New answers tagged secondary-education
5
votes
Special topics for introductory probability
One example of elementary probability is the so-called Birthday problem which asks for the probability that in a room of $n$ people two will share the same birthday. Sometimes formulated as a paradox ...
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Special topics for introductory probability
[Additional to previous answer--can't edit, sorry.]
dt688:
I would be very wary about being too difficult or particular, when teaching in a corporate environment. I.e. if GMers are your target ...
2
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Special topics for introductory probability
I would look ar some of the basic six sigma literature and at doe. It is connected to all kinds of factory snd other process improvement. Very clear business connection.
I would eschew the Bayesian ...
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5
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Special topics for introductory probability
Bertrand's Paradox is an old saw. The point is that trying to randomize an experiment is tricky since there can be different points of view.
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0
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Special topics for introductory probability
I would suggest geometric probability and applications in stereometry!
- 1,935
10
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Accepted
Special topics for introductory probability
A classic application of Bayes' Theorem is in medical testing, and the difference/conversion between "what is the probability I test positive, given I have the condition" vs. "what is ...
6
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Special topics for introductory probability
You might already be aware of this one, given how famous it is, but the first thing that comes to my mind is the Monty Hall Problem. It doesn't require any fancy mathematical machinery, just a basic ...
- 6,191
2
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How to justify teaching students to rationalize denominators?
When we work with numbers of the form $a+b\sqrt{2}$ (with $a$ and $b$ rational), it is useful to rationalize. For example, to determine that the set of numbers of that form is closed under division. ...
- 7,369
4
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Why do so many people hate math?
I'm very fond of Eugenia Cheng's perspective: many people dislike certain parts and/or aspects of mathematics, and it just happens that these are precisely the ones emphasized by most (all?) school ...
- 94
2
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Why do so many people hate math?
In addition to the standard reasons:
Bad teachers,
It's hard,
there is an interesting reason why one hears so much about people hating math that's due to${\ldots}$ Conan Doyle. Arguably he ...
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3
votes
Is there a standard convention for interpreting ambiguous absolute value expressions?
As I was looking at your expression, something just seemed typographically off, and then I realized that it was the missing padding around the bars that you see when mathematics is well-typeset. This ...
- 171
4
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Speed math appropriate for middle-school students
I agree with @DanFox's comment, that speed in arithmetic has no bearing on how well someone can learn higher mathematics. And yet, there are some methods for mental math that help one see ...
- 20.1k
0
votes
Why do so many people hate math?
Being a graduate student and having studied mathematics for almost all my life, I think I am in position to answer this question. Well I love mathematics but that necessarily don’t mean everyone does ...
0
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Importance of complex numbers knowledge in real roots
My favorite goes approximately like this:
The geometric series $\sum\limits_{i=0}^{\infty}\frac{1}{x^n}$ converges to a function $f =\frac{1}{1-x}$ only on $-1\lt x \lt 1$. On the other hand, $f$ is ...
- 151
0
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Importance of complex numbers knowledge in real roots
Complex numbers don't have an ordering like real numbers, i.e. $a + i b\ngtr c + id$. This is both subtle and profound. To explain, assign north as imaginary and east as real and then talk about ...
- 101
7
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Is there a standard convention for interpreting ambiguous absolute value expressions?
I don't know about standards, but I read these things using a left to right, greedy algorithm. More specifically, the bars are like parentheses but you don't automatically know if they are opening or ...
- 5,192
7
votes
Is there a standard convention for interpreting ambiguous absolute value expressions?
If I want to have nested absolute-value expressions, I would use different sizes
$$
\big|x + 2|x + 3|x + 4\big|,
$$
with variations possible
$$
\bigg|x + 2|x + 3|x + 4\bigg|.
$$
- 7,369
1
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Importance of complex numbers knowledge in real roots
The complex numbers are really just the scale-rotations in 2D geometry. So you can get lots of examples from geometry.
We start with two particular scale-rotations that form a basis for building up ...
1
vote
Importance of complex numbers knowledge in real roots
Students who are interested in geometry might find this proof of Ptolemy's theorem to be a compelling application of complex numbers.
$$
AC\cdot BD = AB\cdot CD+BC\cdot AD
$$
- 24.3k
6
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Importance of complex numbers knowledge in real roots
Consider the real initial value problem
$$
\begin{cases}
y'' + 2y' + 10y = 0\\
y(0) = 0\\
y'(0) = 1
\end{cases}
$$
One nice way to do it is to first finding generic solutions with real inputs but ...
- 24.3k
4
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Importance of complex numbers knowledge in real roots
In the setting of single-variable calculus, here is one of the most striking uses of complex numbers: the radius of convergence of the power series at $x = 0$ of a rational function $p(x)/q(x)$, ...
- 3,258
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Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?
A guess: Could it be a matter of time constraints? Thoroughly covering all potential outcomes and their implications is a time-intensive endeavor.
- 1,935
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Importance of complex numbers knowledge in real roots
AThe book 'Visual Complex Analysis' by Tristan Needham highlights the significance of complex numbers, emphasizing their historical importance in mathematics. It details how the real solutions of ...
- 1,935
6
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Importance of complex numbers knowledge in real roots
If series and radius of convergence are within the reach of your syllabus, then a standard example of "needing to go through the complex numbers" is the radius of convergence of the series ...
- 191
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vote
Importance of complex numbers knowledge in real roots
This might be the oldest question in mathematics education! But you are probably not going to like Euclid’s answer.
A youth who had begun to read geometry with Euclid, when he had learnt the first ...
- 10.3k
6
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Importance of complex numbers knowledge in real roots
we need knowledge of complex numbers to work with real numbers
We need to be honest that at the level of your students, there are no examples of this: in all sufficiently elementary uses of complex ...
- 1,164
8
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Importance of complex numbers knowledge in real roots
Another topic that uses complex numbers in service of real numbers, and is immediately accessible to a high schooler who has learned or is learning calculus, is integration using Euler's formula.
Here'...
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