Questions about the process of studying mathematics without formal instruction.

learn more… | top users | synonyms (1)

0
votes
0answers
5 views

Linear functional and Hessian

Consider the vector space $\mathbb{R}^n$ provided with the usual inner product $<.,.>$. Let $A\in \mathbb{M}_n(\mathbb{R})$ a invertible matrix, $b\in\mathbb{R}^n$ and $J:\mathbb{R}^n\rightarrow ...
0
votes
1answer
15 views

Relationship between centralization and floating-point arithmetic

Suppose I have a problem of least squares where I have $n$ independents regressor variables $x_i$, and suppose I applied the process of centralization and scaling to this variable through ...
1
vote
1answer
35 views

Cholesky algorithm

Good afternoon everyone, I'm in need of a factoring algorithm cholesky and algorithms to solve upper and lower triangular systems, but I'm not finding any work in that octave. Recalling that need the ...
2
votes
3answers
44 views

Least Squares method and Octave/Matlab [on hold]

I'll try to be as clear as possible so that you understand what I'm trying to do and can help me I have twelve pairs of data $(x_1,y_1),....,(x_{12},y_{12})$ and from this data we established a model ...
2
votes
1answer
7k views

What is the standard form of a linear programming (LP) problem?

According to Bertsimas' text, the standard form of a LP problem is: According to Vanderbei's text, the standard form of a LP problem is: So, what is the standard form of a linear programming ...
7
votes
3answers
5k views

Functional analysis textbook (or course) with complete solutions to exercises

I am a Ph.D. student in economics and I plan to study functional analysis by myself either this winter or the next summer. I am currently looking for a textbook, and since I am studying it by myself, ...
0
votes
1answer
330 views

Book on discrete mathematics for self study

I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read ...
0
votes
1answer
21 views

statistics - estimator and biased unbiased [on hold]

I am having a problem with this my solving proceducre is that $E(\theta)= 1/2E(X-0.1)+ 1/2E(X+0.1) = 1/2$ So, $E(\theta)1/2 - (\theta)1/2 = 0$ which means it is unbiased. Variance is ...
0
votes
1answer
14 views

calculating variance problem

When calculate variance, It's 1/2E((x-0.1)^2)+1/2E((x+0.1)^2)-E(x)^2 Is it right? So, the answer is 0.01 Am I missing something? And whenever I calculate the vatiance of the second estimator ...
0
votes
1answer
23 views

Probability of winning a simple game

Consider two players, A and B start with 8 and 6 stones respectively. A rolls a six-sided die to determine how many stones to take from B. B performs the same task to determine how many stones to ...
-2
votes
1answer
18 views

variance and sample confused

when solving (b) Is variance $$V(\frac{1}{2}(x_1+x_2)) = \frac{1}{4}V(x_1+x_2)= \frac{1}{4}(v(x_1)+v(x_2))= \frac{1}{2}\sigma^2$$ or should I divide variance by the sample size so that ...
2
votes
2answers
29 views

How to find general inverse of a matrix

Find the general inverse (G) of the matrix $$A=\begin{bmatrix}1 & 2 & 3 \\4 & 5 & 6\end{bmatrix}$$ Also check that $AGA=A$ I am new in G- inverse calculation. I understand ...
0
votes
2answers
56 views

Seeking advice from all [on hold]

I've come back to education after 4 years and I feel very out of practice, currently I am studying a-levels and need to pass with excellent grades for my ill fathers sake as it is his last wish. I am ...
1
vote
1answer
22 views

Conditional expectation and rao-blacwell

I am studying on UMVUE, and I'm struggling to find that conditional expectation Let $X_1,\ldots,X_n$ random sample of $X\sim U[0,\theta]$. i) Show that $2X_1$ is a unbiased estimator for $\theta$ and ...
3
votes
0answers
55 views

How much algebra is necessary to understand Rudin's “Real and Complex Analysis”?

I've been reading up on the finite element method, and the text many people recommend is The Mathematical Theory of Finite Element Methods by Brenner and Scott. As part of the background, the authors ...
0
votes
0answers
10 views

Rao-Blackwell theorem and uniform distribution

Let $X_1,...,X_n$ random sample of $X$~$U[0,\theta]$.Use the fact that $X_{(n)}=max(X_1,..,X_n)$ is a sufficient and complete statistic and Rao-Blackwell theorem for show that ...
0
votes
0answers
16 views

