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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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 ...
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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 $\{k_n\}$: $$k_n(U_n-\...
0
votes
1answer
36 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
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0answers
14 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 $\tau^2$...
2
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2answers
64 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 wondering ...
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0answers
23 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
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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 ...
44
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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
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1answer
60 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
69 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
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1answer
14 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 ...
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4answers
102 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)! \bigg[\sum_{i=0}^{n-2}{\frac{(-1)...
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votes
2answers
188 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
46 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
32 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
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0answers
47 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
103 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
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0answers
31 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 ...
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0answers
34 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
140 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
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0answers
28 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
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0answers
67 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 ...
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0answers
23 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
192 views

Self study plan [closed]

I don't want to go to college and I came up with plan in the following order: ...
3
votes
4answers
162 views

What's the best way for an engineer to learn “real” math?

I'm an electrical/computer engineering student and have taken fair number of engineering math courses. In addition to Calc 1/2/3 (differential, integral and multivariable respectfully), I've also ...
113
votes
9answers
9k views

What's the point in being a “skeptical” learner [closed]

I have a big problem: When I read any mathematical text I'm very skeptical. I feel the need to check every detail of proofs and I ask myself very dumb questions like the following: "is the map well ...
1
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1answer
49 views

Why is the map $f(x)=e^{i2\pi x}$ from $[0, 1)$ to the unit circle continuous?

This seems to be a really silly question, I just couldn't think it straight. The definition of a continuous map: $f: X \to Y$ is continuous if for any open set $U$ in $Y$ , $f^{-1}(U)$ is open in $X$...
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0answers
51 views

How do I memorize mathematical proofs?

I first started wanting to know about the derivation of theorems because certain ones help you memorize the theorems better. But as I take harder math classes, it turns out better for me to use ...
2
votes
3answers
141 views

Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
6
votes
3answers
254 views

How to Catch Up?

I am finishing up my bachelor's degree in mathematics at the University of North Florida, and I plan on going to graduate school, but I feel very behind. One of my professor's gave us this problem: $...
4
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2answers
123 views

recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number theory....
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votes
1answer
33 views

Weak law of large numbers without figuring out the distribution.

let $X_{1},X_{2},\dots$ be i.i.d. random variables with common probability density function. $$f(x)=\begin{cases} \frac{1}{2}e^{-\left(\frac{x-1}{2}\right)},& \text{if } x>1\\0,& \text{...
1
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0answers
68 views

How to learn math by self-teaching [Without books, or outside help]

I'm thinking along the lines of attempting to explore mathematics by making my own discoveries as if it's the new frontier. As if I was a mathematician from 2000 B.C. I know this sounds really ...
1
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1answer
35 views

Testing of hypothesis

Following is a question from my textbook. My approach is different from one explained in the book. I cannot understand what is wrong with my solution. I have explained both solutions below. Kindly ...
1
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1answer
26 views

What does “modulo equivalence relationship” mean?

I am reading something on completion of metric spaces and it says: Let $\hat S$ be $\mathcal{C}$ modulo equivalence relationship of co-Cauchy sequences. Where $\mathcal{C}$ is the set is all ...
0
votes
1answer
65 views

Re-learning Maths for physics (particle and space) [closed]

I know there's a lot of "how do I learn maths" questions out there but I wanted to lay down my history and interest to possibly get a better approach. When I was in secondary school ( high school ) ...
0
votes
0answers
30 views

Is reading a textbook and doing problems the best way to self-study game theory?

In preparation for a research position, I'm supposed to self-study the first six chapters of Osborne Introduction to Game Theory over the next two weeks, and complete corresponding problem sets. Is ...
1
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1answer
50 views

Textbook Accompanying Naive Set Theory

I'm in the process of self-studying from the very popular Halmos book "Naive Set Theory" and I must say I can say only the best about the book. However, although the book has some excercises I would ...
1
vote
1answer
16 views

Functions of Mixing random variables

If $X_t$ and $Y_t$ are independent random processes that are $\alpha$-mixing, is a linear combination, $aX_t + bY_t$ also $\alpha$-mixing? What about other functions $f(X_t,Y_t)$? How does one ...
4
votes
1answer
72 views

Looking Away from the Temptations of the Solution Key [closed]

This is quite a soft question and I believe that it is a very important one and one that many self-learners can relate to. So I recently was going through a problem set in topology and I came across ...
1
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2answers
144 views

Should I continue trying to solve Spivak or pick up a lighter book?

Some background: I have no mathematical maturity. Last year I completed my schooling and the only time I picked up a math/science book was when exams were due, needless to say I haven't actually given ...
2
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0answers
26 views

Website for sharing solutions/proof verification?

Is there a website for sharing solutions to exercises in math books? I'm self-studying math and I find solution manuals like this very helpful. When I do an exercise, I usually scribble down a few ...
1
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1answer
34 views

$f(\alpha _I) \ne 0$

I need help in this question... Let $F$ be a field of characteristic zero and let $V$ be a finite dimensional vector space over field $F$. If $\alpha _1,\dots , \alpha_m$ are finitely many vectors in ...
0
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0answers
15 views

Exterior Robin Boundry Condition

Exterior Robin boundary is expressed as the following in the book $\partial{u}/ \partial{v}-\lambda u=f$ on the boundary and $v$ is normal. Also u satisfies Laplace Equation in exterior domain in $R^...
0
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1answer
66 views

infinite subset of discrete metric space is not compact

The question is Im not really sure how to go about this So far i am trying to show that for an open cover of the infinite subset X, there isn't a finite sub cover and therefore X is not compact I ...
4
votes
1answer
199 views

Properties of Weak Convergence of Probability Measures on Product Spaces

EDIT: For the Bounty, I made a substantial edit revision concerning the structure of the question, to make it more readable (hopefully). Moreover I added a question on problem 2.7 of Billingsley’s ...
0
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2answers
83 views

What are some good resources to review basic university calculus, years later?

So, I have reason to be returning to school, many years (5+) after my last attendance; and although I took (and passed, barely, after much strife) Calculus 1 and 2 at my previous university, I am very ...
3
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3answers
113 views

Permutations and combinations textbook recommendations

I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. ...