Can acing the upper level course compensate background of no basic course in graduate application I am an international master student in Germany who wants to apply graduate schools in US or Canada. I have an unconventional background, I want to study mathematics but I don't have courses of basic analysis and abstract algebra. Due to language problem, I can't take the course in my university. Now if I get good grades in upper lever (graduate) mathematics courses, can it compensate that I don't have basic courses?
Would it be a big disadvantage in Phd application?
It would look slightly odd, but good grades in advanced courses would generally be seen as sufficient to show that you understand the material. In the end, graduate admission committees aren't so much interested in knowing how you acquired necessary background knowledge than knowing that you have it. How that is demonstrated is secondary, and acing upper level courses is certainly one acceptable way to do so.