Notation Definition and 1000 Threads

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. B

    Bra & Ket notation in quantum physics

    Homework Statement If |A> = x |B> + y |C> where |B> and |C> are orthonormal, then what happens when <A|A> ?The Attempt at a Solution Would <A| = x* <B| + y* <C|? I'm not really sure where to go from there
  2. fluidistic

    I don't understand the notation (tensor?, not even sure)

    Homework Statement In order to show that if ##(\vec E (\vec x, t), \vec H (\vec x, t))## is a solution to Maxwell's equation then ##(\vec E (\vec x -\vec L, t), \vec H (\vec x-\vec L, t))## is also a solution, my professor used a proof and a step I do not understand. Let ##\vec x' =\vec...
  3. L

    Understanding Heisenberg Hamiltonian Notation for 4-Site Chain

    Notation for Heisenberg Hamiltonian ## H_{exch}=-\sum_{i<j}2J_{i,j}\vec{S}_i \cdot \vec{S}_j ## where the sumation extends over all spins pair of the crystal lattice. Suppose we have chain with four sites and periodic boundary condition ## H_{exch}=-J_{1,2}\vec{S}_1 \cdot...
  4. Math Amateur

    MHB Direct Products and Sums of Modules - Notation - 2nd Post

    I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation of Section 1-2 Direct Products and Sums (pages 5-6) - see attachment). In section 1-2.1 Dauns writes: ================================================== ====== "1-2.1 For any arbitrary...
  5. Math Amateur

    MHB Direct Products and Sums of Modules - Notation

    I am reading John Dauns book "Modules and Rings". I am having problems understanding the notation in section 1-2 (see attachment) My issue is understanding the notation on Section 1-2, subsection 1-2.1 (see attachment). Dauns is dealing with the product \Pi \{ M_i | i \in I \} \equiv \Pi M_i...
  6. D

    MHB Expressing a number in scientific notation and factoring a cubic

    Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 5) Express .00024 in Sci Notation My answer: 2.4 x 10^-4 6) Factor the following completely: 3x^3 - 18x^2 + 24x My Answer: (3x)(x - 4)(x - 2)
  7. P

    Ambiguity with partial derivative notation

    Suppose I have some function f that depends on three variables, namely x, y, and t; i.e., f=f(x,y,t). Now suppose that y depends on x, i.e., y=y(x). Taking this into account, we see that f is really just a function of two independent variables, x and t. So my question is this: if I write down...
  8. M

    Very specific question about index notation

    I am reading through this text http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf and am having a bit of trouble with one of the arguments that is put in index notation. Specifically, equation (3.3). I was wondering if anyone could have a look at it and clear up a...
  9. P

    Maxwell Equations Lorentz Invariance - Notation

    [This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...
  10. B

    MHB Sets and basic notation.

    I have two questions explain why any subset of a finite set is finite. (prove) and why is empty set is considered to be a subset of any set? I'm confused, because let's say set A is a subset of set B it means that every element of A is an element of B. in the case of empty set being a...
  11. B

    MHB Implied accuracy in scientific notation

    i just want to understand what i read in my algebra book. here what it says: a measurement of 83200 ft. converted to (8.32)x10^4 ft. is now accurate to the nearest hundred feet. if we write (8.320)x10^4 the measurement is now accurate to the nearest ten feet. i want to know why it is nearest...
  12. C

    Is It Correct to Use f and f(x) Interchangeably in Mathematics?

    I have seen over and over statements like: \begin{aligned} &f(x)~\text{is a function of}\dots \\ &\text{Let}~f(x)~\text{be a function that}\dots. \end{aligned} This is probably a dumb question, but am I justified in feeling annoyed at these statements? The annoyance stems from my...
  13. C

    Function notation for the derivative operator

    If we have the function f : x \mapsto f(x) = 3x^2, I am used to Lagrange's prime notation for the derivative: f' : x \mapsto f'(x) = 6x. I'm fond of this notation. But it has been mostly abandoned in my engineering courses in favor of Leibniz's notation, using differential operators such...
  14. T

    Scientific notation, and an exponent question

    I'm curious but usually negative exponents mean you're going to put those numbers on the bottom (sorry forgot the exact term it is much earlier than I normally get up) (example 6^-1 =1/6 so why is scientific notation different? Or is it? (Ex: 5x10^-3=.005)
  15. V

    What is the Meaning of ##:=## in Mathematics?

