Here is the suggested schedule for a typical Algebra/Algebraic Geometry student.
MTH 571: Algebra I
MTH 551: Real Analysis
MTH 671: Commutative Algebra
MTH 561: Topology I
APM 577: Computational Algebra
MTH 569: Graph Theory
............. free elective ..................
.............. free elective ..................
APM 790
MTH 572: Algebra II
MTH 551: Complex Analysis
MTH 672: Algebraic Geometry
MTH 562: Topology II
APM 673: Coding Theory
......... free elective (see catalog) ......
MTH 670: Algebraic Number Theory
APM 790
APM 790