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In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate mathematics students, and for this reason I am looking for:

  1. Material rich in pictures, animations, interactive applets perhaps, which may attract the attention of those young students, and useful for conferences and other activities.

  2. Pedagogical material: showing the power of mathematics perhaps without having studied the topic rigorously.

  3. Material dealing with advanced mathematics: the real challenge is to show the importance of advanced mathematics, because basic mathematics examples are abundant and overused.

Of course, besides material, any idea or suggestion is welcomed. Perhaps it is also helpful to have a look at the same question I asked in Mathematics: https://math.stackexchange.com/questions/1070873/sources-for-mathematics-outside-the-mathematics-world

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Math encounters are a series of lectures given at the Museum of Math in NYC, celebrating the spectacular world of mathematics. The link for these lectures is here. There is a list of lectures at the bottom of this page with links to more information. For example Math at the Movie has the following info:

Filmmaking is undergoing a digital revolution brought on by advances in areas such as computer technology, computational physics, geometry, and approximation theory. Join Tony DeRose, Senior Scientist and lead of the Research Group at Pixar Animation Studios, as he uses examples from Pixar’s feature films to provide a behind-the-scenes glimpse of the role math plays in the revolution. Tony will be introduced by Ira Flatow, Host and Executive Producer of National Public Radio’s popular Science Friday radio program.

Many of these lectures can be found on YouTube or if a particular one intrigues you, you can buy it on CD.

I have attended these lectures and have found that they often place math in the oddest places (juggling) and expand on the math and it's applications beyond my expectations (origami). I suggest you take the time to look through the topics and click on the links so that you can really see what each one is about. Not all will suit your purposes, but those that do will be appreciated by your students.

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Many expository articles about the applicability of mathematics can be found in SIAM News:

http://sinews.siam.org/

and as part of the AMS Feature Column:

http://www.ams.org/samplings/feature-column/fcarc-index

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I've wanted to get a copy of Satyan Devadoss's 36 Lectures on The Shape of Nature for quite some time. I've finally ordered them through an interlibrary loan, as they carry a fairly significant price tag.

It seems the material would certain check all the boxes you care about, the reviews are generally very positive, and I'll be able to update with a personal opinion fairly soon.

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