# 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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### How to study multiple books per math subject? [closed]

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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 ...
154 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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### 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 ...
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### A proof related to diameter of a simplex S

Question: Prove that the diameter $\mathcal p(S)$ of a simplex $\mathcal S$ equals the greatest Eucledian distance between two vectors in the simplex. My opinion: We all know what every vector in the ...
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### Show that a positive definite (not necessarily symmetric) matrix induces a hyperellipse

Consider $A\in M_n(\mathbb{R})$ a positive definite matrix and a matrix $B\in M_{n \times p}(\mathbb{R})$, with $n\geq p$ and $rank(B)=p$. i) Show that $C=B^TAB$ is positive definite. ii) Show that ...
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### Variance of Inhomogenous Poisson process in a given window

Consider some variable $X\sim \operatorname{Poi}(\lambda(t))$ to be Poisson-distributed with some parameter $\lambda$ dependent on time, where we know how the random variable $\lambda$ is distributed. ...
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### An orthogonal projection matrix in $\Bbb{R}^{3}$.

Consider the vector space $\mathbb{R^3}$ with usual inner product. Find the orthogonal projection matrix on the xy plane. I've found sometimes the orthogonal projection of a vector in a given ...
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### Linear algebra, inner product and matrix

Let $A\in M_{m \times n}(\mathbb{R})$, $x\in \mathbb{R}^n$ and $b,y\in \mathbb{R}^m$. Show that if $Ax=b$ and $A^ty=0_{\mathbb{R}^m}$, then $\langle b,y\rangle=0$. Also make a geometric ...
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### Can the given transformation possible for given determinant?

In forth step $(x-1)(x-2)$ is obtained by applying transformation R$1 \frac{1}{(x+1)}$ and R$2 \frac{1}{(x+2)}$. But we get value of $x = -1$ or $x = -2$ so $\frac{1}{(x+1)}$ and ...
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### Reference request for conditional and unconditional covariance of n-times integrated Brownian motion

I'm working through an old Diaconis paper on Bayesian numerical analysis, and am currently calculating the details behind his brief comments on using $n$-times integrated Brownian motion as a function ...
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### Understanding two sided t-test

Assume we have two search engines, A and B. I get a list of scores for 10 different queries. Now, I model this with a t-test in order to test significance. These are my hypothesis: $H_0: B-A=0$ ...
222 views

### Are basic trigonometry functions ( sine, cosine, tangent ) intuitive or memorized?

First, I'm really sorry for this somewhat vague and possibly just silly question. I also apologize if the following context runs a bit long. But please trust me that I'm asking with total sincerity ...
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### The maximum and minimum of five independent uniform random variables

Let $U_1,\dots,U_5$ be independent, each with uniform distribution on $(0, 1).$ Let $R$ be the distance between the minimum and maximum of the $U_i^{'}$s. Find the joint density of the max and the ...
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### What should I study, if I want to learn about higher dimensional spaces and objects? Also, what resources should I obtain?

I am becoming interesting in learning about higher dimensions. What are subjects I could study, and what are some good resources for those subjects?
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### How to partially differentiate an integral with a density function?

I am given this result: $$\frac{\partial}{\partial x(t)} \left[\lambda \int u(x(t)) f(t) \mathrm{d}t\right] = \lambda u^\prime(x(t)) f(t)$$ Where $\lambda$ is a constant, and we have the probability ...
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### Companion Books for Rudin's PMA

S.E friends, I am a college sophomore with double majors in mathematics and microbiology. I wrote this email to seek your recommendation on selecting the introductory analysis textbook, particularly ...
Suppose I have $e^{(\frac{1}{n}b + o(\frac{1}{n}))}$ then $\lim_{n \rightarrow \infty} = e^0 = 1$ so $$e^{(\frac{1}{n}b + o(\frac{1}{n}))} = o(1) +1$$ But if I take the Taylor expansion of ...