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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Self-studying Information Geometry

I was recently exposed to the topic of Information Geometry by a friend of mine, and was looking for a good book to begin self-studying this topic. Any suggestions? Also, what subject matter would ...
0
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1answer
24 views

Show that $(a) + (b)= R$ for $\gcd(a,b) = 1$

The question I am trying to solve it: Let $R$ be a principal ideal domain, $a,b\in R$. Suppose $\gcd(a,b) = 1$. Show that $(a)+(b)=R$. First I have tried to show that $(a)+(b)$ is in R: ...
0
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0answers
5 views

Non-Inductive formula for subdivision operator

This problem is from hatcher 2.1.25. Find an explicit, noninductive formula for the barycentric subdivision operator. I have no idea how to get that formula. The only way I see it geometrically is ...
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0answers
50 views

A very detailed book for calculus 1-3.

Is there a very good book covering the whole calculus in detail, explaining all topics in calculus 1-3 for self-learning? I'm in geometry I, so I will start calculus in two years, and finish in five ...
0
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1answer
35 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 ...
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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 ...
2
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3answers
290 views

Lebesgue covering theorem

I am having trouble understanding Lebesgue covering theorem as stated in Mathematical Encyclopedia. First of all I think I have confusion with the definition of "finite subsystem". Is it finite ...
1
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1answer
1k views

Equivalent systems of Linear equation

I've just begun to re-learn linear algebra because is so important, the book that I chose is naturally the Hoffman's for a lot of reason. Well, In the first chapter I'm stuck with the following, ...
0
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2answers
37 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 ...
2
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1answer
344 views

Proof Verification: Show sequence is bounded and find limit: $x_1 \gt 1$ and $x_{n + 1} = 2 - \frac{1}{x_n}$

Came across the following exercise in Bartle's Elements of Real Analysis and am a little unsure about my solution. Would be extremely grateful if someone could verify it for me. Let $x_1 \in ...
1
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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
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3answers
74 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
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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 ...
1
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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 ...
2
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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 $$ Tf(k)=[f(k)+f(n+1-k)].$$ ...
3
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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
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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 ...
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1answer
33 views
-1
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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
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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
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1answer
21 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, $X_1$, $X_2$, ...
4
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6answers
259 views

How do I show that $\sqrt{5+\sqrt{24}} = \sqrt{3}+\sqrt{2}$

According to wolfram alpha this is true: $\sqrt{5+\sqrt{24}} = \sqrt{3}+\sqrt{2}$ But how do you show this? I know of no rules that works with addition inside square roots. I noticed I could do ...
0
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0answers
67 views

Proving that $\sup(-A) = -\inf(A)$ [duplicate]

Let $A$ be a bounded set of real numbers. Define $-A =$ {$x: -x \in A$}. Show that $-A$ is bounded and that $\sup(-A) = -\inf(A)$. Pf: A is bounded so $\exists x,y \in A $ such that $inf(A) \le y ...
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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 ...
0
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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 ...
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 ...
2
votes
1answer
29 views

Testing statistic $\frac{MSS(X)}{MSS(Y)}$

Suppose a test statistic $\frac{MSS(X)}{MSS(Y)}$, where $MSS$ denotes Mean Sum of Squares, is to be used for testing the significance of the factor $X$. Do we need the assumption $$\mathbb ...
11
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5answers
7k views

Multivariable Calculus books similar to “Advanced Calculus of Several Variables” by C.H. Edwards

I am currently trying to teach myself multivariable calculus using C.H. Edwards' "Advanced Calculus of Several Variables", but the text unfortunately doesn't have very many problems with solutions. ...
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1answer
427 views

Expected value of division

Let $X,Y$ and $Z$ be three indenependent real valued random variables. Al with finite second momennt and all with mean $0$ and variance $1$. Define $$ W= \frac{X+YZ}{\sqrt{1+Z^2}} $$ Show that ...
0
votes
1answer
426 views

How to decide whether PDE is Homogeneous or non-homogeneous.

I am studying second order PDE. And I have seen homogeneous and non-homogeneous PDE. But I cannot decide which one is homogeneous or non-homogeneous. For examples; (1) $(D^3-3D^2D'+4D'^3)u=0$ ...
5
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2answers
239 views

Lie theory for physicists

As an undergraduate on physics seeking a solid education on mathematics, I have recently stumbled upon some theories that make use of the formalism of Lie groups and Lie algebras. In light of this, I ...
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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
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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: ...
26
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9answers
57k 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" ...
0
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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 ...
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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
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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
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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
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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 ...
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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 $\{k_n\}$: ...
0
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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
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0answers
13 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 ...
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3answers
4k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
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5answers
424 views

Solutions to $x+y+z=31$ and $x+2y+3z=41$

For the equations $$x+y+z=31$$ $$x+2y+3z=41$$ is there a elegant way or method to find all the positive solutions in integers? Thus far, I have been using trial and error (which is time consuming). ...
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2answers
143 views

21, Not Touched Maths Since GCSE. Want to start learning again. Where to Start?

I am 21 and have got into computer programming. Doing very well in my degree. Would love to get into computer science but feel I am being held back by my basic knowledge of maths. I got an A at GCSE, ...
2
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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 ...
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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 ...
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2answers
803 views

Introduction into Operations Research

I am a first year graduate student who advisor wants me to learn about operations research and to use stochastic integer programming in my research. He keeps giving me papers to read but they ...
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 ...