TITLE: Teaching Steenrod Operations
QUESTION [16 upvotes]: I am teaching a class on topology and want to introduce Steenrod Operations. I have talked about simplicial sets and classifying spaces of groups but have not talked about Eilenberg–MacLane spaces. What is the easiest/your favorite way of showing Steenrod operations exist? Is there a good way of constructing an explicit chain map $C_*(E S_2) \otimes_{\mathbb Z[S_2]} (C^*(X)\otimes C^*(X)) \to C^*(X)$ for some model of $E S_2$ that gives Steenrod operations?

REPLY [11 votes]: Its nice to look also at Bott's early paper 
"On symmetric products and the Steenrod squares. "
Ann. of Math. (2) 57, (1953). 579–590.
He uses an early version of Smith theory. Depending on how 
you do Smith Theory the homotopy quotient construction lurking somewhere. Anyway worth 
look.