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_.

learn more… | top users | synonyms (1)

0
votes
5answers
20 views

Prove the continuity on an open interval

I need to show, that function $f(x) =\frac{2x +3}{x-2}$ is continuous on the interval $(2,\infty)$ My attempt: We should find the right-hand limit to prove the continuity: and this limit is equal to ...
0
votes
2answers
36 views

What exactly does f'(x)=0 imply from the definition of differentiability?

Let f be a real valued function satisfying $|f (x) −f (a)| ≤ C|x−a|^γ$, for some γ > 0 and C >0. (a) If γ = 1, show that f is continuous at a; (b) If γ > 1, show that f is ...
1
vote
1answer
30 views

What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
2
votes
3answers
72 views

Showing $\mathbb{Q} \times \mathbb{Q}$ is not a field

I am revising and have come across the question Show that $\mathbb{Q} \times \mathbb{Q}$ with element-wise addition and multiplication is not a field I don't understand how to go about this, do i ...
0
votes
1answer
38 views

How should one without any university mathematics background study mathematical logic?

How should someone who hasn't studied any math at a university level start studying mathematical logic? (There are already questions like this but they mostly focus on book recommendation for people ...
0
votes
1answer
32 views

Does equality of the sum of two such series imply equality of each term of that series?

Let a(1)< a(2) < ..< a(m) and b(1)< b(2)<..< b(n) be real numbers such that $$\sum_{i=1}^m |a(i)-x| = \sum_{j=1}^n |b(j)-x|$$ for all x belonging to R. Show that m=n and ...
2
votes
1answer
27 views

Find dimension of a Vector Space.

Let $E=\{1,2,\ldots,n\}$, where $n$ is odd. $V$ is the vector space of all functions mapping from $E$ to $\mathbb R^3$. Find $\dim(V)$. Consider $T:V\to V$ such that $$ Tf(k)=[f(k)+f(n+1-k)].$$ ...
1
vote
3answers
63 views

What does x equivalent to 2 mod 15 mean?

I came across the following question: Consider the following system of equivalences of integers. $$ x \equiv 2 \bmod{15} $$ $$ x \equiv 4 \bmod{21} $$ The number of solutions in $x$, where $1\le ...
3
votes
2answers
47 views

learning linear algebra [duplicate]

So I'm a college student that has taken 3 semesters of calc/diff eq/linear algebra and I think linear algebra has been by far my favorite course so far and I would love to know more in the subject, ...
5
votes
0answers
75 views

How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very ...
-2
votes
1answer
33 views

I'm completely blanking on a simple exponent problem [closed]

Solve for $x$: $5x^{0.7}$ $=$ $y$
-1
votes
1answer
23 views

Markov Chain Market Share Model [closed]

Given that, $$ \begin{matrix} & Coke & Pepsi \\ Coke & 0.8 & 0.2 \\ Pepsi & 0.3 & 0.7 \\ \end{matrix} $$ What is the current market ...
1
vote
2answers
26 views

3D Integration: Why does the shadow method work?

In the link http://mathinsight.org/triple_integral_shadow_method, the shadow method for calculating triple integrals is described. The procedure is given as $$\iiint_Df(x_1,x_2,x_3)\text{d}V=\iint_R ...
0
votes
1answer
20 views

What is the domain of this random variable?

I've been self-studying Introduction to Statistical Learning. From page 16 of the book: "...suppose that we observe a quantitative response $Y$ and $p$ different predictors, $X_1$, $X_2$, ...
0
votes
0answers
25 views

Difficulty during self-studying unique set proofs

I have been following Velleman's How to prove it and working through it on my own. I am working full time now so I can only study after work without any other help. It's been going fairly ok until I ...
1
vote
1answer
54 views

Should I remember the proof of mathematical theorems(every step)?

The problem is, that when I am reading the proof of mathematical theorem(in my case - it is calculus), U understand the idea and every step of proof. But i can't prove the theorem individualy even if ...
1
vote
1answer
35 views

Good book for self study of Continued Fractions

Does anyone have a recommendation for a rigorous while readable book to use for the self study of continued fractions? PS - As examples of "rigorous while readable book" for self-learning, A. ...
1
vote
0answers
36 views

What are hypergeometric functions in layman terms?

