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Real algebraic geometry is the study of real solutions to algebraic equations with real coefficients. Its methods are rather different from classical algebraic geometry, which is typically done over an algebraically closed field (like the complex numbers).

10 votes

How do you not forget old math?

If you want to remember concrete things you can try to a flashcard system like Anki. In my experience, it helps to structure knowledge on several scales, hierarchically. If you remember the corners …