# Questions tagged [self-learning]

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.

3,130 questions
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### Dividing higher-order algebraic expressions

I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am currently on the "Algebra" section. I've been working with division of algebraic expressions, and the book ...
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### To prove special case when a <0

Original Theorem : Given two real numbers $a$ and $b$ with $a < b$, where $a \geq 0$ there exists a rational number $r$ satisfying $a < r < b$. To be proven from above theorem : Without ...
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### Understanding proof of density of $\mathbb{Q}$ in $\mathbb{R}$

I am trouble getting this proof and idea behind it. I have taken example of a and b as (3,4). I have problem with understanding the part where author writes " first step is to choose n large enough so ...
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### Obtaining a second linearly independent solution in an ODE using a known one.

Given the following problem: $\dot{x}(t) = A(t)x(t)$, say A is two by two. We are given a solution $\xi_1$. How can I use this in order to find a second linearly independent solution? Is there a ...
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Let $A$ be bounded below and $B = \{b \in \mathbb{R} : b$ is a lower bound for $A\}$. My Work Now to understand I assumed some values, like set $A = (1,4)$ and $\inf A=1$ and so set $B = (-\infty ... 2answers 57 views ### Are there non-standard roads to research available for gifted students? This is my first post here so I hope this is the right place to ask about this. I am a 22 year old math fanatic in Sweden and have been put in the awkward position of having self-studied quite ... 0answers 20 views ### smart way to calculate expected value of a difficult expectation I have a non-normalized posterior distribution of which I'd like to calculate the expected value: $$P(\mu|\{x_i\})={\Large\Pi_i}\Big{[} \frac{a^v\Gamma(v+\frac{1}{2})}{\sqrt {2\pi}\Gamma(v)} (\frac{1}... 1answer 11 views ### Distribution of negative of standard normal variate Let X be a standard normal variate. Consider another variate Y such that$$Y = \begin{cases} -X & \text{for$-2 < X< 2$} \\ X & \text{otherwise}. \end{cases}$$I need to check ... 3answers 49 views ### Stumped by a pretty basic fraction division I'm self-studying through Stroud & Booths's amazing "Engineering Mathematics", 7th Edition, and am still on the "Arithmetic" section. Even though I've gone through the whole chapter and a lot of ... 2answers 38 views ### Constructing a probability space I am trying to understand the proof that$$\mathbb Eg(X) = \int_\mathbb R g(x)d\mu_X(x),$$where X is a random variable on a probabiliby space (\Omega, \mathcal F, \mathbb P). It starts with the ... 1answer 26 views ### Rescale part of a matrix to bound the maximum eigenvalue module I am working with a matrix A \in \mathbb{R}^{4 \times 4} with structure: A = \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} & a_{1,4} \\ a_{2,1} & a_{2,2} & a_{2,3} & a_{2,4} \... 1answer 33 views ### The average time before a person find their group Imagine there are N people throwing a party. For any two of them, the time before they meet each other and stick together thereafter is independent, and obeys an exponential distribution whose \... 0answers 40 views ### Derivative of \Gamma (1)=-\gamma How to compute \Gamma'(1)=-\gamma where \gamma is Euler's constant i-e the limit of the series (1+\frac12 +\frac13 +\frac14 +...+\frac1n)-\ln(n) where n \rightarrow \infty \gamma= 0.... 0answers 15 views ### Coverting denary numbers into octal, binary and hexadecimal form I'm self studying (after not touching any match for a good 15 years) from Stroud & Booth's amazing "Engineering Mathematics". (This example is from page 55 of the 7th ediction, F.138 of the first ... 1answer 22 views ### Regression model + expected value, variance and autocorrelation of the error term Consider this regression model$$Y_t=X_t\beta+\epsilon_t, ~~~~~~~~~~\epsilon_t \sim WN(0, \sigma^2_{\epsilon})$$with 3 different specifications of the error term: \epsilon_t=\alpha_1\epsilon_{t-1}+... 1answer 35 views ### Linear regression - find b, s^2, R^2 Suppose you want to fit the model Y=\alpha+\beta X+\epsilon but you don't have the full data set \left[\begin{matrix}y&X\\\end{matrix}\right]=C. Instead you only have:$$C'C=\begin{bmatrix} ... 1answer 29 views ### Confidence interval for Poisson variables Let$X_{i},...,X_{n}$be i.i.d. Poisson random variables with parameter$\lambda>0$I have: $$\bar{X}={(1/n)\sum_{i=1}^n X_i}.$$ Find two sequences$(a_n)_{n>=1}$and$(b_n)_{n>=1}$such ... 0answers 177 views ### Which books to use for self-studying calculus and linear algebra? [closed] After years of divorce with mathematics I decided to come back to it. I studied computer science, so had quite a lot of maths in university, but though passing the exams, I didn't feel I fully grasped ... 0answers 33 views ### Graph theory and compact metric spaces: is it possible? Is there a theory to study mathematical objects that are graphs but being its nodes higher dimensional compact metric spaces? Thanks! 1answer 28 views ### Quadratic form inequality? I'm working on a problem, and to finish it I need to show that $$\mu^T (I-X(X^TX)^{-1}X^T)\mu \geq 0$$ But I'm stuck at showing this. My first thought was to write this as trace$$tr(\mu^T\mu) \... 0answers 11 views ### Separation of variables to solve Laplace's equation for the V in a cube 3D rectangular coordinates Watch this videoLaplacian in 3D and tell me whether$C_{n,m}$missing y in the argument of$\cosh{\sqrt{(\frac{n\pi}{a})^2+(\frac{m\pi}{a})^2}}$in the denominator. So the final answer is$V_{(x,y,z)}=...
Let $f : U × U → \mathbb{R}$ be a bilinear form such that $f (u, u) > 0$ and $f (v, v) < 0$ for some $u, v \in U$. I would like to show that $u, v$ are linearly independent. We have that $u , v$...