Anyone have a really good resource to learn about the IVT and EVT for an analysis level proof class? Anywhere online where I can see proofs involving the EVT and IVT?
Not really, sorry ;[ But I'll give you a fun, easy problem I learned that requires only an elementary application of the IVT: suppose I have a metal ring which I heat unevenly. Show that there are two points exactly opposite each other on the ring with the same temperature. In other words, if f is a continuous function on a circle, show that there are points x and -x where f has the same value. Its easy, but it has fun generalizations. For example, there are always two points on the earth opposite of each other with the same temperature AND wind speed.