The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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229
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7answers
16k views

Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
1
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1answer
2k views

Equivalent systems of Linear equation

I've just begun to re-learn linear algebra because is so important, the book that I chose is naturally the Hoffman's for a lot of reason. Well, In the first chapter I'm stuck with the following, ...
0
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2answers
23 views

volume of surface of revolution around y axis

Can anyone help walk me through this problem style? I have a lot of homework problems like this and I really want to understand how to do these problems. Find the volume of the solid generated by ...
1
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1answer
42 views

Are minimizing a function and root finding the same?

What is the relationship between minimizing a function and finding a root of an equation? Are the the same? I know in both problem we have similar algorithms, such as gradient decent, or newton's ...
0
votes
0answers
13 views

Advice for Self-Study(application in financial engineering) [on hold]

I am currently studying statistics and I have such background: 1) Single and multivariable calculus (Stewart Calculus book) 2) Linear algebra(Strang's textbook) 3) Theory of probability(Ross book) ...
0
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0answers
16 views

Introductory Analysis: Abbott or Ross

I am attempting to self study analysis. I've heard mixed reviews on intro analysis books and it seems Abbott and Ross are proper for initial exposure. Does anyone have preference or recommendations on ...
0
votes
1answer
33 views

Logarithmic equation solution

If $ \frac {\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b}$,then what would be the value of $a^{b+c}.b^{c+a}.c^{a+b}$? I'm unable to proceed.
0
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1answer
20 views

Conditional expectation of two independent variables

If E(X) = E(X|Y), does this mean that the expected value of variable X is equal to the sum of expected values of X given all values of Y?
19
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5answers
573 views

Is it necessary to prove everything and solve every problem in the books? [on hold]

I am an undergraduate really passionate about the mathematics and microbiology. I have few big problems in learning which I would like to seek your advice. Whenever I study mathematical books (...
2
votes
0answers
24 views

Estimator bias and consistency

Let $x_1, x_2, \ldots,x_n$ be a simple random sample from a random variable $X$ with support $\{0,1,2,3,4\}$ and probability function $p(0)=\frac{5}{12}(1-\lambda)^2$, $p(1)=\lambda$, $p(2)=\lambda(1-\...
0
votes
1answer
25 views

What's wrong with this proof?- reverse triangle inequality

Subtract this inequality $-|y|\leq y \leq |y| $ , from this inequality $-|x|\leq x \leq |x|$ to get $-(|x|-|y|) \leq x-y \leq |x|-|y|$. Using the property $-a \leq x \leq a \implies |x| \leq a$, we ...
0
votes
1answer
39 views

Real analysis reference for statistician

I'm a undergraduate statistics student, I think that learn Real Analysis can be useful to me in some points, can anyone suggest a introductory book for self-study ? I'm already multivariate calculus, ...
1
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0answers
22 views

Matlab double integration result does not match with my self calculate

Here is a double integration, self learning $$ P=\int_{-w}^{w}\int_{l}^{\frac{y_h(x_b+w)}{x_h}+l}\frac{1}{2}\operatorname{erfc}\left[\frac{\log{\frac{z_h(y_b-l)}{y_h}}-\mu}{\sigma\sqrt2}\right]\space ...
0
votes
1answer
49 views

Counter Example for Limit of $\|f\|_p$ in infinity convergence, When Measure space is not finite [closed]

I found a proof for this fact that limit of $\|f\|_p$ when $p \to \infty $ is $\|f\|_{\infty}$ in here when $f:X \to R $ and $X \in L^p$ measure space is finite. But I need a counter example for ...
1
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4answers
152 views

If $\lim_{n\to\infty}a_{n}=l$, Then prove that $\lim_{n\to\infty}\frac{a_{1}+a_2+\cdot..+a_n}{n}=l$

Given $a_n$ be a sequence and IF $\lim_{n\to\infty}a_{n}=l$, Then prove that $\lim_{n\to\infty}\frac{a_{1}+a_2+\cdot..+a_n}{n}=l$ I do not know how to do this. Can someone help me with this? Thanks ...
1
vote
0answers
51 views

How to become fluent at reading math formulas? [closed]

As part of my studies, oftentimes I need to read research publications which contain mathematical formulas. Whenever I have to do that, I feel discouraged. Somehow I can not comprehend the ...
1
vote
1answer
42 views

a function to make it integrable

I am looking for a function f(x) that by itself is continues, and its integral is infinity but when multiply by $1/\log(1+e^{-x})$ makes it integrable. In other words, $$ \int_R \frac{1}{\log(1+e^{-x}...
0
votes
0answers
26 views

Which functions can be meaningful differentiable?