Rao-Blackwell theorem and conditional distribution

Let $X_1,..,X_n$ random sample of $X\sim\text{Exp}(\lambda)$ with $f(x;\lambda)=\frac{1}{\lambda}e^{-\frac{1}{\lambda}x}I_{[0,\infty]}(x)$ i) Find a unbiased estimator of $\lambda$ based ...
3
votes
1answer
49 views

A question related to reflection principle

Question: $$P(X_1\gt 0, ..., X_n\gt 0, X_n=a-b)=?$$ Its Answer: $= (1,1) \rightarrow (n,a-b) $ that meet neither touch nor cross paths. $=[(1,1) \rightarrow (n,a-b) \ \ \text{all ...
17
votes
10answers
29k views

Calculus book recommendations (for complete beginner)

Well I have not started calculus yet but I am really keen to. I would love if you suggest some books. Points to be noted: I really don't like the way textbooks are written so please no "textbooks" ...
2
votes
0answers
31 views

How should I learn the Mathematical Proofs?

S.E advisers, What is the most efficient way to learn the basic proof methodologies, which are essential for studying the mathematical analysis and number theory? I am very interested in studying ...
0
votes
1answer
41 views

a question related to supremum and infimum

$T_n^*:=sup\{t|\sum ψ(x_i;t)\gt 0\}$ $T_n^{**}:=inf\{t|\sum ψ(x_i;t)\lt 0\}$ As it's seen in the above figure, $-\infty \lt T_n^{*} \le T_n^{**} \lt +\infty$ Then, how to write the two followings ...
2
votes
1answer
28 views

How to practice basic probabilistic modeling?

I'm heavily struggling in learning simple and basic probabilistic modeling. So I'm learning probability from this probability book Introduction to Probability by Dimitri P. Bertsekas. Although I ...
-1
votes
0answers
37 views

Clarify a question's answer related to random walk. [on hold]

I'm studying Problem5.3 and its solution. However, its solution is not clear for me. Please explanatorily show this answer . I need to learn such type of questions. Please help me. Thank you.
0
votes
2answers
15 views

Orthogonal Projection in subspace

Consider the vector space $\mathbb{R}^n$ with usual inner product $<.,.>$. Take $Y\in \mathbb{R}^n$ and $X \in \mathbb{R}^n$ such that $Y=[y_1,y_2,..y_n]^t$ and $X=[1,1,....1]^t$ ...
1
vote
1answer
32 views

A question on Primes in Arithmetic Progression

We know that an arithmetic progression has to have a composite number since there are arbitrarily large gaps between primes. But I was wondering whether the following construction is possible: Can ...
1
vote
2answers
65 views

two objects moving in opposite directions.

I don't need a specific answer for this question, and would rather prefer to know how to solve questions like this one. So far I've tried using the $v=d/t$ formula to form equations, but haven't ...
2
votes
1answer
61 views

limit supremum and infimum question

Question: Show that $\limsup A_n -\liminf A_n = \limsup(A_n A^c_{n+1}) =\limsup (A^c_n A_{n+1})$ the thing I understand from this queston is the following; $$\bigcap_{n=1}^\infty ...
0
votes
0answers
43 views

How do mathematicians choose which formulas are important?

I'm reading a introductory book on elliptic curves and am having some trouble distinguishing between the important formulas and the insignificant ones. For example, some of the equations introduced ...
3
votes
2answers
62 views

what is remainder when $(((3!)^{5!})^{7!})^{9!…}$ is divided by 11

$$(((3!)^{5!})^{7!})^{9!...}$$ when divided by 11 what will be the reminder? Hint is appreciated Sorry I do not know how to start this problem, so I have not shown my efforts!
0
votes
1answer
22 views

Integral transformation

I'm trying to do a transformation of an integration, I have that $$\int_{0.5}^1\int_0^{0.5}e^{xy}xydxdy$$ And I want to get that integrate $$\int_0^1\int_0^1 f(x,y)dxdy$$ Where the value of the ...
6
votes
9answers
2k views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
-1
votes
1answer
33 views
3
votes
3answers
964 views

Is there a problem in studying analysis before calculus?

