# Tagged Questions

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

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### What do [] mean and what does it mean if it is used in an equation?

What do the square bracket symbols mean? Are they what I hear are "sets"? And when it is in an equation, how is it interpreted? Here is an example: $$\dfrac{dy}{dx}[2x2+y(x)2]=50x+2y(dy/dx)=0$$
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### Popular math books with depth

The most wonderful book I have ever read in my life was Fearless Symmetry by Avner Ash and Robert Gross, which is a good book that gives an intuition , and reasons behind the introducing fields, need ...
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### Implication and Interpretation of Banach Tarski

As I understand, the Banach-Tarski paradox says a ball in 3-space may be decomposed into finitely many pieces and reassembled into two balls each of the same size as the original. Despite being called ...
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### A very vague question about the cartesian product in mathematics.

Motivated by this question, I am wondering about Cartesian product analogs in various subfields of mathematics. The set theoretic Cartesian product creates an "output" set from a set of "input" sets, ...
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### Is Mathematics graduation important for a Computer Scientist?

I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all. I am going to graduate in Computer Science in ...
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### Monty hosting a new show

I imagine the following setup. There is a contestant who has to pick one of three doors. How many prizes will be hidden is determined at random in the following way. Monty will toss a fair coin and ...
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### Sleeping Mathematician (Sleeping Beauty)

I came across the following thought experiment, and I would like to understand whether the controversy around it is justified. Imagine an experiment in which a mathematician is put to sleep with some ...
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### Chance of meeting in a bar

Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet? I am mainly ...
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### KY Birds…which book is that from.

I am trying to find the name of this mathematical book, a smart student at my university gave a lecture about it a long time ago, and all I can remember of the talk was it was about mathematics it ...
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### $\max_{y} \min_{x} f(x,y)$ as motif for exploring mathematics

It's been several years since my undergraduate math days, and I would like to spend a bit of time refreshing and then tackling a few things I never completely mastered. Rather than proceeding topic ...
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### z-interval and sample size what is a normal sample size

Can a Z-interval be used when the sample size is between 15-30? does the variable play a role? I'm not too sure if it makes a difference. I know it can be used if the population is a normal or large ...
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### A theorem about inductive inference

In the book 'Introduction of the theory of Statistics' by Mood,Graybill,Boes (third edition)on page 220 (Chapter 6 on Sampling) you can read: 'Inductive inference is well known to be a hazardous ...
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### Ways to visualize the real numbers?

I was just wondering if there are any diagrams for visualizing subsets of the real numbers, or totally 'radically' different ways of looking at them as a real line? The model of the line relies on ...
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### Book Reference for Calculus and Linear Algebra :: Engineer

I'm almost through with my (Mech.) engineering and am trying to touch some advanced concepts in Computational Science which requires me to study Calculus and Linear Algebra in a more theoretical ...
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### Why are groups more important than semigroups?

This is an open-ended question, as is probably obvious from the title. I understand that it may not be appreciated and I will try not to ask too many such questions. But this one has been bothering me ...
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### How to use Hardy and Wright's text and what corresponding exercises/problem books can I do?

I have just started out with Hardy and Wright's An Introduction to the Theory of Numbers today. I find the lack of exercises in the book as a departure from the style of the textbooks we are so ...
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### What can we learn about a group by studying its monoid of subsets?

If $G$ is a group, then $M(G)=2^G$ is has a monoid structure when we define $AB$ to be $\{ab|a\in A,b\in B\}$ and $1_{M(G)}=\{1\}$. How much of the structure of $G$ can be recovered by studying the ...
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### What would be the consequence of restricting multiplication by Zero to only Finite Cardinals? [closed]

What would be the consequence of restricting multiplication by Zero to only Finite Cardinals? Would this lead to contradictions? How could it be achieved?
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### The status of $\mathbb{R}$ in homotopy theory.

The definition of a path as a continuous map $I \rightarrow X$ is a completely natural one. But this raises two questions in my mind. First, what properties of the interval give rise to useful ...
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### What is an honest basis?

In a comment to this question, the commentator stated that "the monomials form an honest basis for your vector space". To be honest, I never heard of that. Is this something elementary?
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### What properties of the absolute value function should one remember? [closed]

When one begins to study real analysis, the absolute value function quickly enters and a large number of exercises involve manipulations with it. What are the basic properties of absolute value that ...
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### Mathematics understood through poems? [closed]

Along with Diophantus mathematics has been represented in form of poems often times. Bhaskara II composes in Lilavati: Whilst making love a necklace broke. A row of pearls mislaid. One sixth fell to ...
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### How do I find partners for study?

I want to find partners to study some post-graduate topics together online (because I'm pretty much out of steam as far as self-study goes, and I have problems finding a decent grad school). Are there ...