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21. I am pursuing mathematics through distance education and I find that it takes me a long time to understand the concepts (e.g. sigma fields, …

In mathematics, inequalities are a set of five symbols used to demonstrate instances where one value is not the same as another value. The five symbols are described as “not equal ... Many posts at Mathematics Stack Exchange include mathematical notation, written using $\mathrm\LaTeX$ commands surrounded by dollar signs. If you see dollar signs with what appears to be gibberish between them, it just means that MathJax, the math rendering we use, isn't working properly for you. Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus …Accessing an array element is O(1) like in a regular array. Just to point out a small detail - initialize the array A (of length 2n^3) so A [i] = 0 in constant time. Now: for all pairs 0 < a < b < n do: A [a^3 + b^3] = A [a^3 + b^3] + 1 and if A [a^3 + b^3] == 2 then print a^3 + b^3.I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. (119.91227722167969, 122.Does watching Outer Banks on Netflix make you want to book a trip to the place the popular show was inspired by? If you're looking to live out your "Pogue Life" dreams, here are th...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange

51. StackOverflow has quite the reputation as a toxic site, mostly for being unwelcoming to new users. But what's MathSE's general reputation? For users …1 answer. 10 views. Minimum k k for which every positive integer of the interval (kn, (k + 1)n) ( k n, ( k + 1) n) is composite. number-theory. prime-numbers. prime …She holds a master's degree in science journalism from Columbia University's Graduate School of Journalism and is also a graduate of New York University's Tisch School of the Arts. More by Carin ...Q&A for those involved in the field of teaching mathematics. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeA very beautiful introduction to algebraic geometry is the book "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra" in the Springer undergraduate texts in mathematics series. (It only requires basic abstract algebra as a prerequisite). The second "half" of Munkres' 2000 Topology ...

Mathematics Stack Exchange. Explore our questions. Ask Question. Interesting 41 Bountied Hot Week Month. 0 votes. 0 answers. 3 views. Show that the function is …An addition to Martin Scharrer's answer. \textcolor has a side effect in math, that the contents is put in curly braces (see definition of \@textcolor).The color implementation of package color is based on groups (the color is restored at the end of the group automatically), but curly braces also make a subformula in math. This affects the …The algebraic degree of a particular sum of algebraic numbers. Let p p be a prime number and let m m be a positive integer. We know that β:=p−1/m β := p − 1 / m is an m m -degree algebraic number (in fact, its minimal polynomial is pXm − 1 p X m − 1 ). I would like to prove that ... number-theory.She holds a master's degree in science journalism from Columbia University's Graduate School of Journalism and is also a graduate of New York University's Tisch School of the Arts. More by Carin ... Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus reference-request algebra textbooks geometry proofs primary-education more tags. Active Hot Week Month. 0 votes. 0 answers. 7 views. I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. (119.91227722167969, 122.

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The short answer is: 'This is the definition, live with it!' While that may sound haughty, it emphasizes the principle that in math we occasionally need to define a precise meaning to a word, and natural languages may fall short in providing a suitable one, so it is up to us the users of math to absorb a possibly new meaning.Apply Stokes theorem on a curve which is intersection of a sphere and plane. Apply Stokes theorem to prove that ∫cydx + zdy + xdz = − 2√2πa2 Where C is the curve given by x2 + y2 + z2 − 2ax − 2ay = 0, x + y = 2a ; and begins at the point (2a,0,0) and it goes first below ... vector-analysis. surface-integrals.Equality case in the Frobenius rank inequality. 3. Rank of the product of 3 matrices. 8. The rank and eigenvalues of the operator T(M) = AM − MA on the space of matrices. 2. On the rank inequality rank(A) + rank(A3) ≥ 2rank(A2) 2. Matrix rank inequality.Mar 28, 2014 · Math Stack Exchange's default style uses a light-colored page background, so avoid using light colors for text. Stick to darker colors like maroon, green, blue, and purple, and remember also that 7–10% of men are color-blind and have difficulty distinguishing red and green. 3 Answers. Sorted by: 376. The two sites are meant for very different audiences, and have very different types of questions. From the MathOverflow … Paper published in the February 2013 issue of Mathematics Magazine. December 2011: TEX T E X support for chat is introduced by robjohn. January 2012: Math.SE becomes the first SE 2.0 site with a 100K user ( Arturo Magidin ), excluding Stack Overflow. August 2012: 100000th 100000 t h answer posted.

