https://math.codidact.com/categories/41/feed New Posts - Q&A - Mathematics Mathematics - Codidact 2021-10-22T14:26:48Z https://math.codidact.com/posts/284651 What does the distribution of a strictly increasing random walk look like if you stop at N steps? SherlockSage‭ https://math.codidact.com/users/53795 2021-10-22T13:48:49Z 2021-10-22T14:26:48Z <p>I have a puzzle inspired by the game Idle Brick Breaker (<a href="https://play.google.com/store/apps/details?id=com.TechTreeGames.IdleBrickBreaker&amp;hl=en&amp;gl=US">Google Play</a> and <a hre... https://math.codidact.com/posts/284557 Does this construction always give a topological vector space? celtschk‭ https://math.codidact.com/users/8056 2021-10-10T08:42:10Z 2021-10-10T19:54:07Z <p>Consider an algebraic vector space $V$ over $\mathbb R$ or $\mathbb C$.</p> <p>Now for each possible basis $B_k = \{e_i^{(k)}|i\in I\}$ of $V$, one can define an inner product $\langle\cdot\ver... https://math.codidact.com/posts/284550 transpose matrix and general matrix is completely messed up Istiak‭ https://math.codidact.com/users/53922 2021-10-09T16:01:33Z 2021-10-10T18:17:17Z <p>I was studying Matrix. I never attend any lecture. So I don't have much more idea of Matrix. I had learned multiplication, addition, subtraction and inverse matrix last year from some YT tutoria... https://math.codidact.com/posts/284561 What does variable in sup represent for matrix? Istiak‭ https://math.codidact.com/users/53922 2021-10-10T15:08:24Z 2021-10-10T15:08:24Z <p>I had seen people were representing matrix 2 way.</p> <ol> <li>$$\sum_{j=1}^n a_{ij}$$</li> </ol> <p>It is representing a column matrix (vector actually) if we assume$i=1$.</p> <p>$$\begin... https://math.codidact.com/posts/284408 What it ≡ called? Istiak‭ https://math.codidact.com/users/54212 2021-09-30T16:23:00Z 2021-09-30T16:38:32Z <p>I saw the text (≡) few times. When I had searched in internet I got that..</p> <blockquote> <p>In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relati... https://math.codidact.com/posts/284279 \int dx dy dz d p_x dp_y dp_z Does it have any physical meaning? Istiak‭ https://math.codidact.com/users/53922 2021-09-21T16:02:49Z 2021-09-22T21:59:36Z <p>I was reading a Physics book. Then I saw an equation which was looking like this :</p> <p>$$\int dx dy dz d p_x dp_y dp_z$$</p> <p>I was thinking it from just a Calculus book. I can see lots o... https://math.codidact.com/posts/284280 Is Pythagorean theorem really valid in higher dimensional space? Istiak‭ https://math.codidact.com/users/53922 2021-09-21T16:25:27Z 2021-09-22T02:17:59Z <p>I saw that someone was writing Pythagorean theorem in 3 dimensional space. The equation was :</p> <p>$$c=\sqrt{x^2+y^2+z^2}$$If it's really correct than Pythagorean should work in higher dime... https://math.codidact.com/posts/282643 If A & B are joint, can Arby recoup some of his loss only when P_{Arby}(A \cup B) < P_{Arby}(A) + P_{Arby}(B)? DNB‭ https://math.codidact.com/users/53628 2021-07-11T06:07:51Z 2021-09-18T08:18:31Z <ol> <li> <p>Please see the sentence alongside the red line below, but the authors didn't write this sentence for the first case ( P_{Arby}(A \cup B) &lt; P_{Arby}(A) + P_{Arby}(B)). Thus if A ... https://math.codidact.com/posts/282966 What's wrong with evaluating n(n-1) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])} at k = 1? DNB‭ https://math.codidact.com/users/53628 2021-07-30T02:00:37Z 2021-09-18T06:35:14Z <p>This snag arose out of <a href="https://math.codidact.com/posts/282606">this post</a>, and <a href="https://math.codidact.com/comments/thread/3555#comment-11900">these comments by r~~</a>. In th... https://math.codidact.com/posts/282645 If Alice must've have classes on at least 2 days, why do you need the intersection of 3 A_i^C's? DNB‭ https://math.codidact.com/users/53628 2021-07-11T06:42:50Z 2021-09-18T06:01:51Z <p>Can someone please rectify my MathJax? Please see the red phrase below.