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$\begingroup$ Note that to use this we must have a basis already chosen (to write down matrices) and that our inner product must match the standard dot product in terms of this basis (so that matrix multiplication corresponds to taking inner product of rows of the left matrix with columns of the right matrix). Also, to apply the first comment, the number of …Add a comment. 6. There are ways to calculate it, modulo is remainder counting basically. 7 = 2 mod 5 because 7 = 5 ∗ 1 + 2 12 = 2 mod5 because 12 = 5 ∗ 2 + 2 and so on, so if you want to calculate for example 73 = a mod 7 you can do this, that is want to get a, take 73 and continue subtracting 7 until you no longer can. 73 − 7 = 66, 66 ...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, …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 …There cannot be explicit algebraic formulas for the general solutions to higher-degree polynomials, but proving this requires mathematics beyond precalculus (it is typically proved with Galois Theory now, though it was originally proved with other methods). This fact is known as the Abel-Ruffini theorem.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 …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

Apr 7, 2014 · 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. LaTeX. Mathematics Stack Exchange uses MathJax to render LaTeX syntax. You can use single dollar signs to delimit inline equations, and double dollars for blocks: The equation $ 3x^2 + 5x +1 = 0 $ has the solutions. $$. x_{1,2} = \frac{-5 \pm \sqrt{5^2-12}}{6} $$. 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 ExchangeJul 9, 2013 at 16:12. @JackM if you are searching for a2 +b2 =c2 a 2 + b 2 = c 2 the Uniquation seems to also get you x2 +y2 =z2 x 2 + y 2 = z 2 and the equivalents. So searching a formula becomes a tricky search for a concept. – …5. Please help me understand swapping the bounds of an integral better. I learned that. ∫b a f(x)dx = −∫a b f(x)dx ∫ a b f ( x) d x = − ∫ b a f ( x) d x. Now when I try to visualize this, take sin(x) sin ( x) for example, ∫2π π sin(x)dx ∫ π 2 π sin ( x) d x and −∫π 2π sin(x)dx − ∫ 2 π π sin ( x) d x both give ...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... 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.

France continues to ease restrictions leading up to its June 9 reopening to tourists. Here's what you need to know. The Louvre and Versailles are about to throw open their doors on... Parameterisation that enforces positivity of linear combination of projections. I have a set of n vectors that form a basis for a subspace, vi. Suppose I take a linear combination w = ∑n i = 0viαi, αi ∈ R such that for a set of vectors, $... linear-algebra. vector-spaces. Stack Exchange Q&A communities are different. Here's how: Expert communities. Each of our 182 communities is built by people passionate about a focused topic. …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.44. This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with LATEX L A T E X code available) high-quality (according to strictly mathematical and pedagogical standard) lecture notes or textbooks on as many mathematical topics as possible.

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P ( A, B, C) = P ( C) P ( B | C) P ( A | C). From a computational perspective, the key thing to note is that conditional dependence here means we can write the 3-variable function P(A, B, C) P ( A, B, C) in terms of 1-variable and 2-variable functions. In a nutshell, conditional independence means that joint distributions are simpler than they ...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 Exchange3 Answers. First consider the simplest case where a(x) = a a ( x) = a and b(x) = b b ( x) = b for all x x. Then the Leibniz formula becomes. d dx(∫b a f(x, t)dt) =∫b a ∂ ∂xf(x, t)dx d d x ( ∫ a b f ( x, t) d t) = ∫ a b ∂ ∂ x f ( x, t) d x. i.e. it is reduced to moving the derivative inside the integral. In this special case, the ...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.A 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 ...

