What is Division: Definition and 486 Discussions

A division is a large military unit or formation, usually consisting of between 6,000 and 25,000 soldiers.
In most armies, a division is composed of several regiments or brigades; in turn, several divisions typically make up a corps. Historically, the division has been the default combined arms unit capable of independent operations. Smaller combined arms units, such as the American regimental combat team (RCT) during World War II, were used when conditions favored them. In recent times, modern Western militaries have begun adopting the smaller brigade combat team (similar to the RCT) as the default combined arms unit, with the division they belong to being less important.
While the focus of this article is on army divisions, in naval usage, "division" has a completely different meaning, referring to either an administrative/functional sub-unit of a department (e.g., fire control division of the weapons department) aboard naval and coast guard ships, shore commands, and in naval aviation units (including navy, marine corps, and coast guard aviation), to a sub-unit of several ships within a flotilla or squadron, or to two or three sections of aircraft operating under a designated division leader. Some languages, like Russian, Serbian, Croatian and Polish, also use a similar word, divizion/divizijun/dywizjon, for a battalion-size artillery or cavalry unit.

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  1. P

    The worst case for trial division factorisation of n?

    What's the worst case for the factorisation of n using trial division? Worst case in terms of arithmetic operations that is. Many places tell me that it's n=pq with p and q prime and close to each other (and hence close to root(n) ), but I can't prove it. Help would be appreciated.
  2. S

    Upper Division Classical Mechanics for Dummies?

    Well, I took a junior level classical mechanics course. We used Marion (the 4th edition). I guess I’m retarded or something because it just didn’t make a whole lot of sense to me… My professor didn’t help much either (most students “got him” but he just didn’t mesh with my learning style)…...
  3. H

    Upper Division E&M: Can I Handle It?

    So I kinda got painted into a corner this upcoming quarter. I am trying to do a Math/Physics double major and with all the req's for both majors, I pretty much got no time to be taking easy quarters (unless I want to waste time going to school an extra year. I am 31 y/o, I still want to do grad...
  4. P

    Division of complex power series

    Homework Statement Find tan(z) up to the z^7 term, where tan(z) = sin(z)/cos(z) Homework Equations sin(z) = z - z^3/3! + z^5/5! - z^7/7! + ... cos(z) = 1 - z^2/2! + z^4/4! - z^6/6! + ... The Attempt at a Solution Hi, Seeing as sin and cos have the same power series as for when...
  5. M

    Simplification of polynomial division

    Homework Statement For all x>2, \frac{2x²+2x-12}{x-2} simplifies to: 2(x - 2), x + 3, 2(x + 3)(x - 2), x - 2 or 2(x + 3). (Problem taken from http://www.analyzemath.com/practice_tests/act/act_sample_1.html" , question five). Homework Equations None, AFAIK. The Attempt at a...
  6. A

    How Do You Solve Complex Polynomial Long Division Problems?

    Divide the polynomials by using long division. (-9x^6+7x^4-2x^3+5)/(3x^4-2x+1) When I attempted it I started by pulling using 3x^2 . multiplied that by the (3x^4-2x+1) and from there I had to use a fraction of 7/3 or something and then couldn't divide into x cubed. If anyone can...
  7. P

    "Cell Division: Is Mitosis the Same?

    Homework Statement Is mitosis the same as cell division? Homework Equations The Attempt at a Solution I want to say yes because mitosis is a type of cell division and when you speak of mitosis, it's usually referred to cell division. However, mitosis doesn't include all of cell...
  8. A

    Polynomial, Division, Remainder

    Homework Statement When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2. Determine the remainder when the polynomial is divided by (x+2)(x-1). EDIT: Took out my attempts lol, there were way off. This was a "Math...
  9. P

    Division algorithm and unique Gaussian integers

    Homework Statement Theorem Let \alpha\neq0 and \beta be Gaussian integers. Then there are Gaussian integers \tau and \rho such that \beta=\tau\alpha+\rho and N\left(\rho\right)<N\left(\alpha\right) Problem Show that the Guassian integers \tau and \rho in the Theorem are unique if and only...
  10. H

