Math.stackexchange

$\begingroup$ I don't find this graphical example helpful in explaining the Fourier Transform. If anything, it is going to add to existing confusion people have with the Fourier Series. The sin and cos expression shown is too general to be meaningful, and the graphic shown for the "transform" is really just a visualization of the magnitudes of the …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.Topology (Undergraduate Texts in Mathematics) K. Jänich (Author), S. Levy (Translator) I should have also noted that many undergraduate students find the transition to these subjects difficult and they want to see and do problems. It doesn't hurt to make these two also available because cost is very reasonable.$\approx$ is used mostly for the approximate (read: calculated) value of a mathematical expression like $\pi \approx 3.14$ In LaTeX it is coded as \approx. $\cong$ is used to show a congruency between two mathematical expressions, which could be geometrical, topological, and when using modulo arithmetic you can get different numbers that are …Combining these steps, the overall 1-norm projection of a vector x can be written as: y = RT(Proj∞(Rx × √2) ÷ √2) This formula represents the entire process of projecting a vector onto the 1-norm unit ball using rotation and scaling in conjunction with the infinity-norm projection. I've tried this in R2 and it is correct.You must have a total score of 100 in at least 20 non-community wiki answers to achieve this badge. 14.6k awarded. Silver Badge. You must have a total score of 400 in at least 80 non-community wiki answers to achieve this badge. 2.7k awarded.Questions tagged [algebraic-geometry] The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. This tag ...Good morning, Quartz readers! Good morning, Quartz readers! South Korea commemorates comfort women. Japan issued a travel advisory warning visitors about anti-Japanese sentiment in...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 set of lines, each of which intersect the others, are either coplanar or share a single common point. geometry. solution-verification. induction. euclidean-geometry. solid-geometry. Anne Bauval. 33.2k. modified 24 mins ago.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 …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.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.I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology. I have decided to fix this lacuna once for all.... differential-geometry. reference-request. differential-topology. book-recommendation. Harddaysknight. 2,271.Good morning, Quartz readers! Good morning, Quartz readers! South Korea commemorates comfort women. Japan issued a travel advisory warning visitors about anti-Japanese sentiment in...Spain’s Jobandtalent, a digital temp staffing agency startup which operates a dual-sided platform that matches temps with employers needing casual labor in sectors like ecommerce, ... This tag is for questions that are asking for online resources in mathematics (references, dictionaries, encyclopaedic collections, online tools, videos and lectures, etc), or asking about the mathematics behind tools and technology found on the internet. Question about the expected value of random variable, using expected value properties. Suppose that the number of children N of a randomly chosen family satisfies P(N = n) = 3 5(2 5)n P ( N = n) = 3 5 ( 2 5) n for n = 1, 2, 3... n = 1, 2, 3... Now suppose that a child is equally likely to be a ...Good morning, Quartz readers! Good morning, Quartz readers! South Korea commemorates comfort women. Japan issued a travel advisory warning visitors about anti-Japanese sentiment in...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 a 2 + b 2 = c 2 for my exam preparation is very specific to your personal situation.10. The Lebesgue integral is a generalization of the usual Riemann integral taught in basic calculus. If the Riemann integral of a function over a set exists then it equals the Lebesgue integral. So the Lebesgue integral of x2 x 2 over [0, 1] is just the old (1/3)13 − (1/3)03.Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...2. Obviously I'm late to answer this, but I have some recommendations. As for a nice introduction, I can recommend Introduction to Probability and Mathematical Statistics by Bain and Engelhardt or Statistical Inference by Casella and Berger. On a slightly higher level is Mathematical Statistics by Shao. Finally, an older but still …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 ExchangeStack 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 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. What 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 characters ... I am very interested in mathematics, particularly mathematical physics, but I currently do not have access to an institution or any professors. ... You can also look on Math StackExchange (e.g., questions with the [book-recommendation] tag) for recommendations about books for either your particular interests, problem solving, proof …We read it so that you don't have to. The first US government to be led by a full-time businessman with no political background is being run like a terrible business overruled by i...Questions tagged [algebraic-geometry] The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. This tag ...I am a second year studying math at university, and have taken theoretical linear algebra, group and ring theory, real and complex analysis, and general topology, as well as some miscellaneous technical courses like probability theory, statistical inference, and algorithms. ... $\begingroup$ Recommendations for inquiry-based learning: math ...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 ...You must have a total score of 100 in at least 20 non-community wiki answers to achieve this badge. 14.6k awarded. Silver Badge. You must have a total score of 400 in at least 80 non-community wiki answers to achieve this badge. 2.7k awarded.If you just upgraded to macOS Sierra and your Dropbox app is acting up, you’re not alone. Even with the latest version of the app, some users are experiencing strange behavior—erro...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 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 Exchange 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. 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 ExchangeSaving for retirement can be difficult in the best of times, but even harder during a pandemic and challenging economy. An underutilized tax credit… April 14, 2021 • By Catherine C...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.