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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Is it useful to learn math by analyzing a formula/theorem?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
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52 views

Which are the operations used in mathematics?

Everyone knows +,-,x,:,^. But I would really like to know which other operations exist, and what they do.
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49 views

Self Teaching Theory for Olympiad. Need advice for books.

(Cross-posted in MESE 8173.) I want to start to do Olympiad type questions but have absolutely no knowledge on how to solve these apart from my school curriculum. I'm 16 but know maths up to the 18 ...
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5 views

hypothesis test type 1 and 2 error

Supporters claim that a new windmill can generate an average of at least 800 kilowatts of power per day. Daily power generation for the windmill is assumed to be normally distributed with a standard ...
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2answers
56 views

How to avoid rote learning and perform deep learning?

I saw this question on brillant's facebook and I didn't even thought of/figure out to use difference of squares to solve this question. All the while, I have been a C student for Maths and barely ...
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1answer
61 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 ...
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59 views

Seeking advice from all [closed]

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 ...
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0answers
58 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 ...
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0answers
33 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 ...
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1answer
33 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 ...
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44 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 ...
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1answer
78 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 ...
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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, ...
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3answers
52 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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13 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 ...
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0answers
90 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 ...
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2answers
156 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
44 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 ...
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1answer
66 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 ...
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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. ...
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2answers
26 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 ...
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1answer
32 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? $$-20a+13b+13c=0$$ $$10a-26b+13c=0$$ $$10a-13b-16c=0$$ ...
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2answers
71 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 ...
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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 ...
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4answers
127 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 ...
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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 ...
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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 ...
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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, $\Delta (X)$ ...
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83 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 ...
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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 ...
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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 ...
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1answer
186 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 ...
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1answer
16 views

Visualizing a probability measures through a probability density functions

I found a previous question with a very nice answer, but still there is something that is not completely clear to me. We start from a space $(X, \Sigma)$, endowed with a $\sigma$-algebra, and we let ...
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47 views

how to prove this function is a probability measure in $U_B$

Let $(\Omega, U, P)$ be a probability space. and $B\in U$, $P(B)\gt 0$ $U_B =\{A: A=B\cap C, C\in U\}$ its class in $\Omega$ is a $\sigma$-algebra and $P_B : U_B \to \Bbb R$ $A \to ...
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2answers
24 views

Transition probability matrix

In the article here it had this question. A walker moves on two positions a and b. She begins at a at time 0, and is at a next time as well. Subsequently, if she is at the same position for two ...
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1answer
58 views

Long term probability in Markov Chains

I was practicing some questions on transition probability matrices and I came up with this question. You have 3 coins: A (Heads probability 0.2),B (Heads probability 0.4), C (Heads probability ...
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58 views

How to think/see point-set topology abstractly?

I've started learning point-set topology this semester. I've learned basic material about: topology on a set topological space open sets closed sets clopen sets closure neighborhoods interior point ...
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2answers
46 views

Understanding proof that sequence $x_n =( -1)^{n}$ is not convergent

To Understanding proof that sequence $x_n =( -1)^{n}$ is not convergent . Here goes the proof :- Firstly i assume that sequence converges to x .i.e -1 and 1 lies between $x$-$\epsilon$ and ...
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5answers
65 views

To show sequence $a_n = n$ is not convergent [closed]

Here is proof that sequence n is not convergent. It is from the book A Basic Course in Real Analysis by Ajit Kumar, S. Kumaresan, page 31. I have not understood last three lines of the proof. Can ...
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1answer
15 views

Regression project in octave/matlab

I'm trying to establish a polynomial model to adjust the variation of the dollar throughout the year. Suppose hypothetically that I have the following data ...
3
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1answer
61 views

Characterize all finite unital rings with only zero divisors

Is it true that for every finite (for simplicity, commutative) ring $R$ in which every element not equal to $1$ is a zero divisor, is isomorphic to the zero ring or $\mathbb{Z}/2\mathbb{Z}$, ...
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30 views

What does $\mathbb P(\overline{\mathbf X} = \mathbf x)$ mean

I am reading Peter Hall's "the bootstrap and edgeworth expansion". In Theorem 2.3 on page 57, it claims that if the characteristic function $\chi$ of a $d$-dimension random variable $\mathbf X$ ...
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1answer
55 views

Moments of a random variable in terms of its cumulative distribution function

Consider a random variable $X$ with distribution function $F(x)$. Calculate the $r$th moment of $X$, $\mathbb E X^r$. I read that the desired moment can be calculated as follows. $$ \begin{align} ...
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124 views

Please help collecting examples of finite/infinite rings satisfying different conditions about units/zero divisors (Added question 4)

0) Every nonzero element of a finite ring is either a zero divisor or a unit. This is proved in Every nonzero element in a finite ring is either a unit or a zero divisor 1) If a ring R satisfies the ...
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1answer
14 views

Complete separable metric space X represented represented as union of closed sets

I have a problem concerning a statement I found in volume 2 of the classic reference book on measure theory by Bogachev. More precisely, I have a problem concerning theorem 6.1.13. I the proof the ...
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1answer
56 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
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1answer
24 views

Solving the equations .

Say , I have two equations : $$y_1=a+bx_{1}+e_1$$ $$y_2=a+bx_{2}+e_2$$ Say , $a=.5$ , $b=2.1$ , $x_1=2$ , $x_2=2.2$ . Now if $e_1=e_2$ , I have to find the relationship between $y_1$ and $y_2$ . ...
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3answers
78 views

What would be an effective way to learn group theory on my own?

I've read the basics of this branch and I found it extremely interesing, and I would really love to learn more about it. I want to study as much as I can on my own, as my course doesn't have group ...
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75 views

Good starting point for learning noncommutative geometry?

Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical ...
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37 views

Double Integral of an Exponential Function with an Absolute Value in the Numerator of the Exponent

This is a question related to statistics, but my major concern relates to the setup and evaluation of integrals. So I decided this question was better suited for Mathematics Exchange than CV. I know ...