Is there a problem in studying analysis before calculus? Most people say that analysis is rigorous calculus, the university I'm studying teaches calculus first because they believe it's better for the ...
1
vote
1answer
390 views

Question about the mathematics in actuarial studies

I tried Google but there isn't much information on this and I would really like some insights into actuarial studies, the mathematics involved and how it compars to the mathematics in a bachelor of ...
2
votes
1answer
71 views

Learning Combinatorics Further

I have completed most of the basic parts in Combinatorics like Generalised Permutation & Combination, Recurrence relations, Pigeonhole Principle, Formal power series, Stirling no, Catalan no, ...
2
votes
1answer
230 views

Permuting the terms of a sequence does not affect its convergence

Let $x_n$ be a sequence such that $x_n \rightarrow 0$. Let $\sigma\colon\mathbb N \rightarrow \mathbb N$ be a bijection. Define a new sequence $y_n:= x_ {\sigma (n)} $. Show that $ y_n \rightarrow 0 ...
0
votes
0answers
10 views

Given $z_n$ = {$ x_{1},y_1,x_2,y_2,x_3,y_3 …$} Prove that $z_n$ is convergent if $x_n$ and $y_n$ both converge to same limit [duplicate]

I f $x_n$ and $y_n$ be the two sequences such that $z_n$ = {$ x_{1},y_1,x_2,y_2,x_3,y_3 ...$} Prove that $z_n$ is convergent if $x_n$ and $y_n$ both converge to same limit ATTEMPT Let us take that ...
1
vote
1answer
74 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
1
vote
1answer
28 views

Let $x_n$ be sequence converging to $0$ . What can you say about sequence $(x_n)^{n}$

Let $x_n$ be sequence converging to $0$ .What can you say about sequence $(x_n)^{n}$ ATTEMPT $|x_n|<\epsilon^{1/n}$ for all $n \geq$ m implies $ |x_n|^{n} < \epsilon $. Thus new sequence is ...
2
votes
0answers
39 views

Wedge product of Lie algebra valued differential forms [duplicate]

Let $\mathfrak{g}$ be the Lie algebra of a matrix Lie group. Furthermore, let us consider the following $\mathfrak{g}$-valued $p$-form and $\mathfrak{g}$-valued $q$-form: \begin{equation} ...
1
vote
3answers
51 views

Let $x_n$ be a sequence. Prove that $x_n \rightarrow 0 $ iff $(x_n)^{2} \rightarrow 0 $

Let $x_n$ be a sequence. Prove that $x_n \rightarrow 0 $ iff $ (x_n)^{2} \rightarrow 0 $ Attempt Assume that $(x_n)^{2}$ converges to zero. So $| x_n|| x_n| \lt \epsilon'$ after some stage. Thus $| ...
9
votes
2answers
3k views

Is Aluffi's book a good second text for Algebra?

I have been trying to relearn parts of algebra (mostly module theory and (advanced)linear algebra) from Lang, which, frankly, is not going too well. Now, I have managed to get my hands on 'Aluffi - ...
0
votes
0answers
12 views

Good introductory texts on modular forms/L-functions

I am relatively new to these areas but would like to gain some understanding through an introductory text. I am an undergraduate math major so ideally these books should be accessible to someone with ...
0
votes
1answer
34 views

Complex number, power series

Develop $\sinh z$ in powers of $z-\pi i$ to show that $$\lim_{z\to \pi i}\frac{\sinh z}{z-\pi i}=-1$$ I know that $\sinh z=\sum_{n=1}^\infty \frac{z^{2n-1}}{(2n-1)!}$. Edit: Following the hint ...
1
vote
3answers
30 views

Complex number, entire function

Let $f(z)=\frac{(e^{cz}-1)}{z}$ if $z\neq0$ and $f(0)=c$ show that f is entire Theorem:A power series represents a analytical function inside their circle of convergence. I know I could prove ...
0
votes
1answer
35 views

Complex Series proof

Integrate the Maclaurin series for$\frac{1}{1+z}$ along a path, inside the circle of convergence, going from $z'=0$ to $z'=z$ and show that $$Log(z+1)=\sum_{i=1}^\infty (-1)^{n+1}\frac{z^n}{n}, ...
1
vote
1answer
63 views

If $x_{n}$ and $x_{n}y_{n}$ are bounded, does it follow that $y_{n}$ is bounded? [on hold]

If $x_{n}$ and $x_{n}y_{n}$ are bounded, does it follow that $y_{n}$ is bounded? Attempt Let |$x_{n}| \leq C$ and |$x_{n}y_{n}| \leq C'$, then |$x_{n}y_{n}|$ $\leq$ $ |y_{n}|$ $\leq C'/C$. If ...
3
votes
0answers
88 views

How to study multiple books per math subject?

S.E advisers, I am a college sophomore in US with double majors in mathematics and microbiology. I apologize for this sudden interruption but I wrote this email to seek your advice regarding to ...
12
votes
1answer
182 views

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
2
votes
0answers
98 views

Unable to understnad how a map is one-to-one in the proof for conjugacy

I need to prove that amp is a homeomorphism. I am following the basics from the book For the proof I have taken the help of the book "An introduction to dynamical system" Download link ...