</p> <ol> <li> <p>The question itself never touts or postulates outright that Alice "must have classes on at least 2 da... https://math.codidact.com/posts/283260 How would you vaticinate to -w_k from both sides of w_{k + 1} = \dfrac{w_k - (1 - p)w_{k - 1}}{p}? DNB‭ https://math.codidact.com/users/53628 2021-08-10T06:25:17Z 2021-09-16T16:22:40Z <p>This question appeared on my pop quiz last week. I got 0%. I achieved everything until the green equation, then I didn't know how to proceed. After reading this solution, I see that you must iso... https://math.codidact.com/posts/283872 Getting backward of partial differentiation's chain rule Istiak‭ https://math.codidact.com/users/53922 2021-08-31T15:08:18Z 2021-09-13T13:09:59Z <p>We know that Chain rule of partial derivatives is something just like this (z is function of x and y variable and, x and y is function of t) :</p> <p>$$\frac{dz}{dt}=\frac{\partial ... https://math.codidact.com/posts/283252 Which vertical line signifies "putting the cutoff for a positive result at a very low level"? DNB‭ https://math.codidact.com/users/53628 2021-08-09T23:44:39Z 2021-09-12T05:14:47Z <p>The author, Karen Stewart <a href="https://www.linkedin.com/in/karen-steward-89036a24/">MA Natural Sciences (Univ. of Cambridge) PhD Veterinary Microbiology (Cambridge)</a>, refers to "a purple ... https://math.codidact.com/posts/284113 What to do when there's lot of function of time? (For integration) Should I consider them as constant? Istiak‭ https://math.codidact.com/users/53922 2021-09-10T09:03:12Z 2021-09-10T18:11:41Z <p>Let I have a function which is looking like this</p> <p>$$f=\int\frac{l \ \mathrm {dt}}{\dot{\theta}r\dot{r}}$$</p> <p>Here$\dot{\theta}$,$r$,$\dot{r}$and$l$all of them are function of$... https://math.codidact.com/posts/283929 Consider the second of these integrals (What's the meaning of second right here?) Istiak‭ https://math.codidact.com/users/53922 2021-09-02T10:51:07Z 2021-09-03T10:32:57Z <p>$$\frac{dJ}{d\alpha}=\int_{x_1}^{x_2}(\frac{\partial f}{\partial y}\frac{\partial y}{\partial \alpha}+\frac{\partial f}{\partial \dot{x}}\frac{\partial \dot{x}}{\partial \alpha})\mathrm dx$$ Co... https://math.codidact.com/posts/283945 What're the orders for equation expressing? Mark Giraffe‭ https://math.codidact.com/users/54114 2021-09-02T23:59:30Z 2021-09-03T04:28:09Z <p>When doing an equation in programming or real calculations, equation expression takes in a specific order. In a single equation, I use the PEMDAS/GEMDAS order, which goes:</p> <ul> <li>Perform... https://math.codidact.com/posts/283111 Why's the true positive rate termed Sensitivity and true negative rate Specificity, not vice versa? DNB‭ https://math.codidact.com/users/53628 2021-08-05T02:11:34Z 2021-09-02T22:39:51Z <ol> <li> <p>To wit, what's "Sensitive" about True Positive Rates, and "Specific" about True Negative Rates?</p> </li> <li> <p>Why weren't these <a href="https://en.wikipedia.org/wiki/Semantic... https://math.codidact.com/posts/282604 Why aren't the "21 possibilities here" NOT equally likely? DNB‭ https://math.codidact.com/users/53628 2021-07-09T03:59:27Z 2021-09-02T14:15:09Z <p>Please see the last sentence below, that I highlighted in red.</p> <hr> <p>Example $1.4 .5$ (Ice cream cones). Suppose you are buying an ice cream cone. You can choose whether to have a cake c... https://math.codidact.com/posts/282603 Without calculations, how can you visualize "that half the squares are white and half are black"? DNB‭ https://math.codidact.com/users/53628 2021-07-09T03:50:39Z 2021-09-02T14:14:35Z <p>Please see the 2nd para. below alongside my red highlighted words. I can't "[i]magine rotating the chessboard 90 degrees clockwise." I can't visualize how "all the positions that had a white squ... https://math.codidact.com/posts/282888 How can I visualize the Law of Total Probability with extra conditioning? DNB‭ https://math.codidact.com/users/53628 2021-07-28T00:06:49Z 2021-09-02T14:14:13Z <p>How can I pictorialized this Theorem 2.4.3? As you can see below, I edited a picture by drawing E inside B.. Is my edit correct? Can my edit be improved?