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 ...Proofs for the properties of μ(σ) μ ( σ), the order of ζ(s) ζ ( s) The following is a text from Section 5.1 of Titchmarsh's book The Theory of the Riemann Zeta-Function: For each σ σ we define a number μ(σ) μ ( σ) as the lower bound of numbers ξ ξ such that $... soft-question. proof-explanation. book-recommendation.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...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 Exchange2. Obviously I'm late to answer this, but I have some recommendations. As for a nice introduction, I can recommend Introduction to Probability and Mathematical Statistics by Bain and Engelhardt or Statistical Inference by Casella and Berger. On a slightly higher level is Mathematical Statistics by Shao. Finally, an older but still …It might be a good idea to say something about the connection between the axiom of choice and the Banach-Tarski paradox. The reason the Banach-Tarski paradox is counterintuitive is that we expect that if you split up a sphere into finitely many pieces, the total "mass" of all the pieces is still the same - so you shouldn't be able to put those …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.Here's your chance to earn bonus Amex points for spending with Four Seasons. Update: Some offers mentioned below are no longer available. View the current offers here. It's new Ame...If you just upgraded to macOS Sierra and your Dropbox app is acting up, you’re not alone. Even with the latest version of the app, some users are experiencing strange behavior—erro...2. Obviously I'm late to answer this, but I have some recommendations. As for a nice introduction, I can recommend Introduction to Probability and Mathematical Statistics by Bain and Engelhardt or Statistical Inference by Casella and Berger. On a slightly higher level is Mathematical Statistics by Shao. Finally, an older but still …This tag is for questions that are asking for online resources in mathematics (references, dictionaries, encyclopaedic collections, online tools, videos and lectures, etc), or asking about the mathematics behind tools and technology found on the internet. Learn more…. The proportion of primes where the sum of the digits of the prime is also prime. elementary-number-theory. prime-numbers. arithmetic. NotMath. 185. modified 30 mins ago. 0 votes. 0 answers. Saving for retirement can be difficult in the best of times, but even harder during a pandemic and challenging economy. An underutilized tax credit… April 14, 2021 • By Catherine C...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".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 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 ... Q&A for people studying math at any level and professionals in related fields Stack Exchange Network 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.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.Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...Sep 11, 2016 · Approach0 is a math-aware search engine. “Math-aware” means you can add math expression (s) as some of your keywords to have search engine help you find similar expressions. Check out here: https://approach0.xyz. To restrict matches to this site paste the string "AND site:math.stackexchange.com" into the search window (this removes AoPS ... Mathematics Stack Exchange. Help center. Our model. How can I format mathematics here? Many posts at Mathematics Stack Exchange include …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.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.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. …Three players toss an unfair coin - Give an intuitive explanation of dependent. Three players toss an unfair coin each, independently of each other, with the same probability p = 1/3 that the coin shows heads. Let X = 1 if player #2 gets the same result as player #1 - Call this a ... probability. independence.Math.StackExchange Math.StackExchange. 1,197 1 1 gold badge 8 8 silver badges 18 18 bronze badges. 5. 7. Is your first sentence saying that your university 1) is a small liberal arts college, 2) is one of the top 15 universities in the country, and 3) does not have a strong mathematics or physics department? I don't think all three of these …Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus 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 ExchangeStack 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. – …Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...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 ...3 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 ...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$\begingroup$ FYI, you can do something similar to "explain" the Chain Rule: Define a space curve by < f(t), h(t), t > where h(t) = g(f(t)), and (assuming it makes sense) let its tangent vector be < a, b, 1 > (with a != 0). The zx-graph is x = f(z), with slope-of-tangent-line dx/dz = a/1 = a; the zy-graph is y = h(z), with tangent slope dy/dz = b/1 = b; the bridging …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.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. $$. x_{1,2} = \frac{-5 \pm \sqrt{5^2-12}}{6} $$.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.By 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 largest operator of Boeing 737 MAX aircraft in the US announced Thursday that the plane would remain off its schedule through September. Southwest Airlines, the largest operato...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.Getting credit for something you’ve accomplished can be a struggle in the business world, but with Microsoft PowerPoint, you’ve got multiple options to put your name or your compan...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 ExchangeHere's your chance to earn bonus Amex points for spending with Four Seasons. Update: Some offers mentioned below are no longer available. View the current offers here. It's new Ame...Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure …A mathematical sentence combines two expressions with a comparison operator to create a fact that may be either true or false. A mathematical sentence makes a statement about the r...Question about the expected value of random variable, using expected value properties. Suppose that the number of children N of a randomly chosen family satisfies P(N = n) = 3 5(2 5)n P ( N = n) = 3 5 ( 2 5) n for n = 1, 2, 3... n = 1, 2, 3... Now suppose that a child is equally likely to be a ...$\begingroup$ I don't find this graphical example helpful in explaining the Fourier Transform. If anything, it is going to add to existing confusion people have with the Fourier Series. The sin and cos expression shown is too general to be meaningful, and the graphic shown for the "transform" is really just a visualization of the magnitudes of the … | Cyyxqfky (article) | Mvpodpr.