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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100 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
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49 views

$W$ intersection of $(n-1)$ dimensional subspaces

I have got a good (I think so) intuition of this problem but I am not being able to write down the crucial steps correctly. Let $V$ be a $n$ dimensional vector space over field $F$ . Let $W$ be a ...
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82 views

Next Step for Self-Learning

I am an undergraduate mathematics major and recently completed a course in real analysis. While I enjoyed this course it left out many topics that I would have liked to learn because of time ...
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2answers
40 views

Existence of maximum and minimum

Let $f:\mathbb{R}_+\rightarrow \mathbb{R}$ be continuous and such that $f(0)=1$ and $lim_{x\rightarrow+\infty}f(x) = 0$. Prove that $f$ must have a maximum in $\mathbb{R}_+$. What about the ...
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3answers
79 views

Express $2\cos (n\theta)$ in terms of $z$ [closed]

How can I show that $$2\cos(n\theta)=z^n + \frac{1}{z^n}$$ if $z=\cos\theta+i\sin \theta$ Can some one help me? thx!
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1answer
65 views

Study materials to help understand the generalized Stokes' theorem both intuitively and rigorously?

Dear MSE: My goal is to understand the generalized Stokes' theorem both intuitively and rigorously. Could someone give advice or recommend study materials to help understand the generalized Stokes' ...
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0answers
24 views

where to find good review resources? [closed]

I am taking my certification test for secondary mathematics next month and I am extremely overwhelmed by the amount of stuff i need to brush up on. http://www.mttc.nesinc.com/PDFs/MI_field022_SG.pdf ...
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4answers
234 views

Proven Studying Habits for a Limited Memory? [closed]

I learned Calculus many years ago and at the time I thought that I knew it well. (i.e. got good grades, was employed as a tutor, etc) I am now going back and studying Calculus again with the hopes of ...
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3answers
454 views

How to determine if I'm talented enough to study math? [closed]

After getting Bachelor's degree from Computer Science I changed my field to Applied Mathematics. The previous degree was mostly programming-oriented, so I know quite a lot about software engineering, ...
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2answers
77 views

What is tangent to a curve or function?

When I read my textbooks or even type "what is a tangent?" on google, I have always got an answer similar to these lines: "A straight line or plane that touches a curve or curved surface at a point, ...
3
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4answers
349 views

Measure theory for self study. [duplicate]

I have good knowledge of Elementary Real analysis. Now I'd like to study measure theory by myself (self-study). So please give me direction for where to start? Which book is good for starting? I have ...
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85 views

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 ...
3
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1answer
63 views

How to interpret the notation of a formula?

I was reading a paper where the property of light known as Illuminance, for a specific setup (as in the figure) is given with the following formula: The description below the formula says: ...
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4answers
171 views

Help Self-Studying Calculus

I wanted to learn calculus but I have been told that you can't learn it without first learning elementary algebra. Can someone help me devise a plan for self-study because I don't know were to begin.
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2answers
99 views

Algebra review for Spivak Calculus

I got a bit bored with High School maths so I picked up a copy of Calculus by Spivak. I am really enjoying the book and have found that the proofs and theorems aren't as hard as others have made them ...
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0answers
40 views

Cesaro summation and convergence

I am trying to makes sense of the proof to following problem: Given: $A_n = \displaystyle \frac{\sum_{k=1}^n a_k}{n}$. Can $\{A_n\}$ converge if $\{a_n\}$ diverges; $\forall n,a_n>0; \limsup{a_n}...
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0answers
19 views

Checking if estimators are sufficient

For an i.i.d. sample of random variables Xi distributed according to a normal distribution, known variance. I found a sufficient statistic—the sample mean. How do I check if other statistic like (...
5
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1answer
91 views

Important topics to know in Algebra [closed]

I'm trying to prepare for graduate algebra but after looking at Dummit and Foote I realized that there's a lot of material (1000 pages). Which topics do you think a student should study in D&F to ...
3
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1answer
78 views

self-teach: In what order should I structure my studies?

