# Tagged Questions

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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### 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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### $W$ 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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, ...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...