51. StackOverflow has quite the reputation as a toxic site, mostly for being unwelcoming to new users. But what's MathSE's general reputation? For users …Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeApr 13, 2017 · MathOverflow is for research level math questions. Math.stackexchange.com is not restricted to any particular level of difficulty (though one expects that it won't get much in the way of research level questions since those are at MO). There was a lot of feeling on SO and MO that it'd be good if there was a site for more elementary math questions. Total variation distance is a measure for comparing two probability distributions (assuming that these are unit vectors in a finite space- where basis corresponds to the sample space ($\omega$)).I know a distance measure need to obey triangle inequality and it should satisfy that orthogonal vectors have maximum distance and the same …In page 92, of Serre's book "Lie algebras and Lie groups" Springer LNM 1500, there is a criterion for X/R X / R to be a manifold, which is named after Godement and says the following. The quotient X/R X / R is a manifold if and only if. 1, R R is a sub manifold of X × X X × X (which means R → X × X R → X × X is a closed embedding), and.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeThe two equations simplify to x2 + y2 = r21 and (x − d)2 + y2 = r22 Use the first to find y2 and substitute in the second. (x − d)2 + r21 − x2 = r22 expand and simplify − 2xd + d2 + r21 = r22 so the points of intersections are (x, y), (x, − y) with x = r21 − r22 + d2 2d and from Pythagorus y = √r21 − x2. This part came from ... How does it work? Meta Mathematics Stack Exchange is the part of the site where users discuss the workings and policies of Mathematics Stack Exchange rather than discussing math itself. It is separated from the main Q&A to reduce noise there while providing a legitimate space for people to ask how and why this site works the way it does. Meta ... I received this question from my mathematics professor as a leisure-time logic quiz, and although I thought I answered it right, he denied. Can someone explain the reasoning behind the correct solution? Which answer in this list is the correct answer to this question? All of the below. None of the below. All of the above. One of the above.She holds a master's degree in science journalism from Columbia University's Graduate School of Journalism and is also a graduate of New York University's Tisch School of the Arts. More by Carin ...1. This might be useful to notice both on main and on meta: You can use several tabs: such as Newest, Active, Bountied, Unanswered, Frequent. Depending on the choice of tab, you're shown different question. If you choose newest, the name of the user which is displayed is the poster of the question.

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The short answer is: 'This is the definition, live with it!' While that may sound haughty, it emphasizes the principle that in math we occasionally need to define a precise meaning to a word, and natural languages may fall short in providing a suitable one, so it is up to us the users of math to absorb a possibly new meaning.Math Stack Exchange's default style uses a light-colored page background, so avoid using light colors for text. Stick to darker colors like maroon, green, blue, and purple, and remember also that … The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 12. The vertices of a triangle are three unifomly random points on a unit circle. The side lengths are, in random order, a, b, c . Show that P(ab > c) = 1 2 . The result is strongly suggested by ... Method to difference between two continuous fractions and keep continued fraction form. elementary-number-theory. fractions. continued-fractions. Nishi. 1. modified 8 mins ago. 0 votes. 2 answers.Find the center of all circles that touch the x -axis and a circle centered at the origin. Given a circle C of radius 1 centered at the origin, I want to determine the locus of the centers of all circles that touch C and the x -axis. This is the red curve in the following Desmos ... geometry. inverse-function. locus.Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeThe first derivative is f ′ (x) = ex − 1 − 1 and the second derivative is f ″ (x) = ex − 1. f is convex everywhere because f ″ (x) > 0, and has a minimum at x = 1. Therefore x ≤ ex − 1 for all x, and the equation is only equal when x = 1. Using this inequality we get. x1 a x2 a ⋯xn a ≤ ex1 a − 1ex2 a − 1⋯exn a − 1.Solving a second order differential question where one solution is known. Problem: Given that y = e2x is a solution of (2x + 1)y ″ − 4(x + 1)y + 4y = 0 find a linearly independent solution by reducing the order. Write the general solution. Answer: Let y = e2xv. ... ordinary-differential-equations. Bob.