SEAT: Get the latest Vivid Seats stock price and detailed information including SEAT news, historical charts and realtime prices. The most overbought stocks in the communication s...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.$\begingroup$ @ParamanandSingh The point of the answer is to show that to 'turn-the-crank' you have to put on your 'abstract hat', and so really, for the $\varepsilon / \delta$ there are cookie cutter solutions - the interested student just has to cross over into mathematical maturity when they are ready.Are you looking for a fun and interactive way to improve your mathematical skills? Look no further than free online math games. These games not only make learning math enjoyable, b...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 … Welcome to Mathematics Stack Exchange. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question ... Newest Questions - Mathematics Meta Stack Exchange. All Questions. Ask Question. 9,522 questions. Newest. Active. Filter. 2 votes. 0 answers. 95 views. …19. 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 ...In any case, I think the problem with your proof (at least with your geodesic argument), is that the exponential map, while it is a local diffeomorphisme on some neighborhood of $0_{\mathfrak g}$, isn't necessarily a local diffeomorphism near all points of $\mathfrak g$.

The second level is a course typically taken by upper level math, physics, and (sometimes) engineering students. At some colleges and universities, students may elect to skip the first level linear algebra course and begin with this level. [This was the case where I did most of my undergraduate work.

Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus …Prove that if p ≡ 7 (mod 8), the solutions to the congruence x2 − 34x + 1 ≡ 0 (mod p) are both quadratic residues modulo p. elementary-number-theory. modular-arithmetic. quadratic-residues. 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. The second part, containing problems from the British Mathematical Olympiad, is much more challenging.) _ [Beginner-Intermediate] E. Lozansky and C. Rousseau, Winning solutions, A good introduction to some useful background material from number theory, algebra, and combinatorics, and to problem-solving techniques.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 ExchangeWhat happens when I comment? The following community members will be automatically notified of your comment: the owner of the post you're commenting on. one additional user when your comment contains a @username 1 reply. 1 You can only @reply to users who have already left a comment, or edited the post. The first three non-whitespace … Understanding predicates and quantifiers ∀ , ∃ (my reasoning) So lets say we are trying to figure out if: P (x, y) is the predicate of x2 < y as defined for x, y ∈ Z. This means using quantifiers: ∀ and ∃, I can logically say: 1. ∀x∃y of P (x,y) is ... discrete-mathematics. logic. first-order-logic. quantifiers. coolcat. Torsion group over Q of Y2 = X3 + DX for D ≡ 2 (mod 3). Let D ∈ N with D ≡ 2 (mod3). Describe the torsion group over Q of the elliptic curve Y2 = X3 + DX. Idea: Firstly we recall that for an ... number-theory. elementary-number-theory. elliptic-curves. algebraic-curves.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 …Solutions to ODE/SDE with singular coefficients dXt = −Xt/tdt + gdWt d X t = − X t / t d t + g d W t. stochastic-processes. differential-equations. stochastic-calculus. …

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Sorted by: 30. For my work in this area, I refer to: Richard Epstein "Classical Mathematical Logic". Wolfgang Rautenberg "A Concise Introduction to Mathematical Logic". Jon Barwise "Handbook of Mathematical Logic". Jean Heijenoort "From Frege to Gödel". Wei Li "Mathematical Logic: Foundations for Information Science".The 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. 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 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.The second part, containing problems from the British Mathematical Olympiad, is much more challenging.) _ [Beginner-Intermediate] E. Lozansky and C. Rousseau, Winning solutions, A good introduction to some useful background material from number theory, algebra, and combinatorics, and to problem-solving techniques.Stack Exchange Q&A communities are different. Here's how: Expert communities. Each of our 182 communities is built by people passionate about a focused topic. …19. 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 ...A 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.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 …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, … ….

About. (Officially John M. Lee.) Professor Emeritus of math at University of Washington, Seattle; author of Introduction to Topological Manifolds, Introduction to Smooth Manifolds, Introduction to Riemannian Manifolds, and Axiomatic Geometry.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 ExchangeNewest Questions - Mathematics Meta Stack Exchange. All Questions. Ask Question. 9,522 questions. Newest. Active. Filter. 2 votes. 0 answers. 95 views. …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 Parameterisation that enforces positivity of linear combination of projections. I have a set of n vectors that form a basis for a subspace, vi. Suppose I take a linear combination w = ∑n i = 0viαi, αi ∈ R such that for a set of vectors, $... linear-algebra. vector-spaces. Some kids just don’t believe math can be fun, so that means it’s up to you to change their minds! Math is essential, but that doesn’t mean it has to be boring. After all, the best ... 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]