I have two functions: $f(x_1,x_2) = \begin{bmatrix} x_1*x_2^2 + x_1^3*x_2\\x_1^2*x_2 + x_1 + x_2^3\\\end{bmatrix}$ $g(u) = \begin{bmatrix} e^u \\ u^2 + u\\\end{bmatrix}$ The questions is:which of ...
1
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1answer
35 views

I've been working on Spivak and I'm on chapter 7. What are some good books to supplement Spivak for someone beginning to learn pure mathematics.

If I have too much difficulty with a concept/problem, then I'll just press on and solidify my understanding when the concept arises later by going back to it. This seems to be a lucrative method at ...
0
votes
1answer
473 views

How to decide whether PDE is Homogeneous or non-homogeneous.

I am studying second order PDE. And I have seen homogeneous and non-homogeneous PDE. But I cannot decide which one is homogeneous or non-homogeneous. For examples; (1) $(D^3-3D^2D'+4D'^3)u=0$ ...
0
votes
3answers
83 views

Probability: Prove that events are independent

I'm self-learning probability and struggle on the following task: If $A$ and $B$ are independent events, prove that $A \cup B$ and $A \cap B$ are also independent. This is one of those cases where ...
1
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1answer
45 views

A question about Lagrange multiplier in optimization

I read @amoeba 's answer in this post, PCA optimization problem is $$ \underset{\mathbf w}{\text{maximize}}~~ \mathbf w^\top \mathbf{Cw} \\ \text{s.t.}~~~~~~ \|\mathbf w\|_2=1 $$ where $\mathbf C$ ...
2
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3answers
73 views

Finding an approximation of a function's root

I have the polynomial function $f (x) = x^5+2x^2+1$. I am trying to find an approximation to its root in $[-2,-1]$, with the precision of $0.1$, and with a minimal number of steps. The answer I was ...
1
vote
1answer
21 views

Showing weak law of large numbers holds

My question: $\{X_n\}$ is a sequence of random variables. Var$(X_n)\le C\ \ \forall \ n$ and $\rho_{ij}=$Cov$(X_i,X_j)\to 0 $ as $|i-j|\to \infty$ . Show WLLN holds. In my book there are 3 ...
0
votes
1answer
22 views

Finding a function based on the tangent line

I need your help with this question: The tangent line to the function f(x) at x=1 is y=3x-2. Find f(x) (without using integrals). I know that the derivative at x=1 should be 3, but without more ...
1
vote
1answer
461 views

Expected value of division

Let $X,Y$ and $Z$ be three indenependent real valued random variables. Al with finite second momennt and all with mean $0$ and variance $1$. Define $$ W= \frac{X+YZ}{\sqrt{1+Z^2}} $$ Show that ...
2
votes
2answers
75 views

Probability: Balls in baskets

I'm self learning and I stumbled upon the following exercise but I'm not sure if I solved it correct as I'm very new to this. Problem: 7 balls fall independently into 7 baskets. Let $X_i$ = number of ...
3
votes
4answers
347 views

Measure theory for self study. [duplicate]

I have good knowledge of Elementary Real analysis. Now I'd like to study measure theory by myself (self-study). So please give me direction for where to start? Which book is good for starting? I have ...
4
votes
1answer
65 views

Study materials to help understand the generalized Stokes' theorem both intuitively and rigorously?

Dear MSE: My goal is to understand the generalized Stokes' theorem both intuitively and rigorously. Could someone give advice or recommend study materials to help understand the generalized Stokes' ...
0
votes
2answers
31 views

One Variabe Chain Rule

$f(x)$ and $g(x)$ differentiable functions. Let $h(x)=f(g(x))$. It is given that $g(2)=1$, $g'(2)=e^{-2}$ and $h'(2)=2/e$. I need to find $f'(1)$. I know how to find $f'(2)$. But $f'(1)$? $f'(2)$ ...
2
votes
2answers
35 views

Calculus: Differentiable Function and Tangent Line

I am not sure how to approach this question: Let $f(x)$ be a continuous and differentiable function of order 2. Let $f ''(x)>0$ for all values of $x$. The tangent line to the function at $x=1$ ...
2
votes
2answers
71 views

Probability: breaking keyboard

I'm trying to self-learn theory of probability, I came across the following basic problem that I think I solved but I'm not sure as I'm very new to this. Problem: A keyboard manufacturer states that ...
1
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1answer
47 views

