What a cool idea: a free software package that simulates a planetarium on your PC!
Preloaded with 600,000 stars, all you have to do is set your coordinates and start gazing!
You can search by name for various heavenly bodies, map the constellations, and even get close-ups of observable planets!
This is a nice collection of links to profiles and biographies of women in mathematics.
http://darkwing.uoregon.edu/~wmnmath/People/index.html
In addition to resources about historical figures, this list contains references to many living mathematicians.
And here is another nice collection of biographies of female mathematicians from the University of St. Andrews.
This is a collection of interview clips with mathematician Benoit Mandelbrot.
https://www.webofstories.com/story/search?q=mathematician&max=10&p=1&sp=mandelbrot&ch
The interview is broken up into different topics like the Hausdorff Dimension, economics and mathematics, fixed points, and the birth of fractals. In addition, Mandelbrot talks about his personal, academic, and professional life. It’s an interesting window into a profoundly important person.
The website WebOfStories.com also offers clips of interviews of other scientists, like phsicists Murrary Gell-Mann and Freeman Dyson and Biologist Francis Crick.
This is a great visualization and explanation, of the curl of a vector field:
http://mathinsight.org/curl_idea
If you interpret a vector field as the flow of a fluid, then you can interpret the curl as a measure of the tendency to rotate at a given point.
One way to think of this is to imagine a tiny sphere, or paddle-wheel, fixed at a point in space, and then consider how that object would rotate if subjected to the flow of fluid as given by the vector field.
This write-up and series of animations from MathInsight.org are very useful in attaching some intuition to this complex idea.
This is another wonderful visual demonstration from Jason Davies: a combinatorial bracelet generator.
http://www.jasondavies.com/necklaces/
Combinatorics is the mathematics of counting things, and one of the classic “advanced” counting problems is this: given a certain number of beads of various colors, how many different bracelets can you make?
The problem may seem easy enough, but it becomes quite difficult when you start to understand what “different” really means.
For example, if you turn one bracelet into another by rotating it, then those two bracelets aren’t different. Even more complicating is that if you can obtain one bracelet from another by flipping it over, then they are also the same!
This visualization can really help develop a sense of the complicated symmetries at work here.
Click here to see more in Representation.