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...Syllabus for fall math algebraic geometry valeryalexeev put concisely is the study of solutions systems poly nomial equations in several variables it studies them from dierent points view straight up algebraically topologically considering solution set as a topological space using tools dierential such forms integrals etc all these are valid and have their own place beginning purely approach seems to be easiest turn heavily used many other elds mathematics number theory algebra representation there textbooks some enduring classics shafarevich hartshorne griths harris also more recent books none perfect so course will taught combination notes this not prerequisites beyond ba sic certainly helpful studied commutative but can done after learning geometric tuition concepts or topology before mandatory references p j principles wiley interscience robin springer verlag new york graduate texts no i r basic vol...