There are three broad areas of math: analysis, algebra, and geometry/topology.
We offer prerequisite, introductory/intermediate and advanced courses in each of these core areas, and we suggest that you explore a broad spectrum of mathematics by taking at least one introductory/intermediate course in each area. Our core courses in these areas are:
Analysis:
(Prerequisite) 180, 200, or 350 (Multivariable Calculus)
(Introductory) 1010 (Analysis on the Real Line)
(Intermediate) 1630 and 1460 (Real Analysis I and Complex Analysis)
(Advanced) 1640 (Real Analysis II)
Algebra:
(Prerequisite) 520 or 540 (Linear Algebra)
(Introductory/Intermediate) 1530 (Abstract Algebra I)
(Advanced) 1540 and 1560 (Abstract Algebra II and Number Theory)
Geometry/Topology:
(Introductory/Elective) 1040 or 1060 (Problems in Geometry or Differential Geometry)
(Advanced) 1710 (Topology)
The introductory courses in each area require only the prerequisites (180 or 200 or 350 and 520 or 540) as background, and are generally good places to start exploring 1000-level courses. (We offer many other courses as well, but the above is a list of core courses.)
Once you've explored all three areas at the introductory/intermediate level, and you see what you like, you can move on to the advanced courses. The advanced courses in each area generally require (at least one of) the intermediate course(s) as a prerequisite: 1640 requires 1630, and both 1540 and 1560 require 1530. In Geometry/Topology, 1710 should be taken after you've seen introductory/intermediate courses in both Analysis and Algebra (1010/1630 and 1530).
There are other courses we offer which don't fit exactly into any of the three areas listed above. These courses include 1110/1120 (ODEs/PDEs) and 1210/1220 (Probability/Statistics). These are also beautiful areas of mathematics and the tools developed there show up all over the place. Other departments offer versions of these courses. Our courses are distinct for the emphasis on theory as much as (or more than) practice.
Here are some suggestions about what to take, given what you've taken so far:
I just took 180 or 200 and 520:
Try 1000 if you want a gentler introduction to proofs.
Try 1010 if you think you're ready for proofs in the context of single variable calculus.
Try 1530 if you think you're ready for proofs in the context of algebra (and don't worry, you don't need to know any algebra beyond linear algebra yet).
Try 1110 if you want the theory behind differential equations.
Try any 10xx level course that looks interesting, for example 1030 (Graph Theory), 1060 (Differential Geometry) or 1080 (Cryptography).
I just took 350 and 540 or at least one of 350 or 540:
Try 1000 if you need more proof practice.
Try 1010 if you think you're ready for proofs in the context of single variable calculus.
Try 1530 if you think you're ready for proofs in the context of algebra (and don't worry, you don't need to know any algebra beyond linear algebra yet).
Try 1110 if you want the theory behind differential equations.
Try 1630 if you feel confident with proofs in the context of real functions of a single variable.
Try any of the 10xx level courses that look interesting, for example 1030 (Graph Theory), 1060 (Differential Geometry) or 1080 (Cryptography).
I took 1530 (Abstract Algebra) and liked it!
Take 1540 or 1560 (Abstract II or Number Theory).
Take an elective with an algebraic flavor, like 1030 or 1080 (Graph Theory or Cryptography).
I took 1010 (Analysis on the Real Line) and liked it!
Take 1630 (Real analysis) and then 1640 (Real analysis II).
Take 1460 (Complex analysis).
Take 1060 (Differential geometry).