# Tagged Questions

For questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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### Advice on taking a Course in Logic.

Is a course in Mathematical Logic necessary for a well-rounded Mathematical education? I asked a question about taking a Set Theory course before and was advised to do so. However the course offered ...
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### How is addition on N formally defined in textbooks on real analysis?

This is a follow-up question to Why does the definition of addition require proofs? In Landau's Foundations of Analysis, his definition of addition on the natural numbers seems a bit strange to me -- ...
204 views

### Using math to help people [duplicate]

So I am currently a graduate student at the University of Colorado. I love math. From calculus to category theory to everything in between, I have tried and, for the most part, loved it. However, I ...
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### Incrementing Number Formula

I am trying to find a formula to express the nth term, the pattern is as follows: n = 4, 5, 6, 7 its corresponding values are as follows: 6, 10, 15, 21 I know this is not worded very well, if ...
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### Why are the areas non-positive?

I learnt that the integral of a function $f(\cdot)$ is the measure of an area, i.e. $\int\limits_{a}^{b}f(x)\,\mathrm{d}x$ is the area of the intersection of $x=a$, $x=b$, and $y=f(x)$. How come some ...
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### What is the history of the use of the term “scalene triangle”?

A "scalene triangle" is a triangle with three unequal sides. As far as I can tell, this term is not in much use in serious mathematics — in fact, before I became a high school math teacher, I'd ...
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### Getting interested in mathematics again after I finished Computer Science program.

So, I finished Computer Science study about 3 years ago (I'm 28 now) and lately I've been craving math. As a daily job I work for a start up company building a web application. I mostly done web apps ...
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### A basis in the $k$-th exterior power of a vector field

Definition: Let $\mathbb R^n$ be the $n$-dimensional real vector space. An exterior $k$-form call any skew-symmetric tensor on $\mathbb R^n$ of rank $k$. Denote the set of exterior $k$-forms by $E^k$. ...
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### Do the things that you don't know in mathematics frighten you? [closed]

I have zillions of things that I don't know in mathematics. I feel I would never know any of them completely. Especially after this age (26)... and I immediately run away since I am a perfectionist. ...
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### Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
391 views

### mental math: approximating fractional exponents

Does anyone have any good tricks for estimating expressions with fractional exponents (besides guess and check)? For example, I want to easily calculate $9.1^{1/3}$. Currently, the best I've got is ...
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### Limits as x approaches 0

I was wondering how this worked when submitted, anything over 0 was infinite.
749 views

### Trigonometry when to divide and times

OK, so I am revising for an upcoming test and am a bit confused. I have previously learn Trigonometry, however that was around a year ago, and i have completely forgotten it now. I went on to ...
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### Instructive video content for High School kids?

I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
3k views

### Is all of mathematics based on logic?

I do not understand the discipline in mathematics that is called "mathematical logic". For me, all of mathematics is based on logic and that is what makes it the exact science. Every theorem or lemma ...
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### $2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if $0^\circ \le x < 360^\circ$

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0^\circ ≤ x < 360^\circ$. For $0^\circ \le x < 360^\circ$, I'm getting $x=111.5^\circ$ and $x=248.5^\circ$. Is this correct? ...
311 views

### Measure Theory or Set Theory?

Having taken Real Analysis I before (the seven first chapters of baby Rudin) I have the option to take Measure Theory now. However I am torn between that and Set Theory. Which course would you go for ...
3k views

### Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up. EDIT: Could anyone suggest books for someone with a math education that just ...
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### Other conditions than necessary and sufficient conditions, $\Rightarrow$, $\Leftrightarrow$?

I know that $$A\Rightarrow B$$ means that $A$ is a necessary condition for $B$ and $B$ is a sufficient condition for $A$. Also, $$A\Leftrightarrow B$$ means that $A$ is necessary and sufficient ...
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### Tools (electronic notebook and ontology viewer) of mathematical formulas (definitions and facts)

I am reading math books and articles (for applications in other disciplines, mostly about logics for computer science and AI) and the hardest part is to memorize formulas, to look up some definitions/...
1k views

### A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
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### One and Two Tailed Independent T Test Questions

The city council for a small town has been receiving complaints from local law enforcement that citizens have been extremely uncooperative when pulled over for minor traffic violations. To remedy ...
3k views

### Are there 3 trig functions or are there 6 trig functions?

In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
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### How to teach newbie multiply of complex number

I want to teach a newbie the arithmetic law of complex numbers. the law of add is acceptable psychological. but multiply is not. for example, assume $$z = a+bi, w = c+di$$ He (She) may ask me: why ...
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### Why all games are not Potential?

A definition given in wikipedia of an exact potential game as follow: A game $G=(N,A=A_{1}\times\ldots\times A_{N}, u: A \rightarrow \mathbb{R}^N)$ is: an exact potential game if there is a ...
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### Why optimization problems cannot be solved by simple derivative?

Let $f(\cdot)$ be a linear function. $f:\mathbb{R}^n\rightarrow\mathbb{R}$ $\;\quad\;\mathbf{x}\;\rightarrow f(\mathbf{x})$. Let $\mathbf{A}$ be a matrix in $\mathbb{R}^{m\times n}$. ...
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### Establishing fairness in test grading

Consider a group of 75 students who sit an exam consisting of 20 open questions, and are then randomly divided into 3 groups of 25 students {A, B, C} for grading by 3 different persons. Let us ...
387 views

### Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
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### What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
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### Why do we use $cm^2$?

I can't seem to wrap my head around why we should use $cm^2$ for area. According to my textbook we use it for converting units of area but I don't understand how $1cm$ is any different from $1cm^2$. ...
8k views

### Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
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### distance Pure Math graduate programs?

I would like to go to a graduate school for pure mathematics, but I do not live where such programs exits. Furthermore, I can not move. Question: Do any Universities have graduate program in pure ...
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### Motivating convex sets.

I am kind of TAing for a class of real analysis, and I would like to speak a little about convex sets tomorrow, and explain why they are important. What kind of examples could I give? I was thinking ...
6k views

### Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
339 views

### How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...