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 ... 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 ...As one activist says, “the world has become a village from which Chadians are excluded.” For almost a year now, people across Chad Republic have not been able to access social medi...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.Each year, millions of students in India rush to get an admission in universities abroad. Often they don’t know which program they should focus on, or the college that is right for...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 Exchangen) For n = 0 n = 0 there isn't any number greater then 0 and lesser or equal to n n, so the product is empty; the empty product is defined by convention as 1. It has many reasons. For example, we can have a power series: ex = ∑nxn/n! e x = ∑ n x n / n! and we would like the first term to be 1 1.Good morning, Quartz readers! Good morning, Quartz readers! The US takes stock of its economy. Fed chair Jerome Powell steps onto the congressional stage over the next two days to ...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...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 …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 ...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.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...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 ... 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, $... linear-algebra. vector-spaces. Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeThis site is for discussion about Mathematics Stack Exchange. You must have an account there to participate. Help. Visit chat. Related. 4015. MathJax basic tutorial and quick reference. 14. Mathjax 2.1 beta. 2. New Line without Space Afterwards. 5. How to indent text and make indents. 18.$\begingroup$ @Om3ga Incidentally, there are at least three different Discord servers of significant size "called 'Mathematics' where people can ask for help to certain questions.", in addition to others not named "Mathematics" (e.g. general STEM help servers - advanced math servers - subject-area-specific servers - servers for math people at a ...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 ExchangeWelcome to Mathematics Stack Exchange. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals …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. 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. 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.$\begingroup$ 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 …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 ...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...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 ExchangeAdvertisement While in prison, cons are subject to the rules set by prison officials. If a con commits an infraction, he gets a hearing before the warden or some lower ranking offi...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 ...Whether you’re a teacher in a school district, a parent of preschool or homeschooled children or just someone who loves to learn, you know the secret to learning anything — particu...Mathematics Educators Stack Exchange. Explore our questions. Ask Question. undergraduate-education secondary-education mathematical-pedagogy calculus …2. It's simple to discover determinants just by solving Ax = b by hand, using high school algebra, in the case where A is 2 × 2 or 3 × 3. You immediately see that the system can be solved for any choice of b if the determinant is nonzero (because you will try to divide by the determinant). It's so easy.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.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...Kiwis can now get paid in crypto, the US securities regulator isn't so sure about bitcoin funds, and news from elsewhere. Kiwis can now get paid in crypto. Bitcoin faces legal unce...This site is for discussion about Mathematics Stack Exchange. You must have an account there to participate. Help. Visit chat. Related. 4015. MathJax basic tutorial and quick reference. 14. Mathjax 2.1 beta. 2. New Line without Space Afterwards. 5. How to indent text and make indents. 18.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 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 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 ExchangeR. geometry. There are exactly four compact manifolds with S2 × R S 2 × R geometry. They are. where M2 M 2 denotes the mapping torus of an orientation reversing isometry of the sphere S2 S 2. RP2 ×S1,M2 R P 2 × S 1, M 2 are both nonorientable. And RP2 ×S1 R P 2 × S 1 has orientable double cover S2 ×S1 S 2 × S 1. 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. Newest Questions - Mathematics Meta Stack Exchange. All Questions. Ask Question. 9,522 questions. Newest. Active. Filter. 2 votes. 0 answers. 95 views. Was the style of the up/down-vote arrows changed? I noticed that the style of the up/down-votes button has changed (for me at least). The call from Consumer Reports is a more aggressive one than the CDC is making, as the second E. coli scare linked to lettuce this year spreads across the US. A major US consumer w...Apr 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. 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. 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. 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 …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. 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.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 ...$\bigstar$ By that, I mean: (1) books that you think may help to develop positively the way one thinks about mathematics (in general or some areas); (2) books that help developing intellectual and mathematical maturity; (3) books that are in any way inspirational; (4) books that are useful because they offer (generally) unknown way to …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 …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.we get for each pair of points : h = b1 a1k − c1 and another reduced equation for the other pair of points would give: h = b2 a2k − c2. Solving above equations , we get : k = a1a2(c1 − c2) (b1a2 − b2a1) Consider the general (implicit) equation that defines a circle, with parameters α, β, γ.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 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. 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 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. Mathematics Stack Exchange is moderated by you. Review queues contain posts (also known as review tasks) that might need community attention, as determined by the system or other community users. You see posts one at a time so that you can evaluate what, if any, action is needed.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 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.n) For n = 0 n = 0 there isn't any number greater then 0 and lesser or equal to n n, so the product is empty; the empty product is defined by convention as 1. It has many reasons. For example, we can have a power series: ex = ∑nxn/n! e x = ∑ n x n / n! and we would like the first term to be 1 1.A 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.There are many branches of mathematics and each branch has its main vocabularies. For example, in number theory, one's main vocabulary is an "integer". Just like this, "openness" is a main vocabulary in general topology. (The question of asking why openness is a main vocabulary is a completely different question and this is well … 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. 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.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 …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 …The road to Cardiology fellowship can be a confusing one. Residency, with its breakneck pace and punishingly long hours, is already a Herculean challenge in and of itself. Simply c...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 ...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. 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.2. It's simple to discover determinants just by solving Ax = b by hand, using high school algebra, in the case where A is 2 × 2 or 3 × 3. You immediately see that the system can be solved for any choice of b if the determinant is nonzero (because you will try to divide by the determinant). It's so easy.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...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.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.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...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 ExchangeIn 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 ...MathJax basic tutorial and quick reference - Mathematics Meta Stack Exchange. Ask Question. Asked 11 years, 6 months ago. Modified 13 days ago. …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 ...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 ExchangeIn 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.
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.. Stout beer
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 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 ... 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. 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 ...MathJax basic tutorial and quick reference - Mathematics Meta Stack Exchange. Ask Question. Asked 11 years, 6 months ago. Modified 13 days ago. …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 ...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 ExchangeIt has always been difficult for me to connect the linguistic sense of the terms "necessary" and "sufficient" with mathematics. However, with practice with the following table, this skill becomes automatic. I'm assuming you understand the meaning of the implication. In any case it is helpfull to think about simple example when looking at this ...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.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 ... 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 …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.What does mathematical logic mean?. In the book Analysis 1 by Terence Tao, it says:. The purpose of this appendix is to give a quick introduction to mathematical logic, which is the language one uses to conduct rigourous mathematical proofs. Checking Wikipedia:. Mathematical logic is often divided into the fields of set theory, model …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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