ? This is just the product rule, so I think: x(df/dx) + f (dx/dx)= x (df/dx) + f But I'm afraid that I don't even understand my own notation anymore (how...
  27. X

    Quantum Mechanics: Evaluate the following using Ket-Bra notation

    This problem has 4 parts to it (that are unrelated to each other). I did the first two parts without too much trouble but these next two parts have me stumped! Homework Statement Evaluate the following using Ket-Bra notation a.)exp[if(A)]=? Where A is a Hermitian operator whose...
  28. N

    Notation for set of limit points?

    Is there a common notation for the set of limit points of a set?
  29. Q

    Ket Notation - Effects of the Projection Operator

    Ket Notation -- Effects of the Projection Operator Homework Statement From Sakurai's Modern Quantum Mechanics (Revised Edition), it is just deriving equation 1.3.12. Homework Equations \begin{eqnarray*}\langle \alpha |\cdot (\sum_{a'}^N |a'\rangle \langle a'|) \cdot|\alpha \rangle...
  30. S

    Writing an expression in summation notation

    How would I write 1 + n + n(n - 1) + n(n - 1)(n - 2) + ･･･ + n! in sigma notation? If it's possible.
  31. D

    Is Big-O Notation Symmetric for f(n) and g(n)?

    Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...
  32. N

    How Does Michaelis-Menten Kinetics Describe Enzyme-Substrate Interaction Rates?

    Homework Statement For the reaction between enzyme and substrate: E + S <-> ES -> E + P E = enzyme, S = substrate, ES = enzyme-substrate complex, and P = product. Where E + S -> ES rate constant = k_{1} For ES -> E + S = k_{-1} For ES -> E + P = k_{2} Homework Equations My...
  33. M

    Question about notation in physics

    So it says that a particle is going with a velocity of 5i m/s at t = 0 and varying acceleration a = 6√t j. it asked me to find the velocity and position of the particle as a function of time. So i did an integral of the acceleration to get velocity and did the integral of the velocity to get...
  34. F

    Multiple integral notation (or abuse of?)

    So I've seen quite a variety of notations that deviate from what we've learned in our "normal" math courses. In math classes we write a volume integral as: \iiint_W \rho\, d V but somehow once we start doing E&M and QM, professors often just drop the extra integral signs: \int_W \rho\, d V...
  35. J

    Index notation - I never know when to introduce a new symbol?

    This isn't strictly a homework problem but anyway... I'm reading through a QFT textbook that is using index notation, and sometimes a new index symbol will be introduced during some mathematics and it always throws me off. I'll give a simple example, take the Minkowski metric: g^{\mu\nu} =...
  36. N

    What does this notation mean? Linear map A = [A^\mu \nu]_\mu \nu

    It's used in a certain proof that I'm reading. A is a linear map from a vectorspace V onto itself. They say they can rewrite the vector space as \mathcal V = \bigoplus_\mu \mathbb C^{m_\mu} \otimes \mathcal V^\mu and I understand this, but they then claim one can (always, as any linear map)...
  37. L

    Vector Notation Inconsistencies

    My teacher writes 3 dimensions like this: My textbook writes it like this: If my online H/W is not directly written by my teacher and not directly written by my textbook (MasteringPhysics online HW), then when presented with a vector such as: A = (2,1,-4) Should I read...
  38. D

    Scientific notation root powers exponents question

    Homework Statement scientific notation I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power Homework Equations 4 . .... ... ... -9 ... sq rt of 5.2 X 10 4 -9 sq rt of 5.2 X 10 The Attempt at a Solution The answer I...
  39. X

    Angular Momentum Problem in Dirac Notation

    Homework Statement http://img857.imageshack.us/img857/2079/dirac.png Homework Equations H|ψ> = E|ψ> L^{2}|ψ> = l(l+1)\hbar^{2}|ψ> L_{z}|ψ> = m_{l}\hbar|ψ> The Attempt at a Solution I know this problem is very simple since I've seen a very similar problem a while ago but I've completed forgot...
  40. J

    What is the speed of light in miles per hour using dimensional analysis?

