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 fact that you're self-studying is what your question is _about_.

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1answer
56 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
0
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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 ...
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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 ...
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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 ...
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 ...
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 ...
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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 ...
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 ...
2
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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 ...
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 ...
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0answers
38 views

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

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.
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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
31 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
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
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2answers
67 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 ...
0
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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!
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1answer
33 views

Understanding proof that real sequence is Cauchy iff it is convergent [closed]

I am having trouble understanding what is motive and idea behnd th proof given here
2
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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
76 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 ...
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, ...
1
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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 ...
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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 $| ...
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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 ...
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 ...
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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? [closed]

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
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0answers
89 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 ...
3
votes
2answers
154 views

A path to more advanced math topics.

I am from Hong Kong and have just finished all the public exams. In my high school life, I've learned some topics on mathematics which are fundamental, yet I think are not in-depth enough. The topics ...
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0answers
21 views

markov process and markov chains

I have learned that Markov processes are stochastic processes possessing certain mathematical properties (memoryless, etc). My question is, if you say that a process is Markov, is it automatic (as a ...
0
votes
0answers
42 views

The Analysis of Linear Partial Differential Operators I Prerequisites

I am a graduate level student in Mathematics and I would like to study the books titled "the analysis of linear partial differential operators I-IV" by Hörmander. As I have been away from mathematics ...
1
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0answers
17 views

Showing $\sum |\hat{f}(n)| \leq C \cdot \int_{0}^{2\pi} |f(t)| \ dt$ [duplicate]

If $f \in L^{1}[0,2\pi]$ define $\hat{f}(n)$ for $n \in\mathbb{Z}$ by $$\hat{f}(n) = \frac{1}{2\pi} \int_{0}^{2\pi} f(t) \cdot (\cos(nt) -i\sin(nt)) \ dt$$ Suppose $M$ is a closed linear subspace of ...
3
votes
1answer
63 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
0
votes
0answers
16 views

Obtaining the transition probability matrix

Seven black balls are distributed among two persons $A$ and $B$ having urns $X_A $ and $X_B$ with three balls in $X_A$ and four in $X_B$. One white ball is in either $X_A $ or $X_B$. A game consists ...
2
votes
0answers
14 views

Linear Programming 3 decision variables (past exam paper question) [duplicate]

This is an exam question I was practising. I have the general understanding of Linear programming, but how would you go about finding the Decision Variables, Objective function and Constraints for ...
1
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1answer
34 views

Find the curve which together with $\gamma$ encloses the greatest area.

I'm working through Gelfand & Fomin's Calculus of Variations by myself, and could use the guidance of someone familiar with the subject. The problem I'm on now is the following: "Given two points ...
3
votes
0answers
23 views

Prove that two functionals with identical differentials differ by a constant.

I am self-studying Calculus of Variations and am struggling to prove results about the variation of a functional that are analogous to results in elementary analysis about differentials/derivatives. ...
0
votes
2answers
25 views

On the horizontal integration of the Lebesgue integral

I'm studying Lebesgue integral and its difference with respect to the Riemann one. I'm reading that the key difference (at least graphically speaking) is that the first slices the function ...
0
votes
1answer
31 views

Strategies for linear systems

Consider I have the following equations. Is there a faster way for me to solve the system without going through a series of substitutions? $$-20a+13b+13c=0$$ $$10a-26b+13c=0$$ $$10a-13b-16c=0$$ ...
3
votes
2answers
68 views

What is a good book for reviewing high school math, and preparing for university?

I'm signing up for University soon (Compsci program) as a mature student. It's been a long time since I've done any math, and I went as far as grade 11 in high school. So, I'm looking for a book that ...
0
votes
2answers
34 views

If $x_n$ $\rightarrow $ 1 Then show that sequence $\frac {4+ (x_n)^{2}}{x_n}$ approaches to limit 5

If $x_n$ $\rightarrow $ 1 Then show that sequence $\frac {4+ (x_n)^{2}}{x_n}$ approaches to limit 5 I have tried to find epsilon proof ,But i am not successful .Can anyone help me with this ...
2
votes
4answers
126 views

Complex number, series

Show that $$\frac{1}{z^2}=1+\sum_{n=1}^\infty (n+1)(z+1)^n$$ when $|z+1|<1$ I'm having problems to resolve this type of exercise since my book has virtually no exercises of this type, these ...
1
vote
1answer
31 views

Complex number, series representation

Show that for any finite value of $z$ $$e^z=e+e\sum_{n=1}^\infty \frac{(z-1)^n}{n!}$$ For $z=1$ $$f(z)=f(z_0)+\sum f^{(n)}(z_0)\frac{(z-z_0)^n}{n!}$$ equality is checked, but I do not know how to ...
4
votes
0answers
33 views

$\sum_{n=1}^{\infty}\frac{a_n}{10^n}$ where $\{a_n\}_{n=1}^{\infty}$ is a sequence in the ten digits {0, 1, 2 , 3 , 4 , 5 , 6 , 7 , 8 ,9}

Let $\{a_n\}_{n=1}^{\infty}$ be a sequence in the ten digits {0, 1, 2 , 3 , 4 , 5 , 6 , 7 , 8 ,9} And consider the sum $\sum_{n=1}^{\infty}\frac{a_n}{10^n}$ $\in$ $[0,1]$ What characteristics of ...
1
vote
1answer
19 views

Topology of weak convergence, linear functionals and probabilistic intuition

One very basic question regarding the topology of weak convergence. We know that given the following: $X$ metrizable topological space, $\mathcal{B} (X)$ Borel $\sigma$-algebra, $\Delta (X)$ ...
5
votes
3answers
81 views

Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R?

Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R? (Counterexamples are easy to find to me when $R$ is an infinite ring or a finite rng.) P.S. I am ...
0
votes
1answer
31 views

column space of a matrix

If $A\in M_{m\times n}\mathbb{(R)}$, show that $\mathcal{R}(AA^t)=\mathcal{R}(A)$ and $\mathcal{R}(A^tA)=\mathcal{R}(A^t)$ where $\mathcal{R}$ denotes the column space of matrix. How can I prove it ...
0
votes
1answer
33 views

Proof that limit of sequence is unique

I am learning real analysis on my own from this book http://books.google.co.in/books?id=TZ-NAgAAQBAJ&printsec=frontcover#v=onepage&q&f=false On page 33 , i do not get proof of that limit ...
12
votes
1answer
184 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 ...