Probability with coins

I'm self learning and I stumbled upon the following task, but I struggle to find the solution: Two players flip coins. The first player flips 3 coins, the second player flips 2 coins. The player that ...
0
votes
1answer
33 views

Probability Question - Paper Notes in a bag

I could do with some help with this question. In a bag there are 18 paper notes. On five of them there is the digit 2, on seven the digit 3, and on six the digit 5. A man takes 3 notes by random. If ...
0
votes
3answers
61 views

To prove $\sup B \leq \sup A$

Assume $A$ and $B$ are non empty and bounded above and satisfy $B \subseteq A$. Show that $\sup B \leq \sup A$ I am thinking of proving using contradiction, but I am getting nowhere. Someone please ...
1
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1answer
46 views

To show that $\sup B=\inf A$

How do i show that To show that $\sup B=\inf A$ , where $A$ is set bounded below and B ={$b \in R$ : $b$ is a lower bound for $A$} Let $x=\sup B$ and $l=\inf A$. Now All lower bounds of A are less ...
10
votes
3answers
274 views

How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed]

[Please reditect me to a different site/sub-site/pretty-much-any-relevent-place if I've posted the question in the wrong forum, please do not downvote before attempting to redirect me to the adequate ...
1
vote
0answers
38 views

Characterize the $\mu^*$- measurable sets where $\mu^∗ = \lambda^* \circ \text{proj}_1 $ and $ \lambda^*$ is the Lebesgue outer measure

Hi I'm working with Cohn's book and I have other problem with the necessity condition, I'd appreciate any help. Let $\lambda^*$ the Lebesgue outer measure on $\bf{R}$, and let $\pi$ be the ...
0
votes
2answers
59 views

Self Study of number theory

I have always wanted to learn about number theory. There is actually no one here who can teach me and it's also not in my regular school syllabus, but the greatness of number theory attracts me ...
-1
votes
1answer
42 views

Proof for functions of matrix [closed]

Let $A \in \text{Mat} (n,n,\mathbb{C})$. Let $I$ be a subset of $\mathbb{R}$ or $\mathbb{C}$. Further, let $f:I\to\mathbb{C}$ and $g:I\to\mathbb{C}$ be two functions for which $f(A)$ and $g(A)$ are ...
1
vote
0answers
99 views

Finding total number of multi-sets

I am provided with a multi-set, let's say S with elements as [num1, num2, num3] and these elements are integers (both negative as well as non negative). As this is a multi-set, elements in the multi-...
0
votes
0answers
22 views

Composition of substitutions of SLD tree

I found a question on my university past paper and it asked to get the SLD tree from a computation rule using some rules and facts. However I obtained the answer and to complete the question I have to ...
2
votes
2answers
4k views

How to find a basis of an image of a linear transformation?

I apologize for asking a question though there are pretty much questions on math.stackexchange with the same title, but the answers on them are still not clear for me. I have this linear operator: $$...
0
votes
1answer
39 views

Joint pdf of X and Y with absolute value

Question. Joint probability function of continuous probability X, Y is here : $f_{X,Y}(x,y) = k(|x|-|y|) \ \ \ \ \ \ \ \ \ \ (-1< y< x< 2)$ Then what is k? I mean how can I differentiate ...
0
votes
1answer
48 views

Transformation matrix

For $x \in \mathbb{C}$ define $A,B \in M(3\times3, \mathbb{C})$ as $$ A = \begin{pmatrix} x & 0 & 0 \\ 0 & x & 1 \\ 0 & 0 & x \end{pmatrix}$$ and $$ B = \begin{pmatrix} x & ...
15
votes
2answers
943 views

Am I reading Bott - Tu right?

Summary: I'm finding Bott - Tu to be too brief and terse. I constantly have to look elsewhere to fill in details. This is not time-efficient. Am I missing something? If not - what other books do ...
81
votes
16answers
11k views

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of ...
3
votes
1answer
51 views

I need to re-learn all highschool level mathemetics in order to attend college. (Please Help) [duplicate]

I know this isn't a research level question, but a lot of you teach, and I'm not sure where else to turn. I will just shoot straight: I am 30 years old. I have not done any type of true mathematics ...
0
votes
1answer
25 views

Understanding the definition of $UV$, where $U$ and $V$ are ideals in a ring

I have the following question at hand: I. N. Herstein Topics in Algebra: Ideals and Quotient Rings : Qn $3.4.6$ If$\ \ U,V$ are ideals of $\ R\ $,let $UV$ be the set of all elements that can be ...