Could someone please explain what are these in layman terms? Someone here told me that and I still can't figure out what they mean on my own after giving Google a number of hits. Wikipedia says this: ...
0
votes
2answers
26 views

$f$ twice differentiable, $f(a)=f(b)=g(a)=g(b)=0$ $\implies$ $\int_a^b f''(x)g(x)dx=\int_a^bf(x)g''(x)dx$

$f:[a,b]\rightarrow \mathbb{R}$ twice continuously differentiable, $f(a)=f(b)=g(a)=g(b)=0$ $\implies$ $\int_a^b f''(x)g(x)dx=\int_a^bf(x)g''(x)dx$ I think this has something to do with integration by ...
0
votes
0answers
34 views

Further Readings on Linear Algebra

I am currently working on Linear Algebra Done right by Sheldon Axler. Out of curiosity I am wondering what would be the next material for Linear Algebra after this book?
0
votes
1answer
15 views

how to find AIC values for both models using R software?

I'm studying survival analysis. I estimated both Cox regression model and Buckley&James regression model. In order to determine which model is better for my dataset, I used Akaike Information ...
0
votes
1answer
38 views

What is the closed form representation of the sum of the first $\text{int}(n/2)$ terms of binomial expansion $(f+(1-f))^n$?

Say that we have this polynomial $(f + (1-f))^n$ where $f$ and $n$ are some positive real numbers, except that $f$ is a constant, but $n$ is a variable. That term can be expanded using the binomial ...
2
votes
1answer
21 views

Help with multivariable transfer function

I am looking to find the transfer function from w to z in this loop. I have been trying for a while looking all the relationships but just don't know how to express w in terms of r,d and n and then ...
0
votes
1answer
45 views

Very basic probability question (counting).

If you choose three jokes randomly from an inventory of 12 each month, what is the probability that, in any given month, at least one of the three jokes will be different from the jokes you told the ...
0
votes
0answers
12 views

Existence of asymptotic variance for an estimator when it doesn't converge to normal.

The definition of an asymptotic variance says: For sequence of estimators $\mathbf{U}=(U_1, U_2,...)$, where: $U_i=U_i(X_1,...,X_i)$, if for a sequence of constants $\{k_n\}$: ...
0
votes
1answer
32 views

Combinatorics books that tackle and intermediate level [duplicate]

I have been studying enumerative combinatorics using the book by George Martin: Counting: the art of enumerative combinatorics. I would like to continue learning the subject, but the problem is that I ...
0
votes
0answers
12 views

Comparing definitions of limiting and asymptotic variances - what is the intuition behind?

In Casella's inference, it says: Definition 10.1.7: For an estimator $T_n$, if $\lim_{n\to \infty} k_n Var T_n = \tau^2 < \infty$, where $\{k_n\}$ is a sequence of constants, then ...
2
votes
2answers
62 views

Confusion of expectation of maximum exponential random variables

Let $X_i \sim \mathrm{Exp}(\lambda_i)$, $i = 1,2,3$ be independent, find $\mathsf E(\max(X_i) \mid X_1<X_2<X_3)$ I have found out two solutions as follow: Solution 1 I am ...
1
vote
0answers
20 views

Book search on statistics

I am searching a book that Analysis of Failure and Survival Data (Chapman & Hall/CRC Texts in Statistical Science) by Peter Smith. Its link is here. I tried to buy it from Amazon, but it is out ...
0
votes
1answer
13 views

when fitting to linear model or non-linear model

What is the residual standard deviation? Can I see whether the model I used is accurate or not by looking at this measure? In fact, I try to understand whether my data set is fitting to linear ...
0
votes
0answers
22 views

Other method instead of using OLS estimation

enter image description here I get that the resulting beta* is the same as the estimated beta 1. But I think something is wrong. If the researcher is true, then why do we learn the OLS estimation, ...
44
votes
25answers
3k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
1
vote
1answer
57 views

a*b = a/b = b/a (what's this symmetry called?)

I was playing around with numbers the other day, and I found an interesting symmetry, that I would like to know if it has any specific name assigned to it. Let's assume the notation n:a to refer to ...
2
votes
1answer
63 views

AM, GM and HM relationship

Question: Prove that $DO$, $DB$ and $DE$ are AM, GM and HM of $a$ and $b$ in the given figure. It is given that $OA$ us the radius of this semi-circle. I have proved $DO$ as AM of $a$ and $b$ ...
0
votes
1answer
10 views

Proving that product of 2 pgfs is a pgf - last obstacle

Let $G_1, G_2$ be probability generating functions of some probability distributions. Prove that $G_1G_2$ is pgf. What I have: $G_1=\sum_{n=0}^\infty p_nz^n$ and $G_2=\sum_{k=0}^\infty q_kz^k$ where ...
1
vote
4answers
101 views