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Total variation distance is a measure for comparing two probability distributions (assuming that these are unit vectors in a finite space- where basis corresponds to the sample space ($\omega$)).I know a distance measure need to obey triangle inequality and it should satisfy that orthogonal vectors have maximum distance and the same …Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange19. As a side comment, you should not cite this particular stackexchange answer unless you have a really good reason to cite it specifically. This is a standard topic in combinatorics ("compositions of n into k parts"), and it can be found in lots of textbooks. For example, it's in Section 1.2 of Stanley's Enumerative Combinatorics volume 1, as ...Make your title interesting for others. Mathematics.SE is designed to be a repository of good mathematical questions and answers. Thus, there is no need to refer to your personal situation in the title. Make your title a question of universal value. For example, the title Help me solve a2 + b2 = c2 for my exam preparation is very specific to ...Q&A for those involved in the field of teaching mathematics. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeA tensor field of type (1, 0) is a vector field. A tensor field of type (0, 1) is a differential 1 -form. A tensor field of type (1, 1) is a morphism of vector fields. A tensor field of type (0, 2) which is symmetric and nondegenerate is a metric tensor. If it is also positive-definite, it is a Riemannian metric.The vertices of a triangle are three random points on a unit circle. The side lengths are a, b, c. Show that P(ab > c) = 1 2. probability. integration. definite-integrals. intuition. geometric-probability. Dan. 21.5k.Peter Winkler included this problem in his puzzle collection Mathematical Puzzles (2020), and gave the following very elegant solution, which I quote below: Since the probability of seeing HHHHH in a particular series of five coin flips is $1/32$, you might think it would take $32$ flips on average to get HHHHH.The two equations simplify to x2 + y2 = r21 and (x − d)2 + y2 = r22 Use the first to find y2 and substitute in the second. (x − d)2 + r21 − x2 = r22 expand and simplify − 2xd + d2 + r21 = r22 so the points of intersections are (x, y), (x, − y) with x = r21 − r22 + d2 2d and from Pythagorus y = √r21 − x2. This part came from ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeBy contrast, the current top response since 2012 on math.stackexchange correctly solves a different problem, in particular the prior probability of winning if you commit to switching regardless of which door Monty opens. What that response is missing is an argument connecting the posterior (conditional) probability to the prior.the quality and relevancy of your questions and answers. These friendly reputation leagues are an informal way of tracking your reputation within the community on a particular Stack Exchange. Reputation is capped at 200 per day, but remember that bounty awards and accepted answers are immune to this daily reputation cap. Rep … ….

Math Stack Exchange's default style uses a light-colored page background, so avoid using light colors for text. Stick to darker colors like maroon, green, blue, and purple, and remember also that … Find a positive integer n n, m m, p p, q q ( p ≠ q p ≠ q, m > 1 m > 1) such that p p and q q divide mn2 − 1 m n 2 − 1 and mn m n divides p − q p − q. modular-arithmetic. arithmetic. Etanche. 310. modified 2 hours ago. 1 vote. To search within specific tag (s), enter them in square brackets: [maintenance] seat searches for mentions of "seat" within the [maintenance] tag. To find a specific phrase, enter it in quotes: "flat tire". To limit your search to just the title of a question, use title: followed by the search term. Likewise, search the body only (exclude the ...I have one triangle in $3D$ space that I am tracking in a simulation. Between time steps I have the previous normal of the triangle and the current normal of the triangle along with both the current and previous $3D$ vertex positions of the triangles.. Using the normals of the triangular plane I would like to determine a rotation matrix that would align the … Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus reference-request algebra textbooks geometry proofs primary-education more tags. Active Hot Week Month. 0 votes. 0 answers. 7 views. A cluster in math is when data is clustered or assembled around one particular value. An example of a cluster would be the values 2, 8, 9, 9.5, 10, 11 and 14, in which there is a c...A First Course In Abstract Algebra-John B. Fraleigh, 7Ed would be very good. Share. Cite. Follow. answered May 9, 2016 at 8:01. Simple. 134 8. 1. This is more suitable for undergraduates than for graduate students.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …Make your title interesting for others. Mathematics.SE is designed to be a repository of good mathematical questions and answers. Thus, there is no need to refer to your personal situation in the title. Make your title a question of universal value. For example, the title Help me solve a2 + b2 = c2 for my exam preparation is very specific to ... Math.stackexchange, [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1], [text-1-1]