    Polynomial Division: Simplifying 3rd Roots in Denominator

    3rd roots in denominator Homework Statement \frac{ \sqrt[3]{25} + \sqrt[3]{5x} + \sqrt[3]{x^2} }{ \sqrt[3]{x} - \sqrt[3]{5} } Rewrite the expression with no roots in the denominator and it being simplified as far as possible.Homework Equations The Attempt at a Solution I'm.. stumped...
  11. C

    Long division where the quotient is larger than the dividend

    The question is "without a calculator, long divide 425/836. Round to the nearest hundredth. Estimate your answer before starting." My attemp at a solution: Well, my estimate would be approximately one half, since 400 divided by 800 would be 0.5; however, I'm not sure how to long divide a...
  12. K

    How do I correctly solve this polynomial long division problem?

    I am trying to solve: \frac{x^6+6x^3-2x^5-7x^2-4x+6}{x^4-3x^2+2} Using the polynomial long division algorithm. I order first the terms of the divident, and leave one blank space between -2x^5 and +6x^3 My problem is, I first put x^2 to the quotient, so I get x^4 * x^2 = x^6, but then I...
  13. D

    How to Divide Complex Numbers in a Balanced Load Star Connected Circuit

    When finding the current in a 4+j3 balanced load star connected circuit. with 400V line voltage at 50Hz. Do you find the current by dividing the phase voltage approx. 230V by 4+j3 ohms? and if so. how do you divide normal numbers with complex numbers? your help is appreciated.
  14. B

    Can Division by Zero Be Defined in a More General Number Group?

    I assume everyone who saw this thread first rolled their eyes. Sorry for that. My question is an innocent one, as I am completely uneducated in number theory. My understanding is that numbers are grouped in a sort of Russian doll fashion, with each successive group encompassing all previous...
  15. S

    Optimal division of a matrix for processing

    I apologies if this is in the wrong place! I'm a Computer science person with a keen interest in maths and occasionally the two topics cross paths. I am working on an matrix manipulation package in Java/C but seriously require some help with the maths, I am witting into it, parallelization at...
  16. M

    Very Interesting Question on Division of Polynomials

    Very Interesting Question on Division of Polynomials! [b]1. Question: 'When a polynomial f(x)= x^4 - 6x^3 + 16x^2 - 25x + 10 is divided by another polynomiall g(x)= x^2 - 2x + k, the remainder is x+a. Find the value of a k and a'. Homework Equations [b]3. I tried solving it by...
  17. Z

    Proving Prime Divisibility for {p \choose k}

    Homework Statement the idea is to prove wether a prime 'p' divides the quantities {p \choose k} for k=01,2,3,...,p-1 Homework Equations The Attempt at a Solution i have tried by inspection for small primes 3,5,7,11,13,17,... but can not guess a simple solution , the idea...
  18. S

    B+ in upper division physics class

    Hello, I am a senior now. I have a B+ in one of my upper division physics classes. How can I still get into a good graduate program ? Its freaking me out.
  19. F

    MATLAB Matlab, for loop simple division problem

    I put down a script like this for u=(10:10:20)' i=(1:size(u,1))' X=zeros(size(u,1),1) X(i,1)=100/u(i,1) end I expect to get a result like X= 10 5 but it came out like X= 0 5 It seems it does work if it contain / in the equation. Please help!
  20. X

    Math Questions: Multiplication, Division & Partial Fractions

    Homework Statement Actually i want to ask something actually very easy... i just don't know the meaning of some words in different questions... firstly... multiplication of A and B means A*B right? how about multiplication of A by B means A*B or A/B?? secondly... division of A by B means...
  21. H

    What is the point of synthetic division?

