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If you teach mathematics to future highschool teachers, you often feel that they are bored because what they learn at university does not have much to do with what they will have to teach in school, and what they will have to teach in school will be boring for their students because it has nothing to do with real life. To remedy this situation, we sometimes offer a course "Mathematics in Real Life" to explain how often mathematics "just happens" in real life, but goes unnoticed. Some sample topics in that course are

I am looking for more examples like those above. They should be accessible to undergraduates (some of the topics above are actually a bit too hard), have some impact on real life, and (ideally) be somewhat surprising for someone who hasn't heard of them yet. Thus, I am neither looking for recreational mathematics as in this question nor for "typical" applications of maths in computer simulation, statistics or finance, which usually involve some deeper mathematics.

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    $\begingroup$ You might find this post helpful mathoverflow.net/questions/2556/… $\endgroup$ Feb 17, 2016 at 15:38
  • $\begingroup$ @TrevorNorton Indeed, some of the topics fit nicely. Thanks. $\endgroup$ Feb 18, 2016 at 13:23
  • $\begingroup$ "GPS as an application of 3d Euclidean geometry" Interesting as the Earth's surface is not Euclidean. However, for practical purposes it is Euclidean as applied relatively small areas of the Earth. $\endgroup$ Jan 31 at 3:31
  • $\begingroup$ @MichaelEjercito To my knowledge, the earth can rather accurately be described as an admittedly complicated body in Euclidean 3-space. Relativistic aspects do play a role in GPS, but I believe that refers to time synchronisation rather than to finding positions in 3-space, and transforming them into some 2-d coordinate system on earth. $\endgroup$ Jan 31 at 8:57

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Bayes theorem is pretty useful in health care. If 5% of people have cancer and we have a test that is 95% accurate at detecting cancer, what's the chance of you having cancer if the test comes back positive? It turns out that even though the test is 95% accurate, we're still only 50% sure that you have cancer. That's because if we take the number of "True Positives" over the total number of positives, it's only 50% of them.

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Symmetry groups have applications to chemistry (crystal structure) and molecular chemistry, to technology and engineering, to architecture, and even to Reactor Calculations, although this is less popular nowadays.

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