Schröter went to (along with mathematicians Alfred Clebsch, Rudolf Lipschitz, Carl Gottfried Neumann) the Altstädtisches Gymnasium in Königsberg, studying mathematics and physics.

After graduating from the Gymnasium in 1845, he entered the University of Königsberg to continue the study of mathematics and physics under Jacobi school's Frederick Richelot (and Franz Ernst Neumann and Otto Hesse).

After his volunteer year in the military, he went to the Berlin Friedrich-Wilhelms-University, where he was taught by Peter Gustav Lejeune Dirichlet and Jakob Steiner.

Schröter was influenced by Steiner's lectures, which were available only as note sheets, on synthetic geometry (projective theory of conics) published in 1867.

His students included Victor Eberhard, Moritz Pasch, Jakob Rosanes, and Rudolf Sturm.