# 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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### convert Hex value to two's Complement

for example, let's say: 0xE5 assume the system is 8 -bit in decimal it's = 229 and in Binary it's = 1110 0101 the Two's Complement rules said: sign-bit, which's the most left, indicates a negative ...
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### Game Theory Projects for Undergrads

I am looking for some project ideas for beginning math students in the topic of game theory. I am not very knowledgeable in the topic so it would be great if I could get an good introductory source to ...
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### recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number theory....
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### Why are surds put on the numerator in the final answer when it is a fraction. [duplicate]

I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it ...
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### consider the coordinates of the bounding area inclusive the range coordinates

I am stuck with a very trivial issue here. I have following coordinates: (xMin,yMin) = (-500,-500) (xMax,yMax) = (764,-26) and the step size is 79. I need to consider all the coordinates inclusive ...
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### E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
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### Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?

I am guilty of writing things like the following in proofs: so by lemma 1.2 we have that for $k<n$ all of the integers $k,k+1,k+2,k+3,\dots ,n$ are pompous. I really like how this looks, the ...
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### Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
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### What's the mathematical symbol to say “It doesn't depend on …”?

If I want to say x doesn't exist I would use the symbol $\nexists$ If I want to say x is a member of... I would use $\in$ But what's the symbol to say y doesn't depend on x? I know I could write ...
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### Logic with numbers

Nick wrote each of the numbers from 1 to 9 in the cells of the 3x3 table below. Only 4 of the numbers can be seen in the figure. Nick noticed that for the number 5, the sum of the numbers in the ...
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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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### New method to solve this fractional differential equation

this is my problem \begin{align} & D{{\text{ }}^{2}}\text{ }y\left( x \right)\text{ }+\text{ }D{{\text{ }}^{\frac{3}{2}}}\text{ }y\left( x \right)\text{ }+\text{ }y\left( x \right)\text{ }=\...
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### why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem? [duplicate]

In standard multivariable analysis texts, the change of variables for multivariable integration in Euclidean space is almost always stated for a $C^1$ diffeomorphism $\phi$, giving the familiar ...
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### Is there a place that lists graduate institutions and their specialties? [closed]

I'm currently a sophomore at a Canadian university, and due to some recent head butts in a few maths classes, I'm realizing I don't know what I want to do in grad school (or if I even want to go for ...
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### New Elementary Function?

In the February 2000 issue of FOCUS magazine, a short article suggests that the Lambert W function could be introduced into curriculum as a new elementary function saying: "... a case can be made for ...
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### How to explain “why study prime numbers” to 5th Graders?

I tend to teach 5th graders math ever so often just so they can be "friendly" with math in a playful manner, instead of being afraid. However, one question that I constantly struggle with is this: ...
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### What is the Pedagogical Justification for Substitution?

My mom is re-learning calculus for the third time (She tutors High School students). And she asked me a question invovling limits: $$\lim_{x\rightarrow \infty} \frac{\ln 2x}{\ln 3x}$$ I led her ...
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### Why does topology rarely come up outside of topology?

I am currently taking topology and it seems like a completely different branch of math than anything else I have encountered previously. I find it a little strange that things are not defined more ...
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### What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

Good examples would be The Square Root of 2 by David Flannery or Math Girls by Hiroshi Yuki.
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### Finding the probability of X_Bar with sample variance included?

The question I am asked is $P(\bar{X} > 3 + 0.4984S)$, where I am additionally provided $n = 25, \mu = 3.0, \sigma^2_\text{pop} = 3.0$. $\bar{X}$ is the sample mean and $S$ is the sample variance. ...
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### Questions wrong or theorems useless because hypothesis impossible [closed]

Consider the following question: The area of a right triangle with integral sides is 5. What is twice its area? The answer is 10. But on closer inspection, there is no such right triangle. What can ...
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### defining the (cw/ccw) in radians (pos/neg) [closed]

are there any negative radians? **deg° 0.0 32.9 /-32.9 **rad* 0.0 0.5742133 / -0.5742133 enter image description here
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### Dividing numbers with dots?!

OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every ...
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### Equation for circle tangent to differentiable functions.

This question addresses a problem from this question. Sketching a possible approach to attack it. If we have the differentiable function $t(x)$ which we want to create a sequence of circles as ...
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### Is it possible to visit all points on a differentiable function by “rolling”?

I recall from a discussion thread some week ago we talked about different ways to pedagogically explain differentiability. So I came up with this idea that if there for each point there exists a ...
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### What to teach first: Riemann sums or anti-derivative? [closed]

In some text books, I see that they teach Riemann sums first. In other texts, I see they teach anti-derivatives first. Is there any pedagogical preference? It seems to me that we should teach ...
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### Trying to learn about kernel PCA but cannot understand some math.

I'm trying to learn about kernel PCA by reading through the paper of it's creators (I assume) "Nonlinear Component Analysis as a Kernel Eigenvalue Problem", Bernhard Schölkopf, Alexander Smola, Klaus-...
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### Suppose that $R_1$ and $R_2$ are reflexive relations?

I need some help with this problem, Suppose that $R_1$ and $R_2$ are reflexive relations on a set $A$. Show that $R_1 ⊕ R_2$ is irreflexive?
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### Are Standalone Introductory Linear Algebra Classes Bad? [closed]

The author of the textbook I will be using for my combination linear algebra/differential equations course next semester, Introduction to Differential Equations by Michael E. Taylor (http://www.ams....