</p> <blockquote> <p><strong>Theorem 2.... https://math.codidact.com/posts/281008 If a repair on a vessel costs $2$ and fully repaired vessel is worth $1$, don't we need know worth of broken vessel to decide whether to repair? Chgg Clou‭ https://math.codidact.com/users/53564 2021-03-09T05:37:11Z 2021-09-02T14:12:49Z <p>I divided all prices by 100,000 to simplify the question. The book beneath doesn't stipulate the current value of the vessel. But don't we need to know it, to calculate if it's worth repairing? ... https://math.codidact.com/posts/282889 How do you calculate $P(X = n|G), P(X = n|G^C)$ by the Law of Total Probability, with extra conditioning? DNB‭ https://math.codidact.com/users/53628 2021-07-28T02:15:02Z 2021-09-02T14:12:22Z <ol> <li> <p>Please see $P(U|G)$ and $P(U|G^C)$ below, beside my red line. Can you please expound these calculations?</p> </li> <li> <p>How was $s$ computed in both equations?</p> </li> </o... https://math.codidact.com/posts/282614 Why $\color{red}{k\dbinom{k}{1}} \neq$ "first choose the k team members and then choose one of time to be captain"? DNB‭ https://math.codidact.com/users/53628 2021-07-09T06:38:52Z 2021-09-02T14:11:53Z <p>Because you "first choose the k team members and then choose one of time to be captain", shouldn’t the RHS be $\color{red}{k\dbinom{k}{1}}$? The captain is chosen from the $k$ team members alre... https://math.codidact.com/posts/283887 Does "both girls, ≥ 1 winter girl" = "both girls, ≥ 1 winter child" let you generalize the problem statement that postulated both children as girls? DNB‭ https://math.codidact.com/users/53628 2021-09-01T08:40:20Z 2021-09-01T08:40:58Z <p>What does "the fact that "both girls, at least one winter girl" is the same event as both girls, at least one winter child"" imply about the problem statement below that posited merely girls? I... https://math.codidact.com/posts/283886 How would you intuit, and soothsay to rewrite, "both girls, ≥ 1 winter girl" as "both girls, ≥ 1 winter child"? DNB‭ https://math.codidact.com/users/53628 2021-09-01T08:35:52Z 2021-09-01T08:37:39Z <ol> <li> <p>Please see the red underline. How can you intuit that "both girls, at least one winter girl" as "both girls, at least one winter child"? I ask this for my 15 y.o.</p> </li> <li> <... https://math.codidact.com/posts/283388 How do I prove Simpson's Paradox, scilicet $P(A|B) > P(A|B^C)$? DNB‭ https://math.codidact.com/users/53628 2021-08-14T08:22:59Z 2021-08-27T09:10:11Z <p>$\forall a,b,c,d &gt; 0, a&lt;b, c&lt;d \implies$ <a href="https://math.stackexchange.com/q/3632752">$0 \le ab &lt; cd$</a>.</p> <ol> <li> <p>The blue, orange and purple inequalities below ar... https://math.codidact.com/posts/283696 Find limits of integration in polar coordinates MissMulan‭ https://math.codidact.com/users/54107 2021-08-24T13:36:10Z 2021-08-25T15:22:45Z <p>Suppose we have this graph and we want to find the area between the 2 curves:</p> <p><img alt="hi" src="https://math.codidact.com/uploads/xum62GPERZqYiqMuiVmgLAq1">.</p> <p>We can calculate th... https://math.codidact.com/posts/283385 How does counting E twice explain the discrepancy between the third between C and E, third between E and G v. fifth between C and G? Chgg Clou‭ https://math.codidact.com/users/53564 2021-08-14T03:55:21Z 2021-08-25T12:09:04Z <p>I still don't grasp the "source of the discrepancy". "the E got counted twice when we went C,D,E and then E,F,G, but only got counted once when we went C,D,E,F,G." — So what? How does this expou... https://math.codidact.com/posts/283255 After $n - 2$ unchosen doors are opened, how does the probability of the $n - 2$ unchosen doors "shift" or "transfer" to the lone unchosen door? DNB‭ https://math.codidact.com/users/53628 2021-08-10T00:43:39Z 2021-08-24T06:08:04Z <p>The second quotation below uses the verb "shift" to describe how Monty Hall's opening the 98 unchosen doors (revealing a goat each) ""shifts" [boldening mine] that 99/100 chance to door #100"? T... https://math.codidact.com/posts/283633 Is $r \times \frac{d}{dt} mv=\frac{d}{dt} (r \times mv)$ Istiak‭ https://math.codidact.com/users/53922 2021-08-21T12:09:40Z 2021-08-22T02:33:29Z <p>Is $$r \times \frac{d}{dt} mv=\frac{d}{dt} (r \times mv)$$</p> <p>I was thinking that it is wrong. Cause, which is outside of differentiation how we can put that inside differentiation no matte... https://math.codidact.com/posts/283118 Why would skyrocketing the numbers of doors help laypeople intuit the Monty Hall Problem? DNB‭ https://math.codidact.com/users/53628 2021-08-05T04:27:25Z 2021-08-20T23:17:49Z <p>Alas, it isn't clear to me that <strong>it becomes clear that the probabilities are not 50-50 for the two unopened doors</strong>. Had I never seen this exercise or problem, even if there were ... https://math.codidact.com/posts/282942 Besides guaranteeing 0 ≤ P(A ∩ B) ≤ 1, why can't Independence be defined as P(A ∩ B) = P(A) +,-, or ÷ P(B)? DNB‭ https://math.codidact.com/users/53628 2021-07-29T08:02:00Z 2021-08-20T23:10:11Z <p>I know that $0 \le P(A \cap B) \le 1$ will be violated if $P(A \cap B) = P(A) +,-,\text{or} ÷ P (B)$. I'm not asking about or challenging this reason.</p> <p>But what are the other reasons agai... https://math.codidact.com/posts/283586 What is "continuous" in Math? JohnDoea‭ https://math.codidact.com/users/36363 2021-08-19T11:30:46Z 2021-08-20T03:43:34Z <p>I understand that in Math, there is a common separation between <em>discrete</em> and <em>continuous</em>.</p> <ul> <li>I understand that in Math we could say that <em>discrete is anything (an... https://math.codidact.com/posts/283400 If a matrix has lots of values in a column but, not in row than, what that actually called? Istiak‭ https://math.codidact.com/users/53922 2021-08-14T16:40:29Z 2021-08-18T15:31:29Z <p>$\begin{bmatrix}a &amp; b &amp; c &amp; d\end{bmatrix}$</p> <p>$\begin{bmatrix}a \\ b \\ c \\ d \end{bmatrix}$</p> <p>Which one is $1$ dimensional Matrix? I think that first matrix is $1$ dime... https://math.codidact.com/posts/283513 How to find constant equal to what in integration? Istiak‭ https://math.codidact.com/users/53922 2021-08-17T08:27:11Z 2021-08-18T15:14:59Z <p>$$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$</p> <p>That's what I did. But, book says</p> <p>$$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$</p> <p>Seems like, $x_0 + \dfrac{a_0}{2... https://math.codidact.com/posts/283516 Is$x=\int \int \ddot{x}\mathrm dx \mathrm dx$? Istiak‭ https://math.codidact.com/users/53922 2021-08-17T08:47:58Z 2021-08-17T12:18:18Z <p>I know that multivariable calculus used like this</p> <p>$$\phi = \int \int x \mathrm dx \mathrm dy$$</p> <p>But, I was thinking to use double integral for single variable (double integral res... https://math.codidact.com/posts/283518 Do these major triangle lines have names? Peter Taylor‭ https://math.codidact.com/users/36356 2021-08-17T11:12:59Z 2021-08-17T11:12:59Z <p>Kimberling's <a href="https://faculty.evansville.edu/ck6/encyclopedia/ETC.html">Encyclopedia of Triangle Centers</a> lists, among other things, lines on which each centre is found, but usually l... https://math.codidact.com/posts/283445 Prove that$\int \ddot{x}(t)\mathrm dt=v_0 + \frac{F_0}{m}t$Istiak‭ https://math.codidact.com/users/53922 2021-08-16T10:38:03Z 2021-08-16T13:13:41Z <p>$$\ddot{x}(t)=\frac{F_0}{m}$$ This is a second-order differential equation for x (t) as a function of t. (Second-order because it involves derivatives of second order, but none of higher order... https://math.codidact.com/posts/283398 Finding the smallest Mersenne-number multiple of an odd integer wizzwizz4‭ https://math.codidact.com/users/53036 2021-08-14T16:20:46Z 2021-08-16T07:35:16Z <h3>Problem</h3> <p>Given an odd integer$a$, there exists some smallest$b$such that$a\times b = 2^n-1$(for some$n$). Find$b$and$n$.