Questions tagged [concept-motivation]

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.

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22
votes
11answers
2k 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-...
20
votes
7answers
881 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 $e$, ...
10
votes
3answers
315 views

How can you explain the importance of $e$ to those who have not taken calculus?

The number $e$ has many interesting and important properties, many of which are related to calculus. How can I explain what $e$ is and why it is important to those who have not had calculus (or even, ...
6
votes
1answer
582 views

What are some good motivating questions for introductory abstract algebra? [duplicate]

When seeing groups and such for the first time, the abstraction often seems pointless and unnecessary to students. (Most students at my school leave their introductory abstract algebra class thinking ...
19
votes
8answers
1k views

What are some good mathematical applications to present in an abstract algebra course?

One of the main difficulties for a student learning abstract algebra is understanding the motivations behind concepts like groups, normal subgroups, rings , ideals etc. Also, many have difficulty ...
16
votes
4answers
536 views

What are some good ways to motivate and introduce reasoning abstractly about abstract algebra?

I've found one of the hardest topics to introduce to students early on is abstract algebra. Even if they've already written proofs, it's hard for them to work directly from axioms. They seem to have ...
24
votes
4answers
2k views

What are some good examples to motivate the implicit function theorem?

I always had problems when teaching the implicite function theorem in advanced analysis courses. This result is motivated by later applications, but it would be great to be able to provide easily ...

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