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Results tagged with concept-motivation
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user 114
For questions how to motivate a mathematical concept (i.e., the motivation and examples of definitions, theorems, etc.) or general concepts of mathematics. Please use the [student-motivation] tag for questions about how to motivate students in general.
6
votes
Counterintuitive consequences of standard definitions
I don't have idea to do better, but some to explain such consequences of definitions.
Some thoughts:
Definition have, of course, a historical development and come from a lot of examples and attempt …
- 9,468
5
votes
What are easy examples from daily life of constrained optimization?
This example is maybe the most easy, but in my opinion it does not highlight the necessity to use methods of constrained optimization since the constrained equation is explicitly invertible.
A gar …
- 9,468
11
votes
4
answers
11k
views
What are easy examples from daily life of constrained optimization?
A standard example of motivating constrained optimization are examples where the setup is described in a lot of lines, e.g., when you own a company and the company is making some products out of resou …
- 9,468
21
votes
7
answers
967
views
Is $e^{i\pi}+1=0$ a good motivation for introducing $e$ or $i$? Why (not)?
Most mathematicians would agree that
$$e^{i\pi}+1=0$$
is one of the most impressive formulas.
Imagine your students have just learned about the definition of $e$ or $i$ (just assume it's $e$, norm …
- 9,468
10
votes
Optimization problems that today's students might actually encounter?
An answer depends on what you mean with their lives. I think, it is more likely that students will face such problems in their working (not academic) life.
The Netflix Prize example
My example is t …
- 9,468
11
votes
Optimization problems that today's students might actually encounter?
As I mentioned in my other answer, it highly depends what is meant by their lives. Here is a every day problem which I, at least, often encounter:
If you do the dishes and finish, there is a lot …
- 9,468
26
votes
13
answers
3k
views
What is a good motivation/showcase for a student for the study of eigenvalues?
Courses about linear algebra make great demands on looking for eigenvalues and transforming matrices to diagonal matrices (or, at least, to Jordan normal form). This is somehow a technical, recipe-lik …
- 9,468
9
votes
For calculus students, what should be the intuition or motivation behind series?
Unfortunately, my example is not a full answer to your question, but I think, it helps students to be at least beware of what can happen.
You can explain series as a inifite summation of areas (at le …
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