    My calc professor always used to use the symbol ##:=## when defining a quantity. For example, say we want to evaluate the integral ## \int x \sqrt{1+x^2} dx ##. So we might say, "Let ##u:=1+x^2 ##" and then continue to easily evaluate the integral. I haven't seen this anywhere else and I'm...
  16. S

    Notation for partial derivatives using indexes

    Is there a standard notation for partial derivatives that uses indexes instead of letters to denote ideas such as the 3 rd partial derivative with respect to the the 2nd argument of a function? As soon as a symbol gets superscripts and subscripts like \partial_{2,1}^{3,1} \ f the spectre of...
  17. W

    Some help with set and vector notation, please

    Preface note: the R and Z in the {}s below should be double-struck, but I couldn't figure out how to do that here. I tried the usual shortcuts to no avail. I am writing pseudo-code for a publication, and am asked to use rigorous math notation, which is new to me. I am trying to express the...
  18. C

    Linear subspace constraints and notation.

    Homework Statement The original printed problems can be found as attachments. The questions ask if a set S is a subset Rn. Give Reasons Question 1.) S is the set of all vectors [x1,x2] such that x12 + x22 < 36Question 2.) S is the set of all vectors [x1,x2,x3] such that: x2= 2x1 x3 = 3x1...
  19. P

    Differentiation: the prime notation

    Hi, I have been using, for the most part, the prime notation when I want to indicate differentiation. As off recently, I have gained more insight into Leibniz's notation. This triggered the following question: how does the prime notation indicate what we are differentiating with respect to? I...
  20. E

    Help with some unfamiliar set notation

    I am reading http://walrandpc.eecs.berkeley.edu/126notes.pdf on the theory of random processes. The authors are making use of some unfamiliar notation early on, and I don't want to move on without understanding their formalisms. First one is the := operator and a union operator that looks like...
  21. M

    Help in calculating the square of a number in sexagesimal notation?

    How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it...
  22. C

    Notation for time in a relativistic graph

    I was just curious as a possible confusion that might occur when graphing a v vs t Graph. Because velocity is a function of time, but time is also dependant on velocity, so how would we denote this on a graph? Hope i got my point across, thanks!
  23. S

    Einstein Notation for Stored Energy Function

    Dear all, I encounter the following formula (for stain energy function) a lot in physics literature: W(\epsilon_{kl}) = \int_0^{\epsilon_{kl}} \sigma_{ij} \textrm{d}\epsilon_{ij} where all indices ranges from 1 to 3, both \epsilon and \sigma are 3x3 matrices. My question is what...
  24. AakashPandita

    Confusion regarding notation of instantaneous velocity wrt something.

    I know that v(t)=dx/dt Then what is v(x) and how? Is it also dx/dt or something else?
  25. L

    A question on notation of derivatives

    I was doing a proof on why the derivative of an even function is odd and vice versa. Now, the way I did the problem was by using the chain rule to rewrite the derivative of f(-x), and the proof worked out perfectly fine. But I had a thought that I can't quite wrap my around, and I think it's...
  26. J

    Sigma Notation and Product Notation

    Homework Statement Notice that ln [∏(k=1)^n a^k] = Ʃ_(k=1)^n * ln (a_k) I couldn't get the LaTeX right on this ^ But k=1 is below the product sign, and n is above. And (a^k) is the formula. From this, as well as some calculus, calculate that: lim as n->∞ ∏_(k=1)^n e^\frac{k^2}{n^3} For...
  27. M

    How Can Division Work with Differential Operators?