I'm a 19 year old, who will be 20 in may. I didn't go to the greatest high school, and I didn't get the proper education to prepare me for college. I need to make a study plan for myself to truly ...
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0answers
87 views

Proof that Poisson process interarrival time $T(N+1)-T(N)$ with $T(N)<t<T(N+1)$ is Gamma$(2,\lambda)$

Suppose a Poisson process $N(t)\sim\text{Poisson}(\lambda t)$. Let $T(N)$ be the time of the last arrival before time $t$ and $T(N+1)$ be the time of the first arrival after time $t$. From simulations,...
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1answer
110 views

Given undergraduate Algebra background, which introductory Homological Algebra textbook?

I have read the answer for graduate-level Algebra background and all answers in stackexchange and mathoverflow discussing Homological Algebra textbooks. But none of them directly answers my question, ...
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0answers
27 views

Let W = X1/(X1+X2), how to prove **W** has a beta distribution?

I am confused when I come across this question, could anyone help? Thanks! Let X1 and X2 have independent gamma distributions with parameters α, θ and β and θ respectively. Now we let W = X1/(X1+X2), ...
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2answers
131 views

How do mathematicians come up with beautiful equations [closed]

In Linear regression for example, we can find weights as following: $\hat{\beta}=(X^{T}X)^{-1}X^{T}y$ how someone invented this? I mean how do they transform a problem to such an equation. And ...
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3answers
153 views

Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
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0answers
62 views

Proving a degree sequence satisfy Chvatal’s criterion

How can I prove that a degree sequence satisfy Chvatal’s criterion? I know that i must prove that sequence A is Hamiltonian if and only if A' is hamiltonian but i am lost on where i should start. for ...
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0answers
26 views

how to construct non-Hamiltonian graphs

I have been asked to construct a hamiltonian graph and a non-hamiltonian graph using the same degree sequence. I have had no problem constructing the hamiltonian graph however I am finding it ...
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1answer
60 views

Min problem by using Lagrange method

$$\min x^2+y^2 $$ $$\text{s.t.}\ \ (x-2)^2+(y-3)^2\le 4 \ \ \ \text{and} \ \ \ x^2=4y$$ Please explicitly solve this question by using Lagrange multiplier method. I accept $(x-2)^2+(y-3)^2=4$ ...
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1answer
185 views

Set all measurable real functions on $[0,1]$ with metric $\int_{0}^1 \min \{1,|f(t)−g(t)|\}dt$ is Fréchet without nonzero continuous linear functional

Bounty Edit: In the following, all the questions will be highlighted by a bold number and a text written in italics. I found the following statement in a book, and I am really struggling to see why ...
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1answer
49 views

Maximization problem on an ellipsoid [closed]

for three variables, $$\max f(x,y,z)= xyz \\ \text{s.t.} \ \ (\frac{x}{a})^2+(\frac{y}{b})^2+(\frac{z}{c})^2=1$$ where $a,b,c$ are constant how to solve the maximization optimization problem? ...
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2answers
33 views

How to write a discrete dynamical system into first order system

I need guidance on how to solve this here. $$x_{n+1} + 3x_n - 4x_{n-1} = (\sqrt{2})^n cos \left(\frac{n\pi}{6}\right)$$ I am required to transform the above equation into a first order finite ...
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0answers
29 views

Marginalizing multivariate-normal distribution canonical form

Regarding the problem of margenalization of canonical forms of multivariate gaussian distribution it was mentioned in probabilistic graphical models text book that $$\int{C(X,Y;k,h,g)}dY$$ is ...
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2answers
57 views

Expectation Functional in Lebesgue and Riemann Terms – Looking for a clarification

Here there is a really central problem I am having self-studying probability theory, that concerns the relation between the definition of expectation in Lebesgue terms and in Riemann terms. I will ...
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1answer
73 views

Negative Mean Square Error

For simple random sampling, I have calculated somemean square errors for ratio-type estimators such as Isaki estimator, and Prasad Singh estimator. But, Mean Square Errors i obtained are negative. ...
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0answers
55 views

Is It Worth It Working Out Every Practice Problem In Math? (Without a calculator)

