I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia.

I am free to choose any topic for the session as long as it can be understood within $10$ minutes.

I would like to teach something that will interest almost everyone. For example, we use online transaction everyday so it might be of interest to everyone to understand underlying mechanism, that is, encryption and decryption. However, to understand it, one needs to understand linear congruences, which I think some of my audience might not have it.

Question: What topics in Mathematics will be of interest to every undergraduate, including non-Maths major?

As I need to write teaching aim and learning outcomes as well, the topic cannot be a puzzle like Knights and Knaves as I am not able to suggest possible learning outcomes in solving the puzzles.

I thought of teaching optimisation calculus in one variable without any constraint. However, I am afraid that I may spend too much time in explaining what is a first and second derivative.

  • 1
    $\begingroup$ This thread on MathOverflow might be useful: How To Present Mathematics To Non-Mathematicians [in 10 Minutes]? Some examples from the top answers: infinite ordinals, the Euler characteristic, Fermat's two squares theorem, Ramsey numbers. Though I guess these are examples of things non-maths majors may find interesting, rather than things they may find useful (like your idea of optimization). $\endgroup$ – Rahul Sep 1 '18 at 6:49

In ten minutes you can't do too much. I would try to explain something puzzling - like why 1 = .9999....

A related idea might be on the difference between a countably infinite set vs. the power of the continuum. Cantor's diagonalization is easy to comprehend and provides a compelling - but curious - result.

  • $\begingroup$ I think a potential question from students would be why do we care about Cantor diagonalization and continuum hypothesis... $\endgroup$ – Idonknow Sep 1 '18 at 6:11
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    $\begingroup$ It's a simple idea to grasp but one most non-mathematical people have never grappled with: are there different types of infinity? The Cantor diag makes a concrete demonstration that is constructive. $\endgroup$ – eSurfsnake Sep 1 '18 at 6:51
  • $\begingroup$ I just did some googling on hand another worry, that is, does infinity even exist in our world? If it does not exist, why do we study it? $\endgroup$ – Idonknow Sep 1 '18 at 12:01
  • $\begingroup$ It is an extension of the real numbers: R' = R + {$-\infty, \infty$} $\endgroup$ – eSurfsnake Sep 12 '18 at 23:18

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