</p> <ul> <li>What is an upper bound for this problem?... https://math.codidact.com/posts/283372 How can I intuit$\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$? Chgg Clou‭ https://math.codidact.com/users/53564 2021-08-13T07:01:36Z 2021-08-14T18:38:58Z <p>I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's <a href="https://betterexplained.com/articles/subtracting-negative-numbers/">intuit subtraction as facing... https://math.codidact.com/posts/283390 Book suggestion for Tensor Calculus (Differential geometry) Istiak‭ https://math.codidact.com/users/53922 2021-08-14T10:16:00Z 2021-08-14T15:26:23Z <p>I have studied Multi-variable calculus. Now, I am thinking to study Tensor calculus. As it is an important topic in <a href="https://en.wikipedia.org/wiki/General_relativity">General Relativity<... https://math.codidact.com/posts/283295 In$w_{k + 1} - w_k = (\frac{1 - p}{p})^{exponent}(w_1 - w_0)$, why isn't exponent$k + 1$? DNB‭ https://math.codidact.com/users/53628 2021-08-11T08:23:25Z 2021-08-14T13:43:51Z <p>Please see the$r^k$underlined in red, which is$(\frac{1 - p}{p})^k$as defined by the green underlines.</p> <ol> <li> <p>How do you deduce that the exponent must be$k$? Why isn't the expo... https://math.codidact.com/posts/283387 Why "only 1/10,000 men with wives they abuse subsequently murder them" ≠ P(A|G,M) & "50% of husbands who murder their wives abused them” ≠ P(G|A)? DNB‭ https://math.codidact.com/users/53628 2021-08-14T07:33:58Z 2021-08-14T07:33:58Z <p>All emboldings are mine. See my red side line — the solution identifies <strong>"only 1 in 10,000 men with wives they abuse subsequently murder their wives"</strong> (in the problem statement) ... https://math.codidact.com/posts/283371 How can I exploit symmetry to intuit P(A wins) + P(B wins) = 1, without performing algebra? DNB‭ https://math.codidact.com/users/53628 2021-08-13T06:55:38Z 2021-08-13T06:55:38Z <p>I'm not asking about algebra that I can execute. How can I intuit P(A wins) + P(B wins) = 1 most quickly, without algebra? Any 15 year old can calculate that for the</p> <p>$p = 1/2$case,$\df... https://math.codidact.com/posts/283366 Scalar that varies across one or multiple scalar axes JohnDoea‭ https://math.codidact.com/users/36363 2021-08-13T01:16:31Z 2021-08-13T01:16:31Z <p>I have recently read:</p> <blockquote> <p>If anything has a quantifiable value that varies across one or multiple scalar axes, it's a signal, and you can study it.</p> </blockquote> <p>What ... https://math.codidact.com/posts/283281 How do mathematicians measure shape perimeters? JohnDoea‭ https://math.codidact.com/users/36363 2021-08-10T22:40:47Z 2021-08-13T00:58:39Z <p>When I create a circle on a computerized plane with a graphic editing program (such as Window's Paint), I can see a group of dots circling around an imagined central point.</p> <p>if the perime... https://math.codidact.com/posts/283297 How to vaticinate calculating $w_{k + 1} = w_1(1 + \dfrac{1- p}{p} + \dots + [\dfrac{1- p}{p}]^k)$ separately for $p = 1 - p$ and $p \neq 1 - p$? DNB‭ https://math.codidact.com/users/53628 2021-08-11T08:35:07Z 2021-08-11T08:36:43Z <p>Please see the orange, green, red underlines. 1. Why does $\color{limegreen}{w_{k + 1} = w_1(1 + \dfrac{1- p}{p} + \dots + p\dfrac{1- p}{p}]^k)}$ beget the two cases of $\color{red}p = 1 - p$ a... https://math.codidact.com/posts/283115 How does P(Monty opens door 2) = P(Monty opens door 3), and $P(\text{get car}|M_2)P(M_2) = P(\text{get car}|M_3)P(M_3)$? DNB‭ https://math.codidact.com/users/53628 2021-08-05T04:07:10Z 2021-08-10T07:20:03Z <p><a href="https://math.codidact.com/posts/283113">"Monty, who knows where the car is, then opens one of the two remaining doors. The door he opens always has a goat behind it (he never reveals th... https://math.codidact.com/posts/283254 How to visualize multiplication in the Odds form of Bayes's Theorem? DNB‭ https://math.codidact.com/users/53628 2021-08-10T00:27:13Z 2021-08-10T00:28:38Z <p>Here I'm asking solely about the circle pictograms. Please eschew numbers as much as possible. Please explain using solely the circle pictograms. Undeniably, I'm NOT asking about how to multipl... https://math.codidact.com/posts/283253 How to visualize division in the Odds form of Bayes's Theorem? DNB‭ https://math.codidact.com/users/53628 2021-08-10T00:04:16Z 2021-08-10T00:28:21Z <p>Here I'm asking solely about the circle pictograms. Please eschew referring to, or using, numbers as much as possible. Please explain using solely the circle pictograms. Undeniably, I'm NOT ask...