Mathematics has many subject areas that don't necessarily need to be learned in order. If you wanted you could start down the path of abstract algebra without a

Mathematics has many subject areas that don't necessarily need to be learned in order. If you wanted you could start down the path of abstract algebra without almost any experience with analysis. Linear algebra is quite approachable and makes a good starting point, all while having interesting applications to help motivate the subject, and it leads directly into a huge swath of serious mathematics. I would argue that the reason analysis is often the first real course American mathematics undergraduates take is due to the fact that calculus is such a staple in high school which makes it a natural progression. Analysis is also a useful way to introduce students to mathematical abstraction by studying familiar things and showing how they can be turned into formal definitions, but this can be accomplished with other subjects as well. For example group theory has plenty of connections to real world objects that you may be familiar with and have intuition for.