    So I was tutoring a friend who is in college algebra and we were working threw synthetic division of polynomials, and I realized I have never used that technique after pre-calc. I think its easier and there is less chance of sign mistakes using good old long division for polynomials why are we...
  22. Y

    Courses Optimal order to persue undergraduate upper division physics coursework

    I've decided to go back to school to study physics. I was a physics minor the last time I was in undergrad, and have an undergraduate math degree an undergraduate computer engineering degree as well as a graduate degree in electrical engineering. So, after meeting with the dean of...
  23. C

    Engineering How can i calculate the voltage division in a circuit like this?

    http://i5.photobucket.com/albums/y160/bornstubborn101/circuit3.jpg This is the circuit. Basically i need to calculate the two resistors that would make up the potentiometer at VR1 to give a voltage of 3V. I was going to use VR1 = R2/(R1+R2)*Vs The make: R1= VR1/Vs*(R1+R2)...
  24. D

    General query: Parallel, series, voltage division, etc

    So now that I'm taking Electronics 1, the course right after Linear Circuits (DC/AC), the whole parallel/series schematic thing is kicking my ***. Pic 1 (idealdiode) is an example of just a tricky way of drawing something in parallel: namely, a voltage drop. With the (ideal) diode off = open...
  25. C

    Binomial Expansion long division

    Homework Statement Using the identity (1+2x) (1-2x+4x^2) = 1+8x^3 to expand (1-2x+4x^2)^(-0.5) in ascending powers of x as far as the term in x^3. (The answer is 1+x-x^2/2-7x^3/2+...) Homework Equations (1+2x)^(0.5) = 1+x-x^2/2+x^3/2+... (1+8x^3)^(-0.5) = 1-4x^3+... The Attempt at...
  26. W

    Long Division isn't working for me

    The problem is that I am weak at long division and need it for ratio and rate.Homework Statement Homework Equations Like big questions such as 236 divided by 6.(I know it doesn't go in by using a calculator but if it has a point. The Attempt at a Solution I just can't do it and...
  27. K

    Cell division during pregnancy

    A baby is born weighing 4kg. It starts its life from a single cell, which then divides into 2 cells, each of those two divide then again, and so on. Use information from the problem above above to calculate how many diffusion process happen in the 9 months of pregnancy. Is this a realistic...
  28. C

    Need Suggestions For An Experiment - Upper Division Undergraduate

    Hello, During the spring semester of school that is just beginning I will be a junior in physics at the University of Minnesota. I'm taking a physics class called Methods of Experimental Physics II in which for the majority of the semester groups of two will be working on an approved...
  29. S

    Synthetic Division: Divide Polynomials by Monomials

    so synthetic division can be used to divide polynomials by monomials. is there a to divide by ax-b as opposed to x-b? ax^2-b? is there a general rule? thanks. or does one have to revert to polynomial long division.
  30. S

    Mental math: Division of remainders

    I'm working on moving away from long time slavery to the calculator Most forms of division and multiplication is going well now (long division and in some instances lattice multiplication) One thing I DON'T get though (and can't find any guides for) is dividing remainders. For example...
  31. MathematicalPhysicist

    Rule of Division by 23: What is it?

    What is the rule of division by 23? Thanks in advance.
  32. T

    Division of Vectors: Legit Operations Explained

    Why aren't there any legit operation for division of two vectors (any kind of vectors)?
  33. S

    How much of an impact does your lower division grades have on jobs?

    I'm a second semester sophomore right now majoring in Computer Engineering and things aren't looking bright for me. First semester, freshmen year, I got a 3.3 with one dropped class, chemistry. Second semester, freshmen year, I got a 2.8 with one dropped class, Calc 2. Both dropped...
  34. M

    Can I Cancel Cubed Radicals with Division?

    Homework Statement -60/120 ^1/3 Homework Equations I've gone through my book, and I'm supposed to find a number that when multiplied by a perfect cube I can bring it out and then cancel with the division. Try as I might with my calculator, I can't find one. Am I doing this wrong?The Attempt...
  35. A

    Help with Long division of functions

    Can anyone explain the correct way to do that type of long division with functions? If you don't get what i mean an example would be like x4+3x2+1 / x2-2x+3
  36. A

    Division, Primes, Divisors & Powers: Solve Them All!

    1) Find the remainder of the division of 15! with 17 2) If (n^2)+2 prime show that 3 divides n 3)If p the smallest divisor for n show that there exist integers a and b such that an+b(p-1)=1 4) For every n>1 show that n does not divide (2^n)-1 Any help?
  37. S

    Synthetic Division: Proving It Works

    is there a way to prove it? if so what is it.
  38. M

    What is the Correct Quotient and Remainder When Dividing this Polynomial?

