The problem I have with the way equations are often presented e.g. on Wikipedia is that the authors are so focused on conciseness that they don't stop to explain the idea in straightforward terms. For example, a while ago I was looking into the Radon Transform.
After reading a number of articles and eventually stumbling across one on MathWorks (http://www.mathworks.com/help/toolbox/images/f21-25938.html) with some great worked out examples I immediately got the idea: if you put your x-ray glasses on and look at an object from many different angles, and make note of what you're seeing at each angle, you can use your notes to rebuild the image or figure out how similar this object is to another object. Pretty intuitive.
With that understanding of the idea, the Wikipedia article made much more sense. Most mathematics is only difficult for me because I spend all my time trying to understand why the author is " the integral transform consisting of the integral of a function over straight lines". Once I get that, the rest is straightforward.
+1 absolutely agree. Wikipedia is terrible for learning mathematical concepts, not surprising given that its a reference site. Its appropriate to be concise in this context.
People are getting excited about education being an area ripe for disruption. What about a site that rips all the Wikipedia maths topics and allows people to add some worked examples and arrange the content to be more pedagogically pleasing? Providing a nice little HTML5 widget toolbox to create simple interactive visualisations would be cool...
The wikipedia page is full of concise technical explanations and equations: http://en.wikipedia.org/wiki/Radon_transform
After reading a number of articles and eventually stumbling across one on MathWorks (http://www.mathworks.com/help/toolbox/images/f21-25938.html) with some great worked out examples I immediately got the idea: if you put your x-ray glasses on and look at an object from many different angles, and make note of what you're seeing at each angle, you can use your notes to rebuild the image or figure out how similar this object is to another object. Pretty intuitive.
With that understanding of the idea, the Wikipedia article made much more sense. Most mathematics is only difficult for me because I spend all my time trying to understand why the author is " the integral transform consisting of the integral of a function over straight lines". Once I get that, the rest is straightforward.