# 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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### 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-...
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 $e$, ...
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, ...
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 ...
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### 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 ...