"Struggle is necessary. If you look up the answer, you rob yourself of the cognitive dissonance that builds neural pathways. Carroll & Ostlie is designed to make you fail a little before you succeed."
"When I’m stuck on problem 6.24 for three hours, seeing the first two lines of the solution unblocks me. I learn more from a worked example than from banging my head against a wall." an introduction to modern astrophysics solutions pdf
However, the dirty secret of astrophysics is this: Professors don't assign book problems verbatim. They twist them. They combine chapters. They ask for physical intuition, not algebraic replication. "Struggle is necessary