    I am finding it unintuitive to follow a calculation in a certain notation I am not too familair with. To write down the equation $$ z(t) = - y(t) + \tau \frac{\partial y}{\partial t} $$ the following notation is employed $$ z(t) = -(1-\tau \frac{\partial }{\partial t}) y $$ So far so gud...
  28. Markus Hanke

    Is There a Difference Between Covariant and Contravariant Tensor Notations?

    I am just wondering, is there a difference in meaning/definition between the indices of a tensor being right on top of each other A_{\mu }^{\nu } and being "spaced" as in A{^{\nu }}_{\mu } I seem to remember that I once read that there is indeed a difference, but I can't remember what it...
  29. Lebombo

    Can this be written in sigma notation: a + ar + ar^2 + + ar^n-1?

    Homework Statement a_{1}r^{1} + a_{1}r^{2} + a_{1}r^{3} +... + a_{1}r^{n-3} + a_{1}r^{n-2} + a_{1}r^{n-1} = \sum_{n=1}^{?} a_{1}r^{n-1} What value would replace the "?" 2. The attempt at a solution EDIT: I edited this post after receiving your reply Cepheid. My gut would say...
  30. H

    Notation for Lists in Math: Symbol, LaTeX

    Greetings, Is there a commonly accepted notation for a list in mathematics, of an identical form to Ʃ for a summation? If so, what is the name of the symbol (that would be used in place of L, below), and how would it be typed in LaTeX? For instance, it might look something like...
  31. L

    Confusion with Einstein tensor notation

    Homework Statement I'm confused about writing down the equation: \Lambda \eta \Lambda^{-1} = \eta in the Einstein convention. Homework Equations The answer is: \eta_{\mu\nu}\Lambda^{\mu}{}_{\rho}\Lambda^{\nu}{}_{\sigma} = \eta_{\rho\sigma} However it's strange because there seems...
  32. ikihi

    Error in my textbook? scientific notation conversion

    Homework Statement The question is: The Earth formed 4.57 x 10^9 years ago. What is this time in seconds? The answer the textbook is giving is 1.44x10^17 seconds. The answer I keep getting is 1.44x10^15 seconds. Is the textbook wrong or am i wrong?
  33. Lebombo

    Understanding Sequence of Partial Sum notation

    {Edit: as of 3:55 eastern time, made corrections to tex and itex mistakes}Is this all kosher in terms of demonstrating accuracy and comprehension of the notation {a_{1} + a_{2}...} = \lim_{n\rightarrow ∞ } \sum_{n=1}^{n} a_{n} So the lower case represents sequences and upper case represents...
  34. H

    P Orbital Notation: Common Conventions

    Hi, Reading http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1 I've run into a notational question of atomic p orbitals. The authors use symbols like p_\sigma and p_\pi. From their fig. 3 (attached), they do look like p_x and p_z orbitals, respectively, rather than anything close to σ or π bonds...
  35. tomwilliam2

    Expectation values of Kin energy in Bra-Ket notation

    Homework Statement Confirm explicitly that ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x \Psi \rangle## cannot be negative. Homework Equations ##-i\hbar \frac{\partial}{\partial x} = \hat{p}_x## The Attempt at a Solution i seem to get: ##\frac{1}{2m}\langle \hat{p}_x \Psi | \hat{p}_x...
  36. MarkFL

    MHB Serina's questions at Yahoo Answers regarding sigma notation

    Here are the questions: Here is a link to the questions: How do you write the summation notation for: 4 - 24 + 144 - 864 + ... ? - Yahoo! Answers I have posted a link there so the OP can find my response.
  37. reenmachine

    How Do You Express a Sequence Using Set Builder Notation?

    Homework Statement Build a notation for the set: ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}## Homework Equations ##2+5(0) = 2## ##2+5(1) = 7## ##2+5(-1) = -3## etc... The Attempt at a Solution ##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}## Take note that you could replace ##2## by any...
  38. B

    Indices Notation: Equivalent Notation to Sigma & Pi

    Is there an equivalent notation to Capital Pi notation (multiplier) and Sigma notation (summer) for raising to the power? e.g. x1^x2^x3^x4...^xn=Notation(i=1 to i=n)(xi) Where "Notation" represents the symbol in question (analogous to Sigma for sums, Capital Pi for multiplication)?
  39. reenmachine

    Set Theory , building a set notation

    Homework Statement Build a set notation for $$\bigcup_{i \in N}R × [i , i + 1]$$ The Attempt at a Solution ##\{(x,y) \in R : x \in R \ \ \exists z \in N \ \ z ≤ y ≤ (z+1)\}## Last time I tried one of these kind of sets I struggled quite a bit , so I'm interested in knowing how much...
  40. reenmachine

    Building a set notation part II

    Homework Statement As an exercise , the book I'm reading ask me to build a set notation for the following set: ##\{... \ , \frac{1}{27} \ , \frac{1}{9} \ , \frac{1}{3} \ , 1 \ , 3 \ , 9 \ , 27 , \ ...\}## The Attempt at a Solution After playing with the numbers a couple of minutes , I came...
  41. reenmachine

    What is the set notation for a sequence with a common difference of 3/4?

    Homework Statement The book I'm reading ask me to build a set notation for the following set: ##\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}##. The Attempt at a Solution I attempted to build a set notation and came with the result: ##\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}## My...
  42. R

    Bra-ket notation and qubit issue.

    I am having trouble understanding the following: Uf: |x>|y> → |x>|y \oplusf(x)> \oplus being a mod 2 operation (nand)? I suppose I don't understand how to read the "ket" states so well. As far as I understand we have that since x and y can be 0,1 only if |x=1>|y=1> then if f(x) = 1 then...
  43. G

    Simple notation question about subsequences

    Hey guys, I was just reading notes on metric spaces and was wondering if the notation of subsequences was such that anm is always further down the original sequence than an? For example suppose you have a strictly decreasing sequnce does the notation imply that anm<an
  44. B

    Need help with writing set notation.

    I need help with some set notation. I am an engineering major and don't know the proper notation. I am trying to write two statements. I have two sets, x_1 = {1,2,3}, and x_2 = {4,5,6}. Verbal Statements: y_1 was measured for all values of x_1 and x_2 y_2 was measured, for all values of...
  45. A

    Circuit Analysis - Laplace notation

    Homework Statement The circuit below uses ideal components and disguises itself as a second order system when in fact it is really two first order systems. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the peak output voltage V_{0max}, and the time taken for...
  46. O

    Notation Confusion in Linear Transformations

    I'm just having trouble understanding some of the notations given, when attempting questions such as the following: {f\inF(ℝ,ℝ): f(3)=5}. Is it just saying that, the function 'f' spans all real values?
  47. M

    How Can I Fix My Indicial Notation Practice?

    Hi there, I am trying to get some practice with indicial notation. I am failing as follows, to start with. Given a vectorial function $$v_j = a_j e^{i(k_k x_k - \omega t)}$$ of spatial variables $$x_i$$ and time, given a tensor $$K_{ijkl}$$ I want to compute the quantity $$K_{2jkl}...
  48. M

    Einstein summation notation for magnetic dipole field

    I can do this derivation the old fashioned way, but am having trouble doing it with einstein summation notation. Since \vec{B}=\nabla \times \vec{a} \vec{B}=\mu_{0}/4\pi (\nabla \times (m \times r)r^{-3})) 4\pi \vec{B}/\mu_{0}=\epsilon_{ijk} \nabla_{j}(\epsilon_{klm} m_{l} r_{m} r^{-3})...
  49. X

    Writing impulse in vector notation

    Homework Statement A baseball strikes a bat. It's moving at 40m/s to the left horizontally. When it hits the bat it leaves at 60m/s with an angle of 30 degrees to the horizontal. The mass of the ball is 0.25kg. Homework Equations P(momentum)=mv Pf-Pi=ΔP ΔP=J(impulse) The Attempt at a Solution...
  50. C

    Converting scientific notation to standard digit numbers

    Homework Statement I'm trying to convert something like 1.25^-03 into it's standard number composed of standard decimals using a calculator (0.0125) - if you know what I mean. Thanks.
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