    The speed of light is 2.99792458 x 10^8 meters/second. What is this speed in miles per hour? (There are 1609 meters in one mile). I used dimensional analysis to get here:(2.99792458 x 10^8 meters/second) * (1 mile /1609 meters) * (3600 seconds / 1 hour) My question is, what do I do with...
  41. T

    Bra-ket notation Schrodinger Equation

    This is a pretty trivial question, but how is the Schrodinger equation written out in full, time dependency and all in Dirac notation? I'm interested in this from a purely aesthetic point of view but I'm also a bit confused as to what the bras and the kets really are.
  42. S

    Understanding the Einstein Notation for Derivatives in Quantum Field Theory

    I'm trying to get into quantum field theory, I've seen Einstein notation before and I think I'm grasping it fairly well, but I've ran into two things that I just could not figure out and they both involved derivatives, or gradients. My problem is just mathematical, doesn't have to do with the...
  43. A

    Derivative notation uniformality

    Homework Statement I have elected to put this in the "math" section because it is primarily a math question however, please read to problem knowing that it came from an engineering dynamics textbook. Given: (as written) A particle moving along y= x - (x^2 / 400) where x and y are in...
  44. A

    What is the <lz> Expectation Value for Given Wave Function?

    Homework Statement Find <lz> using \Psi, where \Psi=(Y11+cY1-1)/(1+c^2)). Ylm are spherical harmonics, and <lz> is the angular momentum operator in the z direction. Homework Equations <lz> Ylm = hmYlm The Attempt at a Solution The brackets around <lz> are throwing me off...
  45. G

    A Question on Notation about Linear Algebra

    Could I write v = 4i + 3j -2k as v = [ 4 | | 3 | * I_3 | -2 ] were I_3 is the 3x3 identity matrix and the other thing it's multiplied by is a 3x1 matrix of values 4,3,-2 I also had a question about the notation f(x) = x^2 + 3 can be written as f: x |-> x^2 + 3 can I write...
  46. Devil Doc

    Facebook: Check Written to Verizon Using Summation Notation

    Good day all, I received this picture through the facebook network last night. I took it as valid at first sight, but for some reason it bothered me; in other words, my skepticism kicked in. The author mentions and assumes the limit as "n goes to infinity" which is annotated in the...
  47. stevenb

    Notation question about min and max functions

    I have a general question about the notation of min and max functions. I'm wondering if there is an accepted notation, used by mathematicians, for the min and max functions, other than the usual min(x,y) and max(x,y) that I typically see. To give similar examples for what I'm looking for...
  48. E

    Dirac Notation in building Path Integrals

    Alright, so I was wondering if anyone could help me figure out from one step to the next... So we have defined |qt>=exp(iHt/\hbar)|q> and we divide some interval up into pieces of duration τ Then we consider <q_{j+1}t_{j+1}|q_{j}t_{j}> =<q_{j+1}|e-iHτ/\hbar|q_{j}>...
  49. J

    How Do You Prove a Sigma Notation Equality Using Induction?

    Homework Statement 2n-1 Sigma (3i+1) = n(6n-1) i=0 prove for all positive n Homework Equations The Attempt at a Solution It holds true for n=1 5=5 then P: m+1 2m+1 Sigma(3i+1) = (m+1)(6(m+1)-1) or 6m^2 + 11m + 5 i=0 then 2m+1 Sigma(3i+1) = m(6m-1) +...
  50. maverick280857

    Writing Down Single Particle State in P&S Notation

    Hello, In the notation adopted by Peskin and Schroeder, the single particle state is \left|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} {a_{p_1}^{s_1}}^{\dagger}\left|0\right\rangle How does one write down \left\langle r|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} \left\langle...
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