    Here is the problem I am working on: Find the quotient and remainder when P(x) = 7 x^6 - 9 x^5 + 8 x^4 + 9 x^3 + 4 x^2 - 6 x is divided by (x + 5). My answer that I came up with is this. Q = 7x^5 - 44x^4 + 228x^3 - 1131x^2 + 5659x R = -28301x I have done this using Long and Synthetic...
  39. T

    Quotienting is a generalisation of division

    Quotients in abstract algebra is a generalisation of division. While the latter works only for single elements, the former is for dividing sets. Amazing stuff!
  40. G

    Synthetic division (small part of a bigger problem)

    (x^3-2)/(x^2+11x+24) can't seem to simplify this I get x+(-11x^2-24x-2)/(x^2+11x+24) that doesn't seem right.
  41. V

    Converting from Cartesian to Cylindrical coords - but division by zero

    Converting from Cartesian to Cylindrical coords - but division by zero! Homework Statement Let's say I want to convert the point P(0, -4, 3) to cylindrical. To convert from Cartesian to Cylindrical coordinates, one must use the formulas listed below. Homework Equations...
  42. K

    Long division with zero to nine substitution

    Substitute the letters by a different digit from 0 to 9 to satisfy this cryptarithmic long division problem. ....N K T ...------------------- F A R |...F R M N K B ...A K K N ...--------------------- ..... A B I K ...AM O K ...--------------- .....R T I B .....R A K T...
  43. P

    Proof of eAe as Division Ring when Ae is a Minimal Left Ideal

    Let A be semiprime ring and e a non-zero idempotent. If Ae is a minimal left ideal then eAe is a division ring. Proof: Suppose that Ae is a minimal left ideal and that exe is different from 0 for x in A. Then $Aexe \subset Ae$ since Ae is an ideal and since Ae is minimal hence...
  44. G

    Using division of power series to find the first 3 nonzero terms

    1. Use multiplication or division of power series to find the first 3 nonzero terms in the Maclaurin series of the function x/sinx. 2. the maclaurin series for sinx is \sum(-1)^{n}x^{2n+1}/(2n+1)! 3. I've tried to divide x/sinx substituting sinx for the maclaurin series but I seem...
  45. H

    Solve Polynomial Division: Find K Given Remainder of 3

    Homework Statement The remainder is 3 when 4x^2 + 9x + k is divided by x-1 Im suppose to find the K. I am just confused because this question they give me the remainder..so what am i suppose to do with it?
  46. C

    Number Theory Division

    Homework Statement If a, b < c, and d are positive integers, prove the following inferences. 1. a|b \wedge c|d \rightarrow ac|bd 2. a|b <=> ac|bc Homework Equations The Attempt at a Solution 1. a|b = x, then b = ax c|d = y, then d = cy bd = axcy thus ac|bd =...
  47. S

    Voltage Division: Troubleshooting Issues

    CHECK IMAGE, I guess I do not understand voltage division properly can someone see why this doesn't work. Why is the first one giving the wrong answer..? thanks
  48. M

    MATLAB Division of Matrices in MatLab: Explained

    As far as I know, matrices cannot be divided, you have to multiply one matrix by the inverse of the other...I believe. However, I am converting MatLab code into ANSI C and MatLab apparently divides two matrices. An example is the following... >>A=[1.5708 1.5708]; B=[0.4937 0.7652]; A/B...
  49. D

    Proving a Division Algorithm for Real Numbers?

    How might I prove a Division Algorithm for the Real numbers? That is to say, if x, \alpha \in \mathbb{R}, then x=k \alpha + \delta for some k \in \mathbb{Z}, \delta \in \mathbb{R} with 0 \leq \delta < \alpha where k, \delta are unique.
  50. S

    Converge or diverge? (partial frac. long division)

    Determine whether the sequence converges or diverges. If it converges, find the limit. An=7+4n^2/n+2n^2 I know you have to compare it to the integral of the same equation, so I do this and the only means of integration I believe to be is by partial fractions, since degree of top equals degree...
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