MathBitsNotebook – Algebra 1 is a series of lesson and practice pages for students studying high school Algebra 1.

Khan Academy is a non-profiteducational website created in 2006 by educator Sal Khan to provide “a free, world-class education for anyone, anywhere.” The website features thousands of educational resources, including a personalized learning dashboard, over 100,000 exercise problems, and over 4000 micro lectures via video tutorials stored on YouTube, including videos that cater to the common core algebra curriculum. Speaking of the Putnam ,if you look it up on you Tube you'll see some wonder solutions to apparently tough problems such as prove that a triangle in the plane formed by a point(a,b) the x-axis and the line y=x has a minimum perimeter and find that number.Key: Site appropriate for P=Parents, S=Students, T=Teachers No wonder Harvard consistently does so well on the Putnam. the remarkable thing about the second exam was that a third of the class got 100+.

I sat for few hours figuring that out the kicked myself.

Well since g=g'.Multiply both sides by (g')^-1 and you'll get the right hand side equal e'9the identity in G' and the left is g.(g')^-1, an element that's in G mapping to the identity so it's in the kernel. Then he says 'so that g.(g')^-1 is in the kernel.' Why you might ask, as I did. In his review of the second exam, one of the questions deal with a homomorphism phi from a group where|G|>N! to a group of order N! must have a kernel.He goes on to say there must be mappings of distinct g and g' in G such that map to the same element in G'.

He also reviews his exams which he acknowledges were too difficult.

Algebra 1 khan