I'm bouncing back between trig, algebra, and calc books. I've noticed that most of the problems at some point seem to distill into very tedious arithmetic. It is nice to have the prowess of ...
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0answers
74 views

Suitable reference for learning symplectic geometry

I am interested in studying symplectic geometry by myself and I'm looking for a good text to use as a reference in the way. I am a bit lost because I've found a lot of notes and books on the subject ...
4
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3answers
912 views

Does the phrase “If you don't use it, you lose it” apply to mathematics? [closed]

I'm asking this because I ran into the following particular situation: I took some calc courses over 2013, where I learned, amongst other things, to integrate some pretty nasty functions, and this ...
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1answer
42 views

writing a piecewise regression model as a linear model

lets write the following piecewise regression model $$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$ $$ y=\beta_0 +\beta_1 x + \epsilon \ \ x\gt x_0$$ according to the variable $x_0$ is known,...
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0answers
47 views

Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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0answers
39 views

Between Oksendal and Karatzas books

I finished Oksendal "SDE , an introduction with applications" , did most of the exercises (not all with success, but I read the solutions for those); my next project would be to read the Karatzas "...
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22 views

Is every Complex Square Matrix similar to its transpose? [duplicate]

I am aware that every complex square matrix is similar to its transpose but I am having a hard time proving this. Should I try to use the previously asked question listed at $A matrix is similar to ...
2
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1answer
56 views

If $B(t)$ is Brownian motion then prove $W(t)$ defined as follows is also Brownian motion

Let $B(t)$ be standard Brownian motion on $[0.1]$ Define $W(t)$ as follows $W(t) = B(t) - \int_0^t \frac{B(1)-B(s)}{1-s} \, ds$ Prove $W(t)$ is also Brownian motion So I'm not sure how to deal ...
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1answer
97 views

Proof that $(t_1, \dots, t_r) \mapsto \sum^{r}_{i=1} | t_i - \alpha_i|^p$ is continuous - Problem with Inequality

Bounty Edit: I already edited the question after some important comments. The questions I have are highlighted below the supposed proof. Any feedback or answer is most welcome. Thus, I just found a ...
0
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1answer
130 views

Who is a mathematician? [closed]

My first question in Math SE. Basically the question itself, who is a mathematician? Is it someone who solves problems on his leisure time or as a part of a job or even as a hobby? who researches ...
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1answer
50 views

Two questions on finding the equation of a parabola word problem- Klein's Calculus: An Intuitive and Physical Approach

I am solving the following word problem "A high voltage cable is supported by two towers 2800 feet apart and 348 feet high. The cable hangs in approximately the shape of a parabola, and the lowest ...
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0answers
51 views

Find the set of undominated strategies in Cournot duopoly

Consider a version of the Cournot doupoly game, where firms 1 and 2 simultaneously and independently select quantities to produce in a market. The quantity selected by firm $i$ is denoted $q_i$ and ...
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1answer
59 views

Unique Positive Definite Square Root of a Positive Definite Matrix

If $A$ be an $n\times n$ positive definite matrix, then there exists a unique positive definite matrix $B$ such that $B^2=A$. My question is how to get this $B$. What is the name of the algorithm for ...
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156 views

What is the expected amount of time until the chain is in state 4?

Consider the continuous-time markov chain with state space {1,2,3,4} and infinitesimal generator $$A=\begin{bmatrix}-2&1&1&0\\0&-1&1&0\\1&1&-3&1\\0&0&1&...
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1answer
68 views

Topics of analysis beyond in $\mathbb{R}$ and beyond of functions of single real variable?

Could someone list the topics of analysis beyond in $\mathbb{R}$ and beyond of functions of single real variable that a new math graduate student should be familiar with? Also could someone list the ...
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2answers
110 views

Where to go after Halmos' *Naive Set Theory*

I'm in the process of finishing Halmos' Naive Set Theory, and I found the subject fascinating, so I would like to carry on reading about Set Theory when I'm done. From what I've been able to gather ...
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1answer
58 views

Bayesian Inference and Disease Testing

I've been working my way through an introduction to Bayesian Inference in a Statistical Physics textbook (Tobochnik and Gould, 2010 - available online, excellent book). I've run across a problem that ...