Any simpler expression for$\frac{\sum_{k=2}^{n-2}{k\big(\sum_{i=0}^{n-2}\frac{(-1)^i}{i!}\big)}}{n\sum_{i=0}^{n}\frac{(-1)^i}{i!}}$

Is there any simpler form for the following expression: $$ \frac{\sum_{k=2}^{n-2}{k\left(\sum_{i=0}^{n-2}\frac{(-1)^i}{i!}\right)}}{n\sum_{i=0}^{n}\frac{(-1)^i}{i!}}$$ Because I have to compute this ...
2
votes
3answers
60 views

Is $n! \sum_{i=0}^n{\frac{(-1)^i}{i!}}- (n-1)! \bigg[\sum_{i=0}^{n-2}{\frac{(-1)^i}{i!}}+…+\sum_{i=0}^{2}{\frac{(-1)^i}{i!}}\bigg]=(n-1)!$ true?

I am in the middle of doing a problem and has this sort of expression. I have a feeling that the following equality holds: $$n! \sum_{i=0}^n{\frac{(-1)^i}{i!}}- (n-1)! ...
-1
votes
2answers
184 views

How to study for hard math proofs?

Most of the content is new to me and there are a lot of theorems and proofs that I am learning; not that I need to know all of them but I enjoy to learn more. Some of the concepts (like open sets) or ...
1
vote
1answer
42 views

where to find good examples of combinatorics (online resources only please)?

one of the most beautiful/hard things in the study of combinatorics is the fact that is not just about memorizing 4 or 5 formulae but developing a whole reasoning ability. Such thing can only be ...
-1
votes
1answer
28 views

A 3D curve correlation

Forgive me if its too basic, but i am looking to read some materials about a subject in which i don't know its name/field. So what we need to do, is to get a 3 axises curve, with unknown shape, that ...
1
vote
0answers
45 views

Are there any online sources/books that could help me further study set theory?

I would like to study set theory more intuitively. Searching the internet for this will only provide study for the basics of set theory (unions, intersections, etc.). There are topics I would like to ...
-2
votes
2answers
66 views

looking for set theory problems or exercises WITH solutions

I have a problem in that I have a burning desire to master set theory and cannot find worksheets with solutions dealing with elementary set theory. This is a really big chink in my chain in that if I ...
1
vote
0answers
27 views

sufficiency of linear combination of bernoulli random variables. [closed]

Let $ X_1$, $X_2$, $X_3$ be a set of three independent Bernoulli random variables with unknown parameter $p$ = $P(X_i=1)$. Where it is given that $p$ = $X_1 + X_2 + X_3 $ is sufficient for $p$. Show ...
1
vote
0answers
20 views

Joint probability distribution of functions of random variables

Let $X_1$ and $X_2$ be jointly continuous random variables with joint probability density function $f(x_1,x_2)$.It is sometimes necessary to obtain the joint distribution of the random variables $Y_1$ ...
4
votes
2answers
66 views

Are there powerful ways to use the topological definition of continuity in real analysis?

In the lectures for introductory real analysis, my professor repeatedly told the class that the topological definition of continuity (preimage of open is open) is the most powerful version of ...
0
votes
0answers
27 views

Understanding foundational terms: notions, objects and meta-objects

I am trying to take my problem solving skill to next level. It looks like It takes a lot of mathematical discipline. Here, This post buys me to get better at proof writing. So, I think is useful to ...
3
votes
0answers
63 views

Self Learning — Number Theory

I was wondering if there were any good online courses/lecture videos (preferably courses/videos but books would work too) for self learning algebraic number theory. I have seen sites like MIT ...
1
vote
0answers
22 views

Good introductory book on mathematical morphology

What is a good introductory book on mathematical morphology? It should outline the basic theory and a focus on applications would be nice. If possible, it should be approachable for a determined ...
0
votes
1answer
24 views

Marginilizing in multivariate Statistical Distributions

Suppose we draw $X = [x_1,...,x_i,...x_r,...,x_t...,x_j,...x_N]$ from $N(0,\Sigma)$. is there any way to compute $E[x_ix_j]$ and how about $E[x_ix_jx_rx_t]$ ? How can I compute the marginal ...
4
votes
3answers
161 views

Self study plan [closed]

I don't want to